Applied Science, Faculty of
Chemical and Biological Engineering, Department of
DSpace
UBCV
Moussavi, Yeganehsadat
Master of Applied Science - MASc
University of British Columbia
Agrochemicals play a vital role in enhancing crop productivity, yet poor retention and unintended spreading during spraying pose environmental and economic risks. This research addresses these challenges by investigating strategies to improve the effectiveness and stability of agricultural spray formulations through a comprehensive assessment of spray application parameters, polymer solution extensional rheology, the influence of surfactant addition, and the effects of stabilizing agents on storage duration. The findings reveal that nozzle pressure and translation speed jointly influence droplet deposition and retention behavior, with deviations observed at higher nozzle speeds. Beyond application mechanics, molecular characterization highlights the critical role of extensional relaxation time (Î»â), the time required for a polymer solution to recover its original structure after stretching, as a key determinant of spray deposition. This parameter serves as a practical and rapid predictor for assessing formulation performance through extensional rheology tests. The study further demonstrates that ionic surfactants alter the rheological response of polymer solutions, whereas nonionic surfactants primarily act as interfacial agents without significantly affecting relaxation dynamics. Polymer-based solutions exhibit superior leaf retention compared with surfactant-only systems, primarily due to their inherent viscoelastic properties. To improve storage stability, isopropyl alcohol (IPA) and α-tocopherol were identified as effective stabilizers, particularly under refrigerated conditions. Overall, this work establishes a mechanistic link between spray operational factors, extensional rheology, and deposition outcomes. It provides a standardized framework for evaluating spray retention and introduces stabilizing strategies that extend formulation shelf life, contributing to the development of more efficient and sustainable agricultural spray technologies.
Evaluating the Impact of Extensional Rheology onAgricultural Spray RetentionbyYeganehsadat MoussaviB.Sc., Amirkabir University of Technology, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Chemical and Biological Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)November 2025© Yeganehsadat Moussavi, 2025The following individuals certify that they have read, and recommend to the Facultyof Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Evaluating the impact of Extensional Rheology on Agricultural Spray Retentionsubmitted by Yeganehsadat Moussavi in partial fulfilment of the requirements for thedegree of Master of Applied Science in Chemical and Biological Engineering.John M. Frostad, Associate Professor, Chemical and Biological Engineering, UBCSupervisorDr. Mark Martinez, Professor, Chemical and Biological Engineering, UBCSupervisory Committee MemberDr. Sean Smukler, Associate Professor, Land and Food Systems, UBCSupervisory Committee MemberiiAbstractAgrochemicals play a vital role in enhancing crop productivity, yet poor retentionand unintended spreading during spraying pose environmental and economic risks.This research addresses these challenges by investigating strategies to improve theeffectiveness and stability of agricultural spray formulations through a comprehensiveassessment of spray application parameters, polymer solution extensional rheology,the influence of surfactant addition, and the effects of stabilizing agents on storageduration. The findings reveal that nozzle pressure and translation speed jointlyinfluence droplet deposition and retention behavior, with deviations observed athigher nozzle speeds.Beyond application mechanics, molecular characterization highlights the critical roleof extensional relaxation time (λE), the time required for a polymer solution torecover its original structure after stretching, as a key determinant of spray deposition.This parameter serves as a practical and rapid predictor for assessing formulationperformance through extensional rheology tests. The study further demonstrates thationic surfactants alter the rheological response of polymer solutions, whereas nonionicsurfactants primarily act as interfacial agents without significantly affecting relaxationdynamics.Polymer-based solutions exhibit superior leaf retention compared with surfactant-onlysystems, primarily due to their inherent viscoelastic properties. To improve storagestability, isopropyl alcohol (IPA) and α-tocopherol were identified as effective stabilizers,particularly under refrigerated conditions. Overall, this work establishes a mechanisticlink between spray operational factors, extensional rheology, and deposition outcomes.It provides a standardized framework for evaluating spray retention and introducesiiistabilizing strategies that extend formulation shelf life, contributing to the developmentof more efficient and sustainable agricultural spray technologies.ivLay SummaryThis research explores methods to improve the effectiveness and longevity of agri-cultural sprays used for fertilizers and pesticides. The study addresses the commonproblem of sprays running off leaves instead of adhering, which reduces their efficacyand increases costs for farmers. A standardized testing method was developed tocompare different spray formulations, helping identify which ones better adhere toplant surfaces. It was found that the extensional properties of certain ingredients inthe spray, how they stretch and recover, can predict how well the spray will stay onleaves.This finding provides a quick and reliable way to screen potential formulations. Thestudy also investigated the role of surfactants and found that polymer solutions wereparticularly effective on plant leaves due to their physical properties. To addressshelf-life stability, isopropyl alcohol and vitamin E (α-tocopherol) were identified aseffective stabilizing agents, especially when stored in cool conditions. These findingsoffer practical, cost-effective strategies to enhance agricultural spray formulations,potentially leading to more efficient crop treatments and reduced environmentalimpact.vPrefaceChapters 3, 4, and 5 are based on the work done in UBCâs Frostad Research Lab.The authorâs responsibilities include running experiments, gathering data, and dataanalysis. Chapter 5 contain the original work done by the author and will be publishedseparately as peer-reviewed manuscripts.During the preparation of this work, I used the generative AI tool ChatGPT solely tocheck grammar and improve clarity in writing. After using this tool, I reviewed andedited all content. These uses were limited to refinements in language and did notinvolve generating data or drawing conclusions.viContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Agricultural Sprays . . . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Droplet Characteristics and Impact . . . . . . . . . . . . . . . 61.1.3 Wetting and Rheological Properties . . . . . . . . . . . . . . . 111.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Methods and Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1 Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Solution preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Extensional rheology via Dripping onto Substrate (DoS) . . . . . . . 192.4 Spray deposition and retention efficiency . . . . . . . . . . . . . . . . 20vii2.5 Shelf-Life Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Preliminary Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 DoS Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Spray Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Baseline Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 PolymerâSurfactant Screening . . . . . . . . . . . . . . . . . . . . . . 374.1.1 Nonionic vs Ionic Surfactant Effect . . . . . . . . . . . . . . . 384.2 Short-term Shelf-life Study . . . . . . . . . . . . . . . . . . . . . . . . 395 Linking Extensional Relaxation Time to Spray Retention andImproving Shelf-Life in Polymer Formulations . . . . . . . . . . . . 415.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 445.2.1 Impact of tank pressure and nozzle speed . . . . . . . . . . . . 445.2.2 Relaxation time is a predictor of mass deposition . . . . . . . 465.2.3 Polymer and surfactantâpolymer mixtures: Non-monotonic re-tention behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2.4 Impact of surfactants on relaxation time: Non-ionic surfactantsshow no improvement . . . . . . . . . . . . . . . . . . . . . . . 495.2.5 Impact of IPA on shelf-life and retention . . . . . . . . . . . . 516 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58viiiList of Figures2.1 Image of the extensional rheometer (Dripping-onto-Substrate method)enclosed to minimize external air currents and prevent droplet oscillation. 202.2 Image of the specially designed spray apparatus, consisting of a pres-surized spray-solution tank, nozzle, gutters for collecting solution atthe initial and final spray stages, a slot holding test substrates, and abalance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3 Image showing substrates covered with 4 different types of leaves forspray experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1 DoS optimization tests with 4 MDa PEO: (a) substrate model and (b)camera frame rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Comparison of relaxation times for PEOs of different molecular weightsand carrageenan polymers, measured under varying camera frame rates. 283.3 Filament radius decay of 4 MDa PEO solutions on aluminum substrateswith varying hole depths and diameters. . . . . . . . . . . . . . . . . 293.4 Filament radius decay of 4 MDa PEO solutions on the second series ofsubstrates with new hole diameters at the same depths. . . . . . . . . 303.5 Relaxation times of PEO solutions measured on aluminum substrateswith different hole diameters and depths. . . . . . . . . . . . . . . . . 313.6 Spray performance at 3.58mph and 60 psi for different polymer types:(a) mass deposition and (b) retention. . . . . . . . . . . . . . . . . . . 323.7 Spray performance at 4.48mph and 60 psi for different polymer types:(a) mass deposition and (b) retention. . . . . . . . . . . . . . . . . . . 33ix3.8 Spray performance at 100 ppm and 4.48mph for different polymers: (a)mass deposition and (b) retention. . . . . . . . . . . . . . . . . . . . . 343.9 Full concentration sweep of 4MDa PEO at 4.48mph: (a) mass deposi-tion and (b) retention. . . . . . . . . . . . . . . . . . . . . . . . . . . 343.10 Comparison of spray performance between new and used nozzles: (a)mass deposition and (b) retention. . . . . . . . . . . . . . . . . . . . . 353.11 Effect of substrate orientation on spray performance: (a) mass deposi-tion and (b) retention. . . . . . . . . . . . . . . . . . . . . . . . . . . 363.12 Viscosity of 4MDa PEO solutions across concentrations, providing theoperational window for spray tests. . . . . . . . . . . . . . . . . . . . 364.1 Initial surfactant screening of 4MDa PEO (1000 ppm) with selected non-ionic and ionic surfactants. Letters âMâ and âCâ indicate concentrationcalculations based on molecular weight or CMC, respectively. . . . . . 394.2 Shelf-life performance of 4MDa PEO solutions at 100 ppm: (a) accel-erated degradation under elevated temperature and (b) degradationunder shear stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.1 (a) Mass deposition on control (paper) and model (plastic) substratesas a function of nozzle translation speed and spray tank pressure. (b)Retention efficiency on the same substrates as a function of nozzletranslation speed and spray tank pressure. . . . . . . . . . . . . . . . 455.2 (a) Detailed mass deposition behavior at 60 psi over the tested speedrange. (b) Detailed retention efficiency behavior at 60 psi over thetested speed range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3 (a) Relationship between relaxation time and mass deposition. (b)Relationship between relaxation time and retention rate. . . . . . . . 475.4 Comparison of polymer and surfactantâpolymer mixtures spray behavioron natural and model surfaces. . . . . . . . . . . . . . . . . . . . . . . 50x5.5 (a) Effect of SDS on relaxation time. (b) Effect of two agricultur-ally conventional non-ionic surfactants on relaxation time. Together,these results show the effect of ionic and non-ionic surfactants on therelaxation time of 100 ppm PEO solutions. . . . . . . . . . . . . . . . 515.6 Effect of isopropyl alcohol (IPA) concentration and storage temperatureon the shelf-life of 1 wt% PEO solutions measured by relaxation timedecay over six months. . . . . . . . . . . . . . . . . . . . . . . . . . . 53xiAcknowledgementsI would like to express my deepest gratitude to my supervisor, Dr. John M. Frostad,for his invaluable guidance and insightful recommendations throughout my research.His mentorship has greatly shaped my academic journey, and the lessons I have learnedfrom him will continue to guide me in the future.I am also sincerely thankful to Hui Yang and Christophe Massip from IFF, ourindustry partner, for their valuable comments on my work and for providing theexperimental materials essential to this research.My heartfelt thanks go to my labmates â Sanket Biswas, for being a true friendand a constant source of support through all the ups and downs of my time at UBC;Alireza Mashayekhi, for his continual generous guidance; Yun-Han Huang, forher thoughtful suggestions and patience with my many questions; Bofan Chen,for his great help with part of the experiments; Lanxin Mo, for her support andencouragement; and all the other members of our group whom I had the pleasure ofmeeting and working alongside.xiiDedicationTo my dear parents, for their unconditional love and unwavering support, and to mysister, for being my constant source of joy and encouragement.xiiiChapter 1IntroductionThe use of agrochemicals, including pesticides and fertilizers, has significantly enhancedagricultural productivity. However, their efficiency is often compromised due to spraylosses, which contribute to environmental pollution and economic losses. These lossesprimarily occur during deposition and retention, the stages where droplets land onplant surfaces and remain there. A major challenge in agricultural spraying is balancingdrift reduction and retention efficiency.To minimize spray drift, larger droplets are used, as they are less susceptible towind. However, these droplets have higher kinetic energy, leading to splashing andbouncing, which reduces adhesion to plant surfaces. Traditional solutions such assurfactants lower surface tension to improve wetting but have limitations, as they worktoo slowly to prevent initial droplet rebound. Polymer additives, such as polyethyleneoxide (PEO), have shown promise in reducing splashing and improving retention bymodifying fluid rheology, yet their real-world effectiveness remains unverified.A technology gap exists in commercially available formulationsâwhile solutions forreducing drift exist, there is no widely adopted method to enhance retention of largerdroplets. Past research, including NSERC Engage-funded studies, has demonstrated1that polymer-based sprays can retain over 90% of the applied solution, indicating apotential breakthrough. However, current research methods are either highly controlledlab studies that fail to reflect real-world conditions or field tests that provide practicaldata but lack mechanistic insights. This project aims to develop an innovativepolymer-surfactant formulation that enhances spray retention while maintaining driftcontrol. Additionally, it seeks to bridge the gap between laboratory and field testingby developing a standardized protocol for evaluating retention efficiency in realisticconditions.1.1 BackgroundSpraying fluids onto surfaces, especially in agricultural contexts, is a multifacetedprocess with various applications. Nonetheless, a major challenge in this practice isspray drift, which refers to the unintended movement of agrochemicals away from theirintended targets to non-target areas during and after application. The ramificationsof spray drift are extensive, leading to harmful effects on non-target plants, animals,and water bodies, while also posing risks of human exposure through illegal residuesfound in food and feed products. The incidence and severity of spray drift are shapedby numerous factors, requiring a thorough understanding of the interactions amongphysicochemical properties, technological parameters, air conditions, and surface traits.Factors such as droplet size, velocity, spray solution formulation, nozzle height, sprayangle, travel speed, and the hydrophobic characteristics of plant surfaces all play arole in the occurrence and consequences of spray drift. To lessen negative impacts andencourage responsible agrochemical usage, it is essential to develop effective strategiesthat consider these intricate factors and foster environmentally friendly practices [1â4].By examining the dynamics of spraying fluids on surfaces and their effect on spray2drift, we can enhance our understanding and reduce the adverse effects of this processacross various applications.1.1.1 Agricultural SpraysSpray characteristicsAgricultural sprays play a vital role in various field applications, including pest control,weed management, fertilizer distribution, growth regulation, and crop protection,all aimed at improving crop yield and quality. A key goal in agricultural sprayingis optimizing the accuracy, efficiency, and safety of pesticide application, whichnecessitates uniform distribution of the active ingredient [5]. Understanding thedifferent characteristics of sprays is essential for effective application.A study investigating the impact of hydraulic nozzles on the properties of spraydroplets for pesticide use revealed that droplet size, velocity, and air inclusion differbased on nozzle design, operating conditions, and spray formulations. Conventionalhydraulic nozzles generate smaller and faster droplets when compared to air inductionnozzles. Additionally, the study uncovered a relationship between the initial dropletvelocity (sheet velocity), droplet size, and spraying pressure [6].Another study focused on evaluating the effect of adjuvant type on foliar spray retentionin aquatic plants, as well as the influence of carrier volume on this retention. Thefindings indicated that spray deposition did not vary significantly among the testedadjuvants. However, spray retention decreased when an adjuvant was omitted fromthe spray solution. Carrier volume significantly affected spray retention, with someaquatic plants showing heightened sensitivity to increased volume. Further research isnecessary to confirm these results under field conditions [7].3To measure spray retention and coverage on plant surfaces, a study employed dyetracers. The sprayed leaves were photographed under appropriate lighting, andthe images were analyzed to determine the visibility of the dye, allowing for thequantification of coverage [8]. These studies enhance our comprehension of agriculturalspray characteristics and their significance for effective pesticide application. Exploringfactors such as nozzle design, droplet properties, adjuvant type, carrier volume, andspray retention improves the accuracy, efficiency, and safety of agricultural sprayingpractices.Spray DriftSpray drift has been the focus of extensive research since its detrimental effects wereidentified. Initial studies concentrated on basic application techniques and agriculturalchemicals, tackling issues such as damage to non-target crops and dispersion patterns[9]. Later investigations broadened to include measurements of spray losses fromdroplet drift and the detection of pesticides in the atmosphere through volatilization,raising concerns about surface water contamination and the protection of aquaticecosystems [2]. Current research on spray drift seeks to understand the risks andeffects of bystander and resident exposure, optimize particle size and drift reductionmethods, develop predictive models, evaluate environmental impacts, and examinedrift management strategies.In one study, the effectiveness of spray drift reduction techniques, including low-driftnozzles and anti-drift adjuvants, was compared to standard nozzles lacking theseenhancements. The study demonstrated that these techniques successfully reduceddrift, preserved pest control, and did not negatively affect beneficial mite popula-tions, showcasing their potential for sustainable pesticide usage and environmentalsafeguarding [10]. Another study assessed the spray drift exposure reduction potentialof various sprayers (axial fan airblast, directed air tower, and multi-headed fan tower)4in an orchard setting and evaluated their role in minimizing pesticide-related illnesses.The findings revealed that tower sprayers significantly lowered spray drift exposurescompared to axial fan airblast sprayers, with the multi-headed fan tower exhibitingthe least drift These results highlight the possible advantages of adopting modernspray technologies to decrease occupational pesticide drift exposures and enhancepublic health policies [11].Furthermore, a study concentrated on evaluating the spray drift potential of a com-mercial quadcopter equipped with centrifugal nozzles using different droplet at sizesvarying wind speeds. The research showed a notable decrease in deposition at 12m downwind compared to the in-swath zone, with drift at 50 m dropping belowdetection limits. The study also formulated a prediction equation to estimate driftmagnitude based on wind speed and droplet size, offering valuable guidance for driftrisk assessment and applicator instructions [12].Finally, an investigation sought to evaluate the performance of Venturi nozzles inreducing drift while maintaining pesticide treatment effectiveness against Californiared scale (CRS) in citrus orchards. The results indicated that Venturi nozzles didnot compromise efficacy, spray distribution, residue levels on fruit, or the popula-tions of beneficial parasitoids. Thus, Venturi nozzles can be regarded as a suitableoption for minimizing drift in pesticide applications against CRS in citrus underMediterranean conditions [13]. These combined studies significantly enhance ourunderstanding of spray drift, providing valuable insights into effective strategies forreducing drift, advancements in application technologies, and the essential need tomitigate environmental and health impacts associated with pesticide drift.51.1.2 Droplet Characteristics and ImpactBeginning of droplet impact studiesThe study of droplet impacts on solid surfaces is a vast and interdisciplinary field thathas undergone extensive research for more than a century. It was the groundbreakingwork of a British mathematician and physicist named Worthington in the 19th centurythat signified a pivotal moment in this area. Worthingtonâs fascination with dropletimpact was ignited by Mu. H. I. Newall, who demonstrated the marks left by waterand mercury droplets falling on a smoked glass plate.Captivated by the symmetrical patterns and their variations depending on drop height,Worthington pursued additional investigations. He carried out a series of meticulousexperiments that unveiled a wealth of new insights about the dynamics of dropletimpacts, including the creation of intricate splash patterns and the emergence of tinydroplets referred to as secondary droplets [14]. Since that time, researchers from adiverse array of disciplines have continued to explore the behavior of droplets uponcolliding with solid surfaces.Droplet Shape and SpreadThe effect of droplets on surfaces has been widely researched, focusing on variouscriteria to gain insights into the dynamics and consequences of the interaction. Onekey criterion is the analysis of droplet shape and spread, which includes examiningthe initial shape, spreading behavior, contact angle, contact diameter, and overallcharacteristics of droplets upon impact. This offers essential information about wettingbehavior and surface interactions. To understand the impact dynamics of liquid dropson solid surfaces, a study explored the effect of adding surfactants to water dropletsstriking a stainless steel surface. The objectives included observing experimental6changes, measuring contact angles, validating the numerical model, studying theinfluence of a constant contact angle, analyzing the effect of surfactants on dynamicsurface tension, and establishing a criterion for ignoring capillary effects in modeling.The study concluded that capillary effects were negligible under specific conditions[15].In the late 20th and early 21st century, various studies used flash photographyto document the deformation, spreading, and collision of droplets, enhancing ourunderstanding of droplet structures in these forms [16â18]. Furthermore, additionalstudies have been conducted to analyze and understand the role of contact angle indroplet impact phenomena, stressing its importance in accurately predicting dropletbehavior during spreading and receding phases. These investigations have underscoredthe significance of precise dynamic contact angle modeling for achieving a quantitativerepresentation of behavior and have explored the impact of contact angle treatmentson simulation accuracy [19â22]. Collectively, these studies illuminate the variousaspects of droplet impact, such as droplet shape and spread, surfactant effects, dropletdeformation, and the role of contact angles, advancing our understanding of theintricate dynamics involved in droplet-surface interactions.Researchers have undertaken numerous studies to investigate the shape and spreadingbehavior of droplets upon impact, providing insights into wetting behavior and surfaceinteractions. In one study, a three-dimensional model was created to simulate dropletimpact on asymmetric surfaces, validated through simulations and photographs,showing strong agreement with experimental results [23]. Another study utilized acoupled level set and volume-of-fluid framework to explore liquid droplet impact on aflat surface, highlighting the importance of accurately modeling the dynamic contactangle to reproduce the quantitative behavior of droplets during spreading and recedingphases [19].7In a separate study, a three-dimensional model was developed to simulate the impact ofmolten metal droplets on a flat substrate, considering fluid dynamics, heat transfer, andphase-change phenomena. The results displayed good alignment between numericalsimulations and experimental photographs, underscoring the importance of preciselyspecifying contact angles and thermal contact resistance [20]. Investigating numericalpredictions of droplet receding on hydrophilic and superhydrophilic surfaces, anotherstudy uncovered the influence of parasitic currents on the dropletâs receding heightand the importance of dynamic contact angles in dictating the movement of thetriple-phase contact line. The study also assessed energy distributions and conversionmechanisms during droplet impact, emphasizing the role of receding contact angles indirecting the movement of the triple line [21].Additionally, a study concentrated on the accuracy of various contact angle treatmentsin simulating droplet impact on smooth surfaces using a VOF-based model. By imple-menting Kistlerâs dynamic contact angle model, the study achieved good agreementwith experimental results, accurately predicting both the advancing and recoilingphases of droplet impact. These findings demonstrate the applicability of the enhancedVOF framework for investigating the post-impact characteristics of droplets on solidsurfaces with varying wettability [22]. Together, these studies significantly enhance ourunderstanding of droplet shape and spread upon impact, providing valuable insightsinto the complex behavior of droplets on different surfaces.Surface Wetting and SpreadingThe wetting behavior of droplets on surfaces is vital in determining whether theyspread out or stay as sessile droplets. Key factors such as contact line movement,contact angle hysteresis, and surface energy play significant roles in influencing wettingand spreading. When a droplet makes contact with a solid surface, it may eitherspread out and wet the surface or maintain its compact droplet form. The spreading8behavior hinges on the interplay between the liquidâs surface tension and the adhesiveforces between the liquid and the solid surface.The contact angle, which represents the angle between the droplet interface andthe solid surface, is a crucial parameter for assessing the wetting behavior. Contactangle hysteresis refers to the discrepancy between the advancing and receding contactangles of a droplet on a surface. It arises from surface defects, roughness, or chemicalvariability. Contact angle hysteresis impacts droplet stability and can lead to thepinning or depinning of the contact line. Pinning occurs when the contact line is stuckat surface defects, while depinning happens when the contact line can move freely.Surface energy is another key factor that affects droplet wetting and spreading. A solidsurfaceâs surface energy dictates its hydrophilicity or hydrophobicity. High surfaceenergy encourages droplet wetting and spreading, whereas low surface energy tendsto make droplets bead up and remain as sessile droplets. Researchers have carriedout numerous studies to explore the wetting and spreading behavior of droplets onvarious surfaces. These investigations have examined the effects of surface roughness,surface chemistry, and surface energy on droplet wetting. Advanced techniques likeatomic force microscopy (AFM) and contact angle measurements have been used toquantify wetting behavior and uncover the underlying mechanisms [24â26].In one study, the spreading behavior of water droplets on hydrophilic and superhy-drophilic surfaces was analyzed. The findings indicated that water droplets spreadmore easily on superhydrophilic surfaces due to their elevated surface energy andenhanced wetting properties [27]. Another investigation centered on the wettingbehavior of droplets on microstructured surfaces with varying geometries. It wasdetermined that the wetting behavior was heavily affected by surface roughness andgeometry, resulting in different spreading dynamics [28].9Additionally, the impact of surface chemistry on droplet wetting was examined bymodifying surfaces with self-assembled monolayers (SAMs) featuring various functionalgroups. The results demonstrated that the choice of functional group significantlyaffected the wetting behavior, underscoring the importance of surface chemistry indroplet spreading [29]. In conclusion, the wetting and spreading behavior of dropletson solid surfaces is a complex phenomenon shaped by factors such as surface roughness,surface energy, contact angle hysteresis, and surface chemistry. Grasping these factorsis crucial for diverse applications, including coating technologies, microfluidics, andsurface engineering.Rebound and SplashingIn addition to spreading and wetting, the impact of droplets on solid surfaces can giverise to rebound or splashing phenomena. Rebound takes place when a droplet strikes asurface and bounces back without significant spreading. Splashing, however, involvesthe ejection of smaller droplets upon impact, leading to a spreading crown or a sprayof droplets. The occurrence of rebound or splashing is influenced by various factors,including impact velocity, droplet size, surface properties, and liquid characteristics.When a droplet impacts a surface at a relatively high velocity, it can overcome surfacetension forces and bounce back, resulting in a rebound. The rebound behavior isshaped by the dropletâs kinetic energy, surface roughness, and the contact time betweenthe droplet and the surface.Conversely, splashing is typically observed when the impact velocity is high or whenthe dropletâs viscosity is low. Upon impact, the droplet deforms and spreads, resultingin the ejection of smaller satellite droplets. The splashing behavior is influencedby the dropletâs Weber number (the ratio of the dropletâs kinetic energy to surfacetension energy), viscosity, and surface characteristics. Understanding the dynamics ofrebound and splashing is vital for various applications, including inkjet printing, spray10coating, and fuel atomization. Researchers have carried out extensive experimentaland numerical studies to explore these phenomena and develop models to predict theiroccurrence.High-speed imaging techniques, such as ultra-high-speed cameras and laser-inducedfluorescence, have been used to capture the dynamics of droplet impacts and elucidatethe mechanisms behind rebound and splashing [30, 31]. Numerical simulations utilizingcomputational fluid dynamics (CFD) have also been employed to model and predictrebound and splashing behavior. These simulations involve solving the Navier-Stokesequations and incorporating suitable models for surface tension and droplet-surfaceinteractions. The simulations offer insights into the dynamics of droplet impacts,including the formation of thin liquid films, the breakup of these films, and the ejectionof satellite droplets [32, 33]. Overall, studying rebound and splashing phenomena indroplet impacts on solid surfaces offers valuable insights into the complex dynamicsinvolved and aids in developing predictive models for various practical applications.1.1.3 Wetting and Rheological PropertiesAfter examining various criteria related to droplet impact, such as shape, spread,surface wetting, rebound, and splashing, it is essential to investigate two additionaltopics: extensional relaxation time and the Trouton ratio. These parameters are vitalfor grasping the behavior of viscoelastic fluids and offer a thorough insight into dropletdynamics. subsection 1.1.3 covered key aspects of droplet impact, concentrating onNewtonian fluids. However, many real-world fluids display viscoelastic characteristics,where extensional relaxation time and Trouton ratio are significant factors.The extensional relaxation time indicates the duration for a viscoelastic fluid to relaxfollowing extensional deformation, which influences droplet deformation and breakup.The Trouton ratio compares extensional viscosity to shear viscosity, highlighting11the effect of fluid elasticity. Grasping these parameters is essential for elucidatingphenomena unique to viscoelastic fluids during droplet impact and has practicalsignificance in fields like inkjet printing and biomedical engineering. In the upcomingsections, we will explore the criteria related to extensional relaxation time and theTrouton ratio, examining their effects on droplet dynamics. Incorporating these topicsinto our discussion will ensure a comprehensive understanding of the interactionbetween viscoelastic fluids and droplet impact phenomena.Extensional Relaxation TimeIn a study examining the capillary thinning and breakup of low-viscosity liquidfilaments, the relaxation time of dilute polymer solutions under extension was evaluated.The researchers utilized high-speed imaging techniques alongside a slow retractionmethod (SRM) to observe and analyze the thinning dynamics. By reducing inertialoscillations, the SRM enabled the precise determination of relaxation times as low as240 µs. The study also established a minimum polymer concentration, below whichan elasto-capillary balance could not be detected. Overall, the research illustrated theefficacy of the SRM technique in exploring thinning dynamics and extracting materialproperties from capillary thinning experiments [32].Another study focused on characterizing the extensional rheology of complex fluidsby investigating the thinning and pinch-off dynamics of an asymmetric liquid bridge.The researchers centered on dilute polyethylene oxide (PEO) solutions and created anoptically-detected elastocapillary self-thinning dripping-onto-substrate (ODES-DOS)method. This approach facilitated the measurement of extensional relaxation time andviscosity in weakly elastic polymeric fluids. The study underscored the applicability ofthe ODES-DOS method for characterizing extensional rheometry and its potential forassessing sprayability, jettability, spinnability, and printability of complex fluids [33].12A study aimed to establish a setup and methodology for accurately measuring theextensional rheology of low-concentration polymer solutions. The researchers developeda new setup that combined the slow retraction method, high-speed imaging techniques,and an immiscible oil bath. This configuration reduced solvent evaporation andenabled particle tracking in the thinning filament. The study successfully measuredthe extensional relaxation time of dilute polymer solutions down to roughly 100 µs,overcoming the constraints of earlier devices [34]. Investigating the pinch-off dynamicsand extensional rheology of semidilute polyelectrolyte solutions, a study employedDripping-onto-Substrate (DoS) rheometry.Poly(sodium 4-styrenesulfonate) (NaPSS) and poly(acrylic acid) (PAA) solutionswere assessed in various solvents. The extensional relaxation time of PAA solutionsdemonstrated different concentration dependencies compared to shear relaxation time,with distinct exponents for unentangled and entangled solutions. Conversely, theextensional relaxation time of NaPSS solutions was unmeasurable in the unentangledregime but showed a weak increase with concentration in the entangled regime. Thestudy highlighted the impact of electrostatics and hydrodynamics on the extensionalrheology response and printability of polyelectrolyte dispersions, emphasizing thesignificance of understanding these properties for practical applications. Furtherinvestigations into the effects of additives, such as salts, on extensional relaxationtimes and rheological behavior were suggested [35].Trouton RatioThe initial application of extensional viscosity, known as the âcoefficient of viscoustraction", can be traced back to Troutonâs work in 1906. In his research, Troutonsought to ascertain the viscosity of an incompressible Newtonian fluid. He establisheda correlation between the shear viscosity (η) and the coefficient of viscous traction(ηT ), with ηT being three times the value of η. The study tackles the confusion13surrounding the concept of extensional viscosity and underscores the significance ofprecise measurement in steady and spatially uniform flows.It discusses the controllability of a flow, emphasizing the dependence on the balanceof viscous, elastic, and capillary forces in preserving sample shape. The study cau-tions against applying extensional viscosity in non-steady flows and warns againstoversimplifications such as âtransient extensional viscosity". However, it proposes thata well-defined transient extensional viscosity, similar to path-dependent functions inthermodynamics or standardized tests like the melt flow index, could be beneficial forcomparative evaluations of fluid properties in actual flows with extensional deforma-tions. The study concludes that strain measurement could yield valuable insights intomaterial rheology in extension, though the use of such functions should be approachedwith care and not seen as a replacement for rheological equations of state in predictingflow behavior under all conditions [36].The objective of this study was to develop an approximate analytical solution to forecastthe flow, vortex behavior, and pressure drop in abrupt axisymmetric contractions,particularly focusing on fluids with large Trouton ratios at elevated extensional rates.The solution considered the steady-state extensional viscosity, disregarding any straindependence and assuming a step change in the Trouton ratio at a critical rate. Themodelâs predictions were compared to for results dilute to experimental semi-dilutesolutions of flexible and semi-rigid polymers, demonstrating good correlation. Thestudy concluded that vortex behavior is affected by the fluidâs characteristic time,while the steady-state extensional viscosity is vital in determining the steady-statepressure drop. Despite its simplifications, the model successfully captured variousphenomena observed in contraction flows and provided accurate predictions for vortexlengths and pressure drops in polymer solutions [37].141.2 Research ObjectivesResearch on spray formulation has studied spray modifiers and surfactants, but thereis no established and standardized method to relate rheological measurements tospray retention and long-term formulation stability. The lack of predictive knowledgeon polymer-enhanced sprays prevents their adoption in agriculture because farmersrequire dependable retention and shelf stability for their products. Therefore, for thisproject, we have the following objectives:Project ObjectivesThe first objective of this research was to develop and standardize a testing protocolfor quantifying spray retention. This involved assessing how tank pressure and nozzlespeed affect spray deposition and retention. A consistent protocol was created tomeasure retention on flat surfaces and later adapted for more complex plant geometries.Commercially relevant plant species were selected to ensure real-world applicability,and the influence of surface type and orientation on retention was systematicallyanalyzed. Based on these experiments, a refined and reproducible standard protocolwas established for future use.The second objective was to optimize polymerâsurfactant combinations to maximizespray retention. Agriculturally suitable polymers and surfactants were selected, andtheir rheological properties and retention efficiencies were first examined individually.Polymerâsurfactant mixtures were then systematically screened to identify promisingformulations that enhanced spray performance. The most effective formulations werefurther evaluated on various plant surfaces to verify their consistency and practicalrelevance.15The third objective focused on identifying suitable stabilizers to improve the shelf-lifestability of polymerâsurfactant mixtures. The maximum acceptable mixing concentra-tions for selected formulations in water were determined, and stabilizers were testedby monitoring changes in extensional viscosity over time. Rheological and retentionperformance were measured to evaluate the influence of stabilizers, particularly theeffects of isopropyl alcohol concentration and storage temperature on long-term stabil-ity. These tests provided insights into maintaining formulation performance duringstorage and handling.The fourth objective was to investigate the relationship between extensional relaxationtime and spray retention for polymers of different molecular weights. By comparingformulations across a range of molecular weights, this study sought to determinehow polymer chain length influences extensional behavior and its predictive value forspray performance. Finally, the fifth objective was to compare the effects of ionic andnon-ionic surfactants on the extensional rheology and spray performance of polymersolutions. This analysis provided a clearer understanding of how surfactant typealters both the flow behavior and deposition efficiency of polymer-containing sprays.By addressing these objectives, this thesis provides a practical and cost-effectiveframework for improving agricultural spray technology while reducing the reliance onempirical, trial-and-error formulation methods.16Chapter 2Methods and Materials2.1 ChemicalsThe chemicals used in this study were polyethylene oxide (Dupont, Collegeville, PA,USA) of five molecular weights (1 MDa, 2 MDa, 4 MDa, 8 MDa, and 8.5 MDa),two carageenan polymers (GP209 and GP379), isopropyl alcohol (Sigma Aldrich,Canada), (Â±) alpha tocopherol (Sigma Aldrich, Germany), and three surfactants:sodium dodecyl sulfate (BP166-100, Fisher Scientific, China), ECO Brij O10 MBAL-LQ-AP (Croda, NJ, USA), and ECO Brij S20 MBAL-SO-AP (Croda, NJ, USA). Allthe water used in this study was deionized water from ELGA LabWater PURELABChorus 1 Complete water purification system (ELGA LabWater, PURELAB Chorus 1Complete). We chose these surfactants because they are commonly used in agriculturalformulations and, therefore, allow the results to be linked to practical applications.172.2 Solution preparationAll concentrations in this study are reported on a weight/weight (w/w) basis. Thepolymers used were all water-soluble; however, due to their high molecular weight,direct addition of polymer powders to water typically resulted in clumping and theformation of âfish eyesâ. To avoid incomplete hydration and ensure homogeneity,high-concentration stock solutions were prepared first. Polymer stock solutions weremixed for 1â2 minutes using a three blade propeller (40 mm in outer diameter) in a1000 mL beaker (107 mm outer diameter). The amount of prepared stock solutionranged between 400 and 500 grams, depending on the number of tests expected tobe performed. This was followed by placement on a roller mixer, in 500 mL amberbottles (80 mm diameter) at low speed (15 rpm) overnight (12-16 hours) to promoteuniform hydration and dispersion while preventing polymer chain degradation causedby high shear forces [38].Therefore, for long-term use, polymer stock solutions were prepared at relatively highconcentrations (1 wt% for spray testing and 2 wt% for preparing 1 wt% solutionsin shelf-life tests), and were stored for up to two months. These stock solutionswere later diluted to the desired concentrations (typically in the ppm range) forextensional rheometry and spray testing. This procedure was particularly necessaryfor polyethylene oxide (PEO) solutions, which were observed to degrade over time,making batch preparation and controlled storage essential for experimental consistency.For long-term shelf-life tests, (Â±) alpha tocopherol was first dissolved in isopropanol(IPA), followed by combination with a 2 wt% stock solution of PEO and deionizedwater to reach the desired concentration. The solution was stirred with a magneticstirrer (37.8 mm length) at 400â500 rpm for 6-8 minutes in a 250 mL beaker (68 mmouter diameter) to ensure initial dispersion. Subsequently, in a 250 mL polypropylene18bottle (61.77 mm outer diameter) the solution was transferred to a roller mixer androtated at 30 rpm for 2 hours to achieve complete hydration and uniformity.For surfactant-containing samples, surfactant stock solutions were prepared as multiplesof the critical micelle concentration (CMC) of each surfactant. The appropriate volumeof surfactant stock was then added to the polymer stock solution, followed by dilutionwith DI water to reach the final desired concentrations. This approach ensured betterreproducibility due to the very low concentrations tested.2.3 Extensional rheology via Dripping onto Sub-strate (DoS)Extensional relaxation times of the polymer formulations were determined using theDripping onto Substrate (DoS) method [33]. The setup, shown in Figure 2.1, consistedof a diffuse backlight, a 2500 µL threaded plunger syringe (Hamilton, Reno, NV, USA)with a 14 gauge blunt-tip needle, a stainless steel substrate and a high-speed camera(1.4 CHRONOS, Kron Technologies Inc., Canada) that operates at varying fps andpixel resolution values. After the initial and preliminary works, we used 1762 fps and800Ã980 pixel resolution for our tests. The lens used for the camera was a Fujian35 mm f/1.7 GDS-35 (Fujian, China) with a 30 mm spacer behind the lens. Theneedle tip was positioned â¼6 mm above the substrate, from which a droplet of fluidwas dispensed onto a clean substrate.The extensional relaxation time, λE, was obtained from the slope, m, of log(R/R0)versus time in the elasto-capillary regime, identified by a transition to a constant,shallower slope.λE =13m. (2.1)19Threaded plunger syringeLight sourceS.S substrateHigh speed cameraFigure 2.1: Image of the extensional rheometer (Dripping-onto-Substrate method) enclosedto minimize external air currents and prevent droplet oscillation.Data beyond the finite extensibility limit, where slope deviations occur, were ex-cluded [33]. Each sample was measured in sextuplicate (n = 6).2.4 Spray deposition and retention efficiencyThe spray deposited onto various substrates was quantified using a custom-built,spray-testing apparatus. As shown in Figure 2.2, the system comprises a pressureregulator (AR20-B, range 0â150 psi; SMC Corporation, Japan), a pressurized supplytank, a push-button directional control valve, and a conventional agricultural nozzle(Airmix 110-06, Agrotop, Germany). The nozzle was mounted 18 in. above the testsubstrates and operated with the supply tank at pressures between 40 and 60 psi(gauge). Two gutters were positioned directly beneath the nozzle at both ends of thetravel range to prevent unintended overspray on the test substrates and to allow thespray to develop fully before translating the nozzle.The nozzle assembly was mounted on a precision linear rail driven by a TXM24Q-3AGintegrated StepSERVO motor, with motion parameters controlled via Step-Servo20Push buttonPressurized tankGuttersBalancePaper (control) and model substrates ()Figure 2.2: Image of the specially designed spray apparatus, consisting of a pressurizedspray-solution tank, nozzle, gutters for collecting solution at the initial and final spray stages,a slot holding test substrates, and a balance.Quick Tuner software (V3.0.19.0109). There is a period of acceleration in all sprayswith a constant (17.7m/s2 or 221 rps/s, for all tests after preliminary work), duringwhich the maximum translation speed in the speed profile varied between 0.9 and5.38 mph to achieve the desired spray coverage conditions. Directly beneath the nozzle,a smooth aluminum platform held two sample mounts, arranged in parallel, to holdthe spray substrate coupons. Each sample mount consisted of a rigid plastic plate(thickness 0.75 mm, width 1 in., length 5 in.) with embedded magnets on the reverseside to secure the mounts in a consistent place on the aluminum platform.For model surfaces, coupons of low-density polyethylene (LDPE) sheets (thickness0.17 mm; P1525 Frost King, Thermwell Products Co., Inc., NJ, USA) were cut to sizeto fully cover the sample mount (1 in. by 5 in.). Each coupon was wrapped aroundthe sample-mount plate and held firmly in place with tape on the underside. Forleaf tests, plant leaves were first affixed to LDPE backing sheets using tape and then21placed onto the substrates in the same manner. An analytical balance (Entris224-1S,Sartorius AG, Goettingen, Germany) positioned adjacent to the spray system wasused to record sample mass immediately before and after spraying.Paper towels (Bounty, Toronto, ON, Canada) served as control substrates for allexperiments. We selected Bounty paper towel as the porous standard because (i) itoffers high liquid uptake with low variability across rolls and batches, (ii) mechanicalintegrity when wet (no fiber shedding), and (iii) a stable surface structure duringrepeated spray and measurement cycles. These properties reduced noise in gravimetricdeposition measurements compared with generic tissue or laboratory wipes.In addition to the LDPE model substrates, fresh leaves from four plant species âblueberry, corn, potato, and soybean â were obtained from the University of BritishColumbia Farm. Leaves were collected with branches intact when possible, stored insealed bags in a shaded, cool environment, and used the same day to preserve naturalsurface properties. For all species, care was taken to cut leaf sections from equivalentpositions to minimize variability due to surface heterogeneity (see Figure 2.3).In each spray experiment, approximately 1000 mL of spray solution was added into thepressurized tank. A control coupon (paper towel) and a test coupon (leaf or LDPE)were placed on the two separate sample mounts. The paper towel was assumed toabsorb all droplets impinging upon it, thereby serving as a reference for the totalmass that could reach the test coupon under a given set of spray conditions. Thesample mounts were positioned symmetrically beneath the nozzle, with a separationdistance of 2.35 inches (center to center), and the spray started at its designated speed.The holders, each 5 in. in length, were selected to be sufficiently long to reduce localvariability in the spray pattern while remaining of practical size for handling.22Blueberry Corn Potato SoybeanFigure 2.3: Image showing substrates covered with 4 different types of leaves for sprayexperiments.The dry substrates were weighed before spraying. After each spray, both the controland test samples were re-weighed, and the retention efficiency, ϵ, was calculated asϵ = sâ s0câ c0 , (2.2)where s and c are the masses of the test (leaf or plastic) and control (paper) substratesafter spraying, respectively, and the subscript 0 denotes the corresponding masses priorto spraying. This ratio represents the mass of droplets retained on the test surfacerelative to that on the control substrate, providing a fractional measure of depositionefficiency with respect to a fully absorbing surface (paper). To minimize the possibilityof systematic bias from potential spray asymmetry, the positions of the control andtest samples were alternated between replicates. For each solution composition in theleaf tests, three samples of identical concentration were prepared and each sample wassprayed ten times, resulting in thirty total sprays for each solution composition. All23experiments were conducted under ambient laboratory conditions of 54â62% relativehumidity and 22â24.6 â¦C.2.5 Shelf-Life TestingLong-term shelf-life testing was performed to evaluate the long-term stability of selectedformulations. When assessing the influence of storage temperature, two independentsets of stock solutions were prepared. Each set contained four formulations of 150 g,prepared with 0.03 g vitamin E, varying amounts of isopropanol (IPA), 1.5 g PEO(from 75 g of a 2 wt% stock solution), and water. In each case, the final polyethyleneoxide (PEO) concentration was 1 wt%, obtained by diluting from a 2 wt% PEO stocksolution.The first solution contained 5.0 wt% IPA, 1.0 wt% PEO, 93.98 wt% water, and0.02 wt% vitamin E. The second contained 10.0 wt% IPA, 1.0 wt% PEO, 88.98 wt%water, and 0.02 wt% vitamin E. The third contained 20.0 wt% IPA, 1.0 wt% PEO,78.98 wt% water, and 0.02 wt% vitamin E. The fourth contained 49.99 wt% IPA,1.0 wt% PEO, 48.99 wt% water, and 0.02 wt% vitamin E.Preparation proceeded as follows: (Â±) alpha-tocopherol was first dissolved in theappropriate amount in isopropyl alcohol. The appropriate amount of 2 wt% PEO stocksolution was then added, and the remaining volume was made up with deionized (DI)water to achieve the target concentration of PEO. Each formulation was stored underone of two conditions: ambient laboratory temperature (20â25â¦C) or refrigeratedstorage (â¼4â¦C). At predetermined time intervals, samples were diluted to a final PEOconcentration of 100 ppm, and then extensional relaxation times were measured. Foreach condition, six replicate measurements were performed.24Chapter 3Preliminary WorksAs noted in the introduction, prior research has laid the groundwork for quantifyingretention efficiency. Nevertheless, the methods used in earlier studies lack standard-ization, posing a challenge in maintaining consistency and reliability. To fill thisgap, the current research engaged in a thorough optimization process to enhance theexperimental setups, ensuring that the measurements would be both resilient andrepeatable.Obtaining reliable spray retention measurements under real-world conditions necessi-tates careful consideration of system parameters such as spray speed, pressure, andnozzle type. These parameters were methodically optimized to guarantee reproducibil-ity across trials. For extensional rheology, employing the dripping-onto-substrate(DoS) method, we also investigated the effects of substrate properties (e.g., geometry)and camera frame rates. Assessing these factors was essential for establishing theaccuracy and repeatability of the relaxation time measurements.This chapter provides the results of these optimization studies. Each section outlinesthe parameters tested, the reasoning behind the modifications, and the final conditions25selected. The objective was to create a robust methodology that could yield reliableand repeatable data for future analyses.3.1 DoS OptimizationBuilding toward a predictive framework for spray retention, this section establishes stan-dardized measurements of extensional rheology (λE) using a Dripping-onto-Substrate(DoS) method. To begin extensional rheology measurements using the DoS method,we first assessed the impact of substrate material. We employed 4 MDa polyethyleneoxide (PEO) solutions for these tests. At measurable concentrations (50 ppm andabove), Figure 3.1a indicates that switching the substrate from a plate to a glassslide resulted in no notable differences in the measured relaxation time. At lowerconcentrations, however, variances emerged due to systematic limitations. In thiscase, filament thinning happened so quickly that the recorded video lacked enoughdata points to reliably compute relaxation times, thus establishing a practical lowerconcentration limit for the method.We next assessed the impact of camera frame rate. At 100 ppm, 4 MDa PEO solutionsrecorded at two different frame rates produced indistinguishable relaxation times(Figure 3.1b). Data variability, based on six replicates per condition, primarily reflectsinconsistencies introduced during sample preparation and handling. The notabledeviation observed at 50 ppm resulted from a single outlier rather than a reproducibleor systematic effect.To evaluate robustness across materials, we expanded the study to three differentframe rates and six polymers: two carrageenan polymers (GP209 and GP379) andfour PEOs with varying molecular weights. As illustrated in Figure 3.2a, the 4 MDaPEO solutions again demonstrated consistent relaxation times across all frame rates.The 8 MDa and 8.5 MDa PEO solutions, assessed over a more limited concentration26101 102 103Concentration (ppm)10 1100101Relaxation Time (ms)Substrate TypeGlassPlate(a) Effect of Substrate101 102 103Concentration (ppm)100101Relaxation Time (ms)2873 fps6000 fps(b) Effect of frame rateFigure 3.1: DoS optimization tests with 4 MDa PEO: (a) substrate model and (b) cameraframe rate.range, also exhibited minimal variability between replicates. In contrast, the 1 MDaPEO solutions showed high variability, reflecting their very short filament decay times,which hinder precise measurement. Likewise, the carrageenan polymers (Figure 3.2b)failed to form stable filaments, resulting in noisy data.We then investigated the influence of substrate geometry to guide the design of astainless steel DoS substrate for future use. Aluminum substrates were fabricatedwith hole diameters ranging from 2/32â²â² to 6/32â²â² in one set and from 5/32â²â² to 8/32â²â²in another, with depths varied between 0.01â²â² and 0.03â²â². Solutions overflowed whenhole diameters were below 5/32â²â².Measurements conducted with 4 MDa PEO solutins on aluminum substrates werecompared to those obtained from flat glass substrates and cases without any substrate.The resulting radiusâtime plots were time-shifted in Figure 3.3 so that the start offilament decay aligned with the x-axis origin, as video recordings captured a briefsteady droplet phase prior to release. In the no-substrate condition, droplets fell freely,27101 102 103Concentration (ppm)100101Relaxation Time (ms)1MDa4MDa8.5MDa8MDa2837 fps3587 fps6000 fps(a) PEO polymers1028Ã101 9Ã101Concentration (ppm)101102Relaxation Time (ms)GP209GP3792837 fps3587 fps(b) Carrageenan polymersFigure 3.2: Comparison of relaxation times for PEOs of different molecular weights andcarrageenan polymers, measured under varying camera frame rates.which prevented gradual necking and resulted in inconsistent data. In contrast, theflat glass substrates produced filament thinning slopes similar to those observed withthe aluminum designs. These comparisons indicated that substrate geometry did notplay a significant role in determining relaxation time, reinforcing the reliability andrepeatability of the DoS method for extensional rheology measurements.We then created a second aluminum substrate featuring larger hole diameters butmaintaining the same depth. Testing with 4 MDa PEO once more revealed nosignificant differences in filament decay slopes (Figure 3.4). At this stage, enough datahad been gathered to choose a standardized substrate geometry. A hole diameter of6/32â²â² and depth of 0.02â²â² was selected, balancing containment without overflow andensuring reproducibility.Finally, Figure 3.5 presents relaxation times derived from slope data. Relaxationtime refers to the period over which a stretched polymer chain returns to equilibriumfollowing deformation in extensional flow. The values were consistent across differ-280 100 200 300 400Time (ms, shifted)1012345Neck RadiusTime shift = 45 msHole geometry / Sub. typeD= 2/32 inD= 3/32 inD= 4/32 inD= 5/32 inD= 6/32 inFlat Sub(a) 0.01 â²â² hole depth0 100 200 300 400Time (ms, shifted)1012345Neck RadiusTime shift = 60 msHole geometry / Sub. typeD= 2/32 inD= 3/32 inD= 4/32 inD= 5/32 inD= 6/32 inFlat Sub(b) 0.02 â²â² hole depth0 100 200 300 400Time (ms, shifted)1012345Neck RadiusTime shift = 75 msHole geometry / Sub. typeD= 2/32 inD= 3/32 inD= 4/32 inD= 5/32 inD= 6/32 inFlat Sub(c) 0.03 â²â² hole depthFigure 3.3: Filament radius decay of 4 MDa PEO solutions on aluminum substrates withvarying hole depths and diameters.29(a) 0.01 â²â² hole depth (b) 0.02 â²â² hole depth(c) 0.03 â²â² hole depthFigure 3.4: Filament radius decay of 4 MDa PEO solutions on the second series ofsubstrates with new hole diameters at the same depths.30ent substrate geometries. The variability seen in the plots mainly reflects samplepreparation and handling, which is crucial given the millisecond timescales of themeasurements. Occasional outliers were attributed to measurement variability ratherthan a systematic departure from the overall trend.Flat Sub.No Sub.D= 2/32 inD= 3/32 inD= 4/32 inD= 5/32 inD= 6/32 inSubstrate Type050100150200Relaxation TimeConcentration1001000Depth0.010.020.03No SubFlat SubMolecular Weight4 MDa (filled)1 MDa (empty)(a) First diameter variationFlat Sub.No Sub.D= 2/32 inD= 3/32 inD= 4/32 inD= 5/32 inD= 6/32 inD= 8/32 inD= 7/32 inSubstrate Type050100150200Relaxation TimeConcentration100 ppm1000 ppmDepth0.010.020.03No SubFlat SubMolecular Weight4 MDa (filled)1 MDa (empty)(b) Second diameter variationFigure 3.5: Relaxation times of PEO solutions measured on aluminum substrates withdifferent hole diameters and depths.3.2 Spray OptimizationParallel to the rheological studies, spray experiments were carried out to optimize thesetup and evaluate the performance of different polymer solutions under operationalconditions. In all tests, the speed profile included an initial acceleration phase beforereaching the target translation speed. Figure 3.6 presents the results obtained at3.58mph and 60 psi with four PEOs of different molecular weights and two carrageenanpolymers. Due to the time-intensive nature of the experiments, a full concentrationsweep was performed only for the intermediate PEOs (4 and 8MDa), while the otherpolymers were tested at selected concentrations.31Consistent with the rheological measurements, carrageenan polymers did not exhibitmeasurable improvements, and 1MDa PEO provided only minimal effects that werenot significant in the spray tests. By contrast, higher molecular weight PEOs producedclear improvements in deposition, particularly at higher concentrations.0 25 50 75 100Concentration (ppm)0.050.100.150.200.25Mass (g)PaperUncovered1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water(a)0 10 25 50 75 100Concentration (ppm)050100150Retention (%)1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water(b)Figure 3.6: Spray performance at 3.58mph and 60 psi for different polymer types: (a) massdeposition and (b) retention.To better mimic realistic field conditions, the tests were conducted again at a highernozzle speed of 4.48mph (Figure 3.7). At this speed, a complete concentration sweepwas performed for all polymers. Each condition underwent testing with ten replicates,ensuring that variability could be accurately quantified. This replication is illustratedin the error bars displayed in the plots, which indicate the natural variability inspray deposition and retention. Differences in mass deposition became clearer at100 ppm, where higher molecular weight PEOs led to increased deposition. While errorbars showed considerable variability, the overall retention trends indicated significantdifferences among PEOs with varying molecular weights.At 100 ppm, the results are summarized in Figure 3.8. Carrageenan polymers againshowed no improvement compared to water, while PEOs demonstrated molecular-320 25 50 75 100Concentration (ppm)0.050.100.150.200.25Mass (g)PaperUncovered1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water(a)0 10 20 50 100Concentration (ppm)050100150200Retention (%)1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water(b)Figure 3.7: Spray performance at 4.48mph and 60 psi for different polymer types: (a) massdeposition and (b) retention.weight-dependent increases in mass deposition. Retention values for the highestmolecular weight PEOs (8 and 8.5MDa) occasionally exceeded 100%, which is theo-retically unexpected but arises from differences in spray pattern coverage. Based onthese observations, carrageenan polymers and the highest molecular weight PEOs wereexcluded from further consideration due to limited or inconsistent performance. The4MDa PEO emerged as the most suitable candidate, providing reliable improvementsin both mass deposition and retention while maintaining reproducibility, confirmingits role as the baseline polymer for future experimentsIn the next step of the work, nozzle condition was also assessed, as illustrated inFigure 3.10. Sprays conducted with a replacement nozzle exhibited enhanced consis-tency compared to an older nozzle that had been utilized for one year, emphasizingthe significance of nozzle maintenance in achieving reproducible results. Substrateorientation was also examined to replicate the natural leaf angles found in agricul-tural fields. As illustrated in Figure 3.11, steeper substrate angles led to decreaseddeposition and heightened variability in retention, highlighting the difficulties posed331 MDa4 MDa8 MDa8.5 MDaGP209GP379Water0.050.100.150.200.25Mass (g)PaperUncovered1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water(a)1 MDa4 MDa8 MDa8.5 MDaGP209GP379Water050100150200Retention (%)(b)Figure 3.8: Spray performance at 100 ppm and 4.48mph for different polymers: (a) massdeposition and (b) retention.20 40 60 80 100Concentration (ppm)0.060.080.100.120.14Mass (g)WSR 301 - PaperWSR 301 - Uncovered(a)10 20 50 75 100Concentration (ppm)020406080100Retention Rate (%)(b)Figure 3.9: Full concentration sweep of 4MDa PEO at 4.48mph: (a) mass deposition and(b) retention.34New OldNozzle Type0.050.060.070.080.090.100.11Mass (g)PaperPlastic(a)New OldNozzle Type020406080100120Retention Rate (%)(b)Figure 3.10: Comparison of spray performance between new and used nozzles: (a) massdeposition and (b) retention.by non-horizontal surfaces in real-world field scenarios. Finally, Figure 3.12 illustratesthe viscosity profile of 4MDa PEO at various concentrations. This offers a usefuloperating range for sprays, matching rheological properties with spray performance.350 Degree 45 Degrees 90 DegreeOrientation0.000.020.040.060.080.100.12Mass (g)2nd Round - Paper2nd Round - Plastic1st Round - Paper1st Round - Plastic(a)0 Degree 45 Degrees90 DegreeOrientation020406080100120Retention Rate (%) 2nd Round1st Round(b)Figure 3.11: Effect of substrate orientation on spray performance: (a) mass depositionand (b) retention.Figure 3.12: Viscosity of 4MDa PEO solutions across concentrations, providing theoperational window for spray tests.36Chapter 4Baseline ExperimentsSince agricultural sprays typically include non-ionic surfactants to improve adhesionand spread on plant surfaces, this chapter evaluates their combined impact with PEOson extensional rheology to identify formulations that could maximize spray retentionperformance. By systematically assessing polymer-surfactant interactions, this workestablishes a foundation for future spray experiments. In addition, because adoptionof polymer-enhanced sprays in real agricultural practice requires formulations thatremain stable over extended storage periods, this chapter also addresses the criticalbarrier of shelf-life doing a short-term study on polymer formulations.4.1 PolymerâSurfactant ScreeningThe next stage of the project investigated the interplay between the selected polymer,4MDa PEO, and surfactants. To establish a robust baseline, polymer solutions wereprepared at 1000 ppm. Using this higher concentration allowed us to capture cleardifferences in relaxation time, as the longer relaxation ranges at 1000 ppm madechanges more detectable than at 100 ppm.37A set of nonionic surfactants was obtained from Croda Chemicals, a manufacturer ofconventional agricultural surfactants. For each surfactant, two concentrations wereselected for preliminary testing to identify potential extensional effects. Figure 4.1summarizes the initial screening results. In this figure, the letters âMâ and âCâ aftereach surfactant name indicate whether the concentration was calculated based onmolecular weight (M) or on the critical micelle concentration (C).For each surfactant concentration, six droplets were measured per trial, and each trialwas repeated three times, giving a total of 18 measurements per condition. Theserepetitions enabled us to evaluate measurement certainty and examine how variabilityacross trials, including differences between operators, influenced the results. Two keyoutcomes emerged from this phase. First, a clearer and more standardized samplepreparation protocol was required, as some trials showed noticeable deviations. Second,surfactant candidates were evaluated both on their ability to enhance relaxation timeand on the repeatability of measurements across the three trials.Sodium dodecyl sulfate (SDS), an ionic surfactant, was also included as a reference.Previous studies have shown that SDS can enhance the relaxation time of PEOsolutions, and this served as a validation point for our measurements. Based on thescreening results, BrijS20 and BrijO10 were identified as the most promising nonioniccandidates for further testing, showing consistent enhancement of relaxation time andreproducible results.4.1.1 Nonionic vs Ionic Surfactant EffectThe comparison of nonionic and ionic surfactants highlights their differing impactson polymer relaxation times. Among the nonionic surfactants tested, BrijS20 andBrijO10 produced consistent improvements with reproducible measurements, makingthem suitable candidates for further optimization. In contrast, SDS (ionic) served38SDSCSDSMSynperonic 13 MSynperonicPE MTween20CTween20MTween28MTween80CTween80MBrijO10CBrijO10MBrijO20CBrijO20MBrijS20CBrijS20MCompound Name with concentration marker02004006008001000Relaxation Time (ms) Trial 1Trial 2Trial 3Figure 4.1: Initial surfactant screening of 4MDa PEO (1000 ppm) with selected nonionicand ionic surfactants. Letters âMâ and âCâ indicate concentration calculations based onmolecular weight or CMC, respectively.primarily as a control, confirming previously reported enhancements in relaxation timebut also showing less stability in repeatability across trials. Together, these resultsshows the potential advantages of nonionic surfactants for agricultural formulations,where consistency and reproducibility are critical.4.2 Short-term Shelf-life StudyThe next stage of the project focused on the stability of the selected formulations,as PEO solutions are known to degrade rapidly, which is a critical limitation foragricultural applications. Following the recommendation of the industrial partner, weconducted an accelerated shelf-life test on 100 ppm 4MDa PEO solutions. Elevatedtemperatures were used to simulate one to two years of storage under industrialconditions.39As shown in Figure 5.6, the solutions degraded within only a few days under high-temperature conditions. Visual inspection confirmed complete breakdown of thesolutions, highlighting the severity of thermal instability. Similarly, exposure to highshear rates accelerated degradation, indicating that both storage and operationalstresses significantly reduce solution stability. Therefore, there was a clear need toidentify suitable stabilizing agents and formulation strategies to improve the shelf lifeof these polymer solutions.(a) Effect of temperature (b) Effect of shear rateFigure 4.2: Shelf-life performance of 4MDa PEO solutions at 100 ppm: (a) accelerateddegradation under elevated temperature and (b) degradation under shear stress.40Chapter 5Linking Extensional RelaxationTime to Spray Retention andImproving Shelf-Life in PolymerFormulations5.1 IntroductionAs mentioned agrochemicals are essential for sustaining crop health and increasingagricultural productivity [2, 39]. However, their widespread use is often accompanied bypoor spray retention and off-target deposition, where chemicals unintentionally reachnon-target areas during and/or after application. This poses significant challenges,including environmental pollution and economic losses [1, 2]. Building on theseconsiderations, previous research has approached the problem of spray retention frommultiple perspectives, including droplet and spray behavior, the role of formulationadditives, and the influence of surface properties.41Among the various parameters affecting spray behavior, droplet size plays a pivotalrole in determining the off-target movement due to drift in the wind. Numerous studieshave shown that finer droplets are more susceptible to wind drift and can travel greaterdistances, whereas larger droplets are better at reducing drift but may suffer frompoor adhesion and increased splashing or bouncing [2, 6, 12, 40â43]. In realistic fieldconditions, coarse droplets are often preferred to control drift, a preference supportedby advancements in nozzle design and regulatory standards [6, 40, 41]. However, largerdroplets tend to splash or bounce upon impact, particularly on surfaces of plants thatare difficult to wet. Splashing and bouncing are governed by factors such as dropletsize, velocity, and surface wettability, and are typically quantified through the use ofdimensionless numbers (e.g., the Weber number, Reynolds number, etc.) which arecritical in understanding droplet dynamics [44, 45].Owing to the complexity of the underlying chemistry and physics of dropletâsurfaceinteractions, numerous fundamental studies have investigated single-droplet impactevents, the role of dynamic surface tension, and the influence of surface and additives[46â56]. Building on these insights, more applied research has focused on strategiesto improve droplet adhesion and retention under practical spraying conditions (i.e.,with larger droplet sizes). In particular, surfactants have been incorporated intospray formulations to shift the wetting regime and enhance droplet adhesion [57, 58].However, the effectiveness of surfactants can vary significantly depending on plantspecies and environmental conditions [59, 60], and natural surface variability continuesto hinder the standardization of retention assessments [61, 62].Scientists have investigated new methods to enhance surfactant performance underdifferent field conditions because of their current variability and limited effectiveness.In particular, scientists have identified the addition of flexible high-molecular-weightpolyethylene oxide (PEO) at ppm levels as a promising method to boost spray retention.The process of droplet dissipation through energy reduction leads to better retention42because it reduces both bouncing and splashing behavior by increasing the extensionalrheology of the spray without a significant increase in the shear viscosity [47, 63â65].Thus, the deployment of PEO brings a major advantage to spray formulations, buttheir susceptibility to mechanical and oxidative degradation has been a hurdle toadoption [66â71].The present work follows recent work in which a lab-scale approach was introducedfor quantifying the extent to which PEO can enhance spray retention [64]. Thatwork showed that test coupons of synthetic material can be used in a compact spraysetup to allow reproducible measurements of spray retention that may be consideredrepresentative of plant surfaces. However, the setup in [64] was manually controlledand the operating parameters had not been optimized. That work was also suggestiveof the possibility that the extensional relaxation time (in the limit of large Troutonratios) was predictive of the spray enhancement for a given formulation. If the latterwere true, then formulation efforts could be sped up by using extensional rheology asa screening tool before spray testing in the lab and in the field.In the present work, we first aimed to refine the apparatus developed in [64] so thatautomated testing can be performed. With the refined apparatus, we evaluated theimpact of varying the spray pressure and nozzle speed in order to select operatingconditions to use for further testing. We then aimed to use the refined apparatus totest two hypotheses. First, we hypothesized that a rheological property, the extensionalrelaxation time, is predictive of spray retention regardless of the molecular weight ofthe PEO. Second, we hypothesized that a combination of non-ionic surfactant andPEO would lead to a synergistic improvement in spray retention.After testing these two hypotheses, we expected to have identified a leading surfactant-PEO combination. In order for this to be of practical use in the spray applicationof agrochemicals, it would need to be stable in a concentrated form for an extendedperiod of time. Thus, we also aimed to measure the stability of PEO dissolved in a43solution of isopropyl alcohol and water, since isopropyl alcohol is a known chemicalstabilizer and already used in some agrochemicals.5.2 Results and Discussion5.2.1 Impact of tank pressure and nozzle speedAs outlined in the introduction, our first objective was to explore the influence oftank pressure and nozzle speed in our newly refined spray apparatus, using pure wateras the spray solution. It is well known that increasing tank pressure will increasethe volumetric flow of the spray and increasing the nozzle speed will decrease theamount of spray that is deposited [72, 73]. Thus, we expected to confirm these trendsas validation the our spray setup was working well and to identify a suitable tankpressure and nozzle velocity to use in all subsequent testing.In Figure 5.1a and Figure 5.2a we see clear confirmation of the expected trends whenvarying the tank pressure and nozzle speed. From this we concluded that the newsetup was performing as intended. What has not been shown before is how these trendsquantitatively impact the retention rate of the spray. What we show in Figure 5.1band Figure 5.2b is that the more mass that is deposited on the surface, whether byincreased volumetric flow rate of decreased nozzle speed, the lower the retention rate.We suggest that this is the result of an increased number of droplets impacting areasthat have already been wetted, resulting in more splashing.Another important takeaway from these measurements is that even with many repeats,there is a relatively large variability from one spray to the next. This is perhapsnot overly surprising due to the chaotic nature of the spray, but it illustrates theimportance of maintaining a very consistent protocol and collecting a sufficient numberof replicates. In this case, we believe that 30 replicates was sufficient to give trustworthy4440 45 50 55 60Pressure (psi)0.000.050.100.150.20Mass (g)PaperPlastic3.58 mph4.48 mph5.38 mph(a)40 45 50 55 60Pressure (psi)707580859095100Retention Rate (%)3.58 mph4.48 mph5.38 mph(b)Figure 5.1: (a) Mass deposition on control (paper) and model (plastic) substrates as afunction of nozzle translation speed and spray tank pressure. (b) Retention efficiency on thesame substrates as a function of nozzle translation speed and spray tank pressure.     6SHHG PSK 0DVV J SDSHUSODVWLF(a)     6SHHG PSK  5HWHQWLRQ5DWH  (b)Figure 5.2: (a) Detailed mass deposition behavior at 60 psi over the tested speed range.(b) Detailed retention efficiency behavior at 60 psi over the tested speed range.45average values. Finally, based on these results we elected to proceed to further testingusing a tank pressure of 60 psi since it gives a lower retention rate As a starting pointfor improvement, and a nozzle speed of 5.38 mph as it is closest to realistic tractorspeeds.5.2.2 Relaxation time is a predictor of mass depositionWith the spray parameters selected, we then tested our first hypothesis that as long asthe rheological properties of the fluid are the same, then the spray results should be thesame. More specifically, we wanted to see if the extensional relaxation time (λE) alonewas predictive of the mass of spray retained on the substrate and the retention rate,regardless of the polymer type, as suggested by previous work [64]. Unfortunately, afterscreening a few of other high-molecular-weight polymers (e.g., carageenan, polyacrylicacid, and 2-hydroxyethylcellulose), we found that only polyethylene oxide (PEO) metthe critical requirement of having an extensional viscosity that is much larger than thebulk viscosity (i.e., large Trouton ratio). So the best we could do was to test differentmolecular weights of PEO to see if the same extensional relaxation time resulted inthe same spray performance.In Figure 5.3a, the mass of spray solution retained on the surface correlates with theextensional relaxation time. In other words, a lower concentration of 8 MDa PEO canproduce the same retained mass as a higher concentration of 4 MDa PEO, providedthat both have similar relaxation times. However, the 2 MDa PEO deviates from thistrend. This deviation arises because achieving a comparable relaxation time requiresa much higher concentration, which increases bulk viscosity and reduces the Troutonratio, resulting in a less developed (more stream-like) spray. Overall, the relationshipbetween relaxation time and retained mass is approximately proportional. Doublingthe relaxation time roughly doubles the retained mass, indicating that the effect isstrong and direct rather than marginal.465 10 15Relaxation Time (ms)0.00.20.40.60.8Mass (g)1.8 mph3.58 mph5.38 mph2MD4MD8MDPaper (filled)Plastic (unfilled)(a)5 10 15Relaxation Time (ms)406080100120140Retention Rate (%)(b)Figure 5.3: (a) Relationship between relaxation time and mass deposition. (b) Relationshipbetween relaxation time and retention rate.While the total retained mass for paper and plastic substrates appears similar, thedifferences we observe are in the relative trends, indicating that substrate propertiesdo influence retention dynamics under controlled conditions. This suggests that whilethe absolute magnitude of retained mass may remain comparable, the underlyingmechanisms of liquidâsubstrate interaction differ. Consequently, the apparent similarityin total retained mass does not imply insensitivity to substrate effects, but ratherhighlights the complex interplay between substrate porosity, surface energy, and fluidrheology.When the results of Figure 5.3a were replotted as the retention rate vs. extensionalrelaxation time (see Figure 5.3b) the trend was less obvious, even when ignoringthe data from 2 MDa. For the slowest nozzle speed, there does not seem to be anyincrease in the retention rate as the relaxation time increases, despite a very clearincrease in the retained mass. One might argue that there is a slight increase in theaverage retention rate as the relaxation time is increased, though there is enoughvariability in the spray results that it would be difficult to justify. Nevertheless, with47a baseline retention efficiency of nearly 90% one can expect that gains will be difficultto see. Thus, we speculate that these results suggest that even very small extensionalrelaxation times produce significant improvements in retention efficiency.Although the differences in retained mass between substrates may appear small (e.g.,80% vs. 90%), in large-scale agricultural applications these correspond to substantialenvironmental differences. Even modest percentage increases in retention translate totons of additional material remaining on target surfaces, reducing environmental runoffand chemical waste. Thus, small laboratory-scale improvements can have significantfield-scale implications for both efficiency and sustainability.Overall, these results help improve our theoretical knowledge and create practicalmethods for testing spray retention. In particular, that the extensional relaxation timeserves as a compact rheological descriptor that enables the prediction of depositionresults without needing to perform spray testing. In turn, this can simplify thescreening process for spray formulations through direct measurement of rheologicalproperties.5.2.3 Polymer and surfactantâpolymer mixtures: Non-monotonic retention behaviorCombining interfacial modification by surfactants with polymer-driven extensionalstresses is a strategy to improve agricultural sprays [64, 74]. Surfactants reduce surfacetension and promote spreading, while polymers increase λE and suppress rebound. Ifthe effects were synergistic, polymer+surfactant mixtures would outperform polymer-only formulations.The polymer-based formulations showed better retention than water across all fourleaf types including blueberry, corn, potato and soybean which proved the effectivenessof polymers on complex leaf surfaces Figure 5.4b. However, no statistically resolvable48improvement was observed for PEO+surfactant relative to PEO alone under the testedconditions. The observed significant variation in the data points most likely stemsfrom the natural variations in leaf surface characteristics that exist in real-world leafsamples.These results indicate that, at ppm polymer levels, retention enhancement is dominatedby polymer rheology rather than by non-ionic surfactant addition. The results frommodel-substrate tests show that PEO performs better than surfactant-only solutions inboth deposition and retention processes as shown in Figure 5.4c and Figure 5.4d. Thisextends prior reports [64, 75â78] by showing that non-ionic surfactants act primarily aswetting modifiers, whereas the contribution to retention arises from polymer-controlledextensional dynamics.5.2.4 Impact of surfactants on relaxation time: Non-ionicsurfactants show no improvementBecause λE predicts deposition, we examined whether surfactants alter relaxationbehavior of PEO solutions. We expected ionic SDS to measurably affect λE, andnon-ionic surfactants to have negligible effect. The results confirm this picture. SDSshifted λE relative to PEO alone across concentrations Figure 5.5a. By contrast,the non-ionic surfactants Brij O10 and Brij S20 produced negligible changes overthe similar range Figure 5.5b. The experimental findings demonstrate that non-ionic surfactants modify surface characteristics yet they do not improve extensionalrheological properties. Accordingly, retention gains in our system remain polymer-driven rather than surfactant-driven.49brijO10 brijS20 PEO only Water0.00.10.2Mass (g)PlasticPaper(a) Mass deposition on four leaf types.brijO10 brijS20 PEO only Water0153045607590105Retention Rate (%)(b) Retention efficiency on four leaf types.Blueberry Corn Potato SoybeanLeaf type0.00.10.2Mass (g)brijO10 + PEObrijS20 + PEOPEO onlyWaterLeafPaper(c) Mass deposition for surfactant-only and PEO-only formulations on model substrates.Blueberry Corn Potato SoybeanLeaf type020406080100120140160Retention Rate (%)brijO10 + PEObrijS20 + PEOPEO onlyWater(d) Retention efficiency for surfactant-only andPEO-only formulations on model substrates.Figure 5.4: Comparison of polymer and surfactantâpolymer mixtures spray behavior onnatural and model surfaces.50100 101Rel. Conc. to CMC051015202530Relaxation Time (ms) PEO, 100PPMRelaxation Time(a)10 3 10 2 10 1 100Rel. Conc. to CMC051015202530Relaxation Time (ms)PEO, 100PPMBrijO10BrijS20(b)Figure 5.5: (a) Effect of SDS on relaxation time. (b) Effect of two agriculturally conventionalnon-ionic surfactants on relaxation time. Together, these results show the effect of ionic andnon-ionic surfactants on the relaxation time of 100 ppm PEO solutions.5.2.5 Impact of IPA on shelf-life and retentionPEO degradation in solution and in the solid state proceeds largely by autoxidation,involving hydrogen abstraction, peroxy radical formation, hydroperoxide buildup,and hydroperoxide decomposition that ultimately cause chain scission and carbonylformation [79]. The autoxidation framework shows that PEO stability depends on thecontrol of radical sources and competing substrates. In early work, C. W. McGary(1960) reported that aqueous polymer solutions containing alcohols such as isopropylalcohol are remarkably stable under normally detrimental aging conditions. Heattributed this stability to the relative ease of α-hydrogen abstraction from alcohols,which leads to selective autoxidation of the alcohol rather than the polymer backbone.The interpretation of isopropyl alcohol (IPA) as a sacrificial substrate follows thisperspective because its α-hydrogen gets abstracted first which leads radicals to avoidPEO chains and maintain polymer structure.51In parallel, the classical antioxidant α-tocopherol (vitamin E) has been extensivelystudied for its ability to stop radical chain reactions by giving hydrogen to peroxy andalkyl radicals which prevents polymer oxidative scission [80]. Applied aging studies onUHMW polyethylene formulations further show that α-tocopherol markedly extendsoxidative lifetime under accelerated conditions, demonstrating its practical protectiveeffect [81]. Based on this mechanistic understanding, we hypothesized that additionof IPA and ppm levels of α-tocopherol could enhance the shelf life of PEO stocksolutions.The shelf-life tests showed that stability levels directly depended on both the amountof IPA and the storage temperature according to the results presented in Figure 5.6.PEO underwent total degradation during one month at room temperature whenIPA concentrations spanned between 5.05â20.2%, whereas the polymer functionalitystayed intact when the solution contained 50% IPA. This suggests that reducedwater activity and preferential radical scavenging at high IPA content suppresseddegradation. Nevertheless, some decline was evident after extended storage. Storageunder refrigeration conditions resulted in better stability as low-IPA samples kept theirfunctionality for one month and 50.51% IPA samples showed minimal degradationafter five months.Together, these experimental results confirm the predicted behavior of IPA as asacrificial oxidant and water-activity modifier and α-tocopherol as a direct radicalscavenger. High IPA content in combination with cold storage allows PEO formulationto maintain its performance capabilities throughout agricultural storage periods. Theresearch validated previous findings which showed that IPA and α-tocopherol serve asdependable preservatives for polymer solutions.520 50 100 150 200Days036912Relaxation Time (ms)5.05% IPA10.10% IPA20.20% IPA50.51% IPAFridgeRoomFigure 5.6: Effect of isopropyl alcohol (IPA) concentration and storage temperature onthe shelf-life of 1 wt% PEO solutions measured by relaxation time decay over six months.53Chapter 6ConclusionThe results of this research demonstrate how spray application parameters, togetherwith polymer rheology and formulation composition, influence the process of spraydeposition and its subsequent retention and stability. The research provides operationalguidelines through its systematic analysis of nozzle pressure, speed, and relaxationtime, polymer and surfactant functions, and stabilization methods. The findingscontribute to a deeper theoretical understanding while outlining specific methods toimprove agricultural spray applications.Our findings highlight that spray conditions exert a strong influence on performance,with deposition and retention shaped by a trade-off between throughput and adhesion.Intermediate pressures and translation speeds were shown to offer the most reproduciblebalance, providing a practical operational window for formulation comparisons. Beyondapplication conditions, we demonstrated that relaxation time (λE) serves as a reliablerheological predictor of deposition for atomized sprays, offering a compact descriptorof performance without the need for detailed atomization analysis.Polymer-containing formulations consistently outperformed water across diverse leaftypes, confirming that polymer rheology is the dominant factor driving retention54enhancement. In contrast, non-ionic surfactants primarily acted as interfacial modifiersand did not measurably influence extensional rheology, whereas ionic surfactants suchas SDS altered relaxation time through polymerâsurfactant interactions. Theseresults emphasize that the retention benefits of polymers arise principally from theirrheological properties rather than from synergistic effects with non-ionic surfactants.A further important outcome of this work concerns formulation stability. The additionof IPA and α-tocopherol substantially extended the shelf life of PEO solutions, withpreservation most effective when combined with refrigerated storage. This stabilizationstrategy addresses a practical barrier to adoption by ensuring that polymer-basedsprays remain functional throughout agricultural use cycles.55Chapter 7Future workThe findings of this research provide a mechanistic framework linking spray parameters,relaxation time, and formulation composition to agricultural spray performance. Theyalso suggest practical strategies to enhance both spray efficacy and formulationlongevity.Future research should build on this foundation by systematically varying substrateproperties (e.g., porosity, wettability, and roughness) and environmental parameterssuch as humidity, temperature, and airflow to quantify their influence on retentiondynamics. Further work could also investigate the synergistic potential of alternativepolymerâsurfactant systems, including bio-based or biodegradable surfactants, toimprove droplet stability and reduce environmental persistence. Field-scale studiesusing real plant surfaces should be conducted to validate laboratory-scale findingsand capture the complex interplay between canopy architecture, leaf microstructure,and spray deposition. Additionally, future studies should examine the stability of theformulation over a prolonged period of time, measure the droplet size distributionand rebound kinetics under dynamic spraying conditions, and develop predictivemodels that integrate rheological and interfacial properties with spray parameters.56Finally, assessing the ecological implications of optimized formulations such as theirrunoff potential, biodegradability, and non-target effects, will be critical to ensure thatimprovements in spray performance translate into sustainable agricultural practices.By pursuing these directions, this line of work can advance the development of sprayformulations that achieve improved crop protection efficiency while reducing environ-mental impact. Furthermore, the insights gained from this study may have broaderapplications in other fields where controlled deposition of polymer-containing spraysis crucial, such as pharmaceutical aerosols, coatings, and environmental remediationtechnologies.57Bibliography[1] Allan S. Felsot et al. âAgrochemical spray drift; assessment and mitigationâAreview*â. en. In: Journal of Environmental Science and Health, Part B 46.1(Dec. 2010), pp. 1â23. doi: 10 . 1080/03601234 .2010 .515161. url: http ://www.tandfonline.com/doi/abs/10.1080/03601234.2010.515161 (visited on09/22/2025).[2] Emilia Hilz and Arnoldus W.P. Vermeer. âSpray drift review: The extent towhich a formulation can contribute to spray drift reductionâ. en. In: CropProtection 44 (Feb. 2013), pp. 75â83. doi: 10.1016/j.cropro.2012.10.020. url:https://linkinghub.elsevier.com/retrieve/pii/S0261219412003006 (visited on09/22/2025).[3] M. Al Heidary et al. âInfluence of spray characteristics on potential spray driftof field crop sprayers: A literature reviewâ. en. In: Crop Protection 63 (Sept.2014), pp. 120â130. doi: 10.1016/j.cropro.2014.05.006. url: https://linkinghub.elsevier.com/retrieve/pii/S0261219414001604 (visited on 09/22/2025).[4] C Neinhuis. âCharacterization and Distribution of Water-repellent, Self-cleaningPlant Surfacesâ. en. In: Annals of Botany 79.6 (June 1997), pp. 667â677. doi:10 . 1006/anbo . 1997 . 0400. url: https : / / academic . oup . com/aob/article -lookup/doi/10.1006/anbo.1997.0400 (visited on 09/22/2025).[5] K.L. Hughes and A.R. Frost. âA review of agricultural spray meteringâ. en. In:Journal of Agricultural Engineering Research 32.3 (Oct. 1985), pp. 197â207. doi:5810.1016/0021-8634(85)90080-0. url: https://linkinghub.elsevier.com/retrieve/pii/0021863485900800 (visited on 09/23/2025).[6] Gary J. Dorr et al. âA comparison of initial spray characteristics produced byagricultural nozzlesâ. en. In: Crop Protection 53 (Nov. 2013), pp. 109â117. doi:10.1016/j.cropro.2013.06.017. url: https://linkinghub.elsevier.com/retrieve/pii/S0261219413001725 (visited on 09/23/2025).[7] Benjamin P. Sperry, Christopher R. Mudge, and Kurt D. Getsinger. âSimulatedherbicide spray retention on floating aquatic plants as affected by carrier volumeand adjuvant typeâ. en. In: Weed Technology 36.1 (Feb. 2022), pp. 56â63. doi:10.1017/wet.2021.85. url: https://www.cambridge.org/core/product/identifier/S0890037X21000853/type/journal_article (visited on 09/23/2025).[8] Justin J. Nairn and W. Alison Forster. âDue diligence required to quantifyand visualise agrichemical spray deposits using dye tracersâ. en. In: Crop Pro-tection 115 (Jan. 2019), pp. 92â98. doi: 10.1016/j.cropro.2018.09.009. url:https://linkinghub.elsevier.com/retrieve/pii/S0261219418302849 (visited on09/23/2025).[9] Norman B. Akesson and Wesley E. Yates. âProblems Relating to Applicationof Agricultural Chemicals and Resulting Drift Residuesâ. In: Annual Review ofEntomology 9.1 (1964), pp. 285â318. doi: 10.1146/annurev.en.09.010164.001441.[10] Diego Fornasiero et al. âEffect of spray drift reduction techniques on pests andpredatory mites in orchards and vineyardsâ. en. In: Crop Protection 98 (Aug.2017), pp. 283â292. doi: 10.1016/j.cropro.2017.04.010. url: https://linkinghub.elsevier.com/retrieve/pii/S026121941730114X (visited on 09/23/2025).[11] Magali N. Blanco et al. âReal-Time Monitoring of Spray Drift from ThreeDifferent Orchard Sprayersâ. en. In: Chemosphere 222 (May 2019), pp. 46â55.doi: 10.1016/j.chemosphere.2019.01.092. url: https://linkinghub.elsevier.com/retrieve/pii/S0045653519300992 (visited on 09/23/2025).59[12] Guobin Wang et al. âField evaluation of spray drift and environmental impactusing an agricultural unmanned aerial vehicle (UAV) sprayerâ. en. In: Science ofThe Total Environment 737 (Oct. 2020), p. 139793. doi: 10.1016/j.scitotenv.2020.139793. url: https://linkinghub.elsevier.com/retrieve/pii/S0048969720333131(visited on 09/23/2025).[13] Cruz Garcerá et al. âComparison between standard and drift reducing nozzlesfor pesticide application in citrus: Part II. Effects on canopy spray distribution,control efficacy of Aonidiella aurantii (Maskell), beneficial parasitoids and pesti-cide residues on fruitâ. en. In: Crop Protection 94 (Apr. 2017), pp. 83â96. doi:10.1016/j.cropro.2016.12.016. url: https://linkinghub.elsevier.com/retrieve/pii/S0261219416303829 (visited on 09/30/2025).[14] A. M. Worthington. âOn the forms assumed by drops of liquids falling verticallyon a horizontal plateâ. In: Proceedings of the Royal Society of London 25 (1876),pp. 261â272. doi: 10.1098/rspl.1876.0048.[15] M. Pasandideh-Fard et al. âCapillary effects during droplet impact on a solidsurfaceâ. en. In: Physics of Fluids 8.3 (Mar. 1996), pp. 650â659. doi: 10.1063/1.868850. url: https://pubs.aip.org/pof/article/8/3/650/259171/Capillary-effects-during-droplet-impact-on-a-solid (visited on 09/30/2025).[16] S. Chandra and C.T. Avedisian. âObservations of droplet impingement on aceramic porous surfaceâ. en. In: International Journal of Heat and Mass Transfer35.10 (Oct. 1992), pp. 2377â2388. doi: 10.1016/0017-9310(92)90080-C. url:https://linkinghub.elsevier.com/retrieve/pii/001793109290080C (visited on09/30/2025).[17] H. Fujimoto, S. Ito, and I. Takezaki. âExperimental study of successive collisionof two water droplets with a solidâ. en. In: Experiments in Fluids 33.3 (Sept.2002), pp. 500â502. doi: 10.1007/s00348-002-0471-2. url: http://link.springer.com/10.1007/s00348-002-0471-2 (visited on 09/30/2025).60[18] S CHANDRAt and C T Avedisian. âOn the Collision of a Droplet with a SolidSurfaceâ. en. In: (1991).[19] Kensuke Yokoi et al. âNumerical studies of the influence of the dynamic contactangle on a droplet impacting on a dry surfaceâ. en. In: Physics of Fluids 21.7 (July2009), p. 072102. doi: 10.1063/1.3158468. url: https://pubs.aip.org/pof/article/21/7/072102/314898/Numerical-studies-of-the-influence-of-the-dynamic (visitedon 09/30/2025).[20] M. Pasandideh-Fard, S. Chandra, and J. Mostaghimi. âA three-dimensionalmodel of droplet impact and solidificationâ. en. In: International Journal ofHeat and Mass Transfer 45.11 (May 2002), pp. 2229â2242. doi: 10 . 1016 /S0017-9310(01)00336-2. url: https://linkinghub.elsevier.com/retrieve/pii/S0017931001003362 (visited on 09/30/2025).[21] Chun Shen et al. âInvestigation of effects of receding contact angle and energyconversion on numerical prediction of receding of the droplet impact ontohydrophilic and superhydrophilic surfacesâ. en. In: International Journal of Heatand Fluid Flow 74 (Dec. 2018), pp. 89â109. doi: 10.1016/j.ijheatfluidflow.2018.09.015. url: https://linkinghub.elsevier.com/retrieve/pii/S0142727X1830496X(visited on 09/30/2025).[22] Konstantinos Vontas et al. âNumerical Investigation of Droplet Impact onSmooth Surfaces with Different Wettability Characteristics: Implementationof a dynamic contact angle treatment in OpenFOAM.â en. In: ProceedingsILASSâEurope 2017. 28th Conference on Liquid Atomization and Spray Systems.Universitat Politècnica València, Sept. 2017. doi: 10.4995/ILASS2017.2017.5020.url: http://ocs.editorial.upv.es/index.php/ILASS/ILASS2017/paper/view/5020 (visited on 09/30/2025).[23] M. Bussmann, J. Mostaghimi, and S. Chandra. âOn a three-dimensional volumetracking model of droplet impactâ. en. In: Physics of Fluids 11.6 (June 1999),61pp. 1406â1417. doi: 10.1063/1.870005. url: https://pubs.aip.org/pof/article/11/6/1406/254548/On-a-three-dimensional-volume-tracking-model-of (visitedon 09/30/2025).[24] Haixiang Zhang et al. âEffect of wettability on droplet impact: Spreading andsplashingâ. en. In: Experimental Thermal and Fluid Science 124 (June 2021),p. 110369. doi: 10.1016/j.expthermflusci.2021.110369. url: https://linkinghub.elsevier.com/retrieve/pii/S0894177721000224 (visited on 10/01/2025).[25] Yulei Wang, Yuxiang Wang, and Shaorong Wang. âDroplet impact on cylindricalsurfaces: Effects of surface wettability, initial impact velocity, and cylinder sizeâ.en. In: Journal of Colloid and Interface Science 578 (Oct. 2020), pp. 207â217.doi: 10.1016/j.jcis.2020.06.004. url: https://linkinghub.elsevier.com/retrieve/pii/S0021979720307499 (visited on 10/01/2025).[26] Jae Bong Lee and Seong Hyuk Lee. âDynamic Wetting and Spreading Charac-teristics of a Liquid Droplet Impinging on Hydrophobic Textured Surfacesâ. en.In: Langmuir 27.11 (June 2011), pp. 6565â6573. doi: 10.1021/la104829x. url:https://pubs.acs.org/doi/10.1021/la104829x (visited on 10/01/2025).[27] Jiayu Du et al. âAnalytical Consideration for the Maximum Spreading Factorof Liquid Droplet Impact on a Smooth Solid Surfaceâ. en. In: Langmuir 37.24(June 2021), pp. 7582â7590. doi: 10.1021/acs.langmuir.1c01076. url: https://pubs.acs.org/doi/10.1021/acs.langmuir.1c01076 (visited on 10/01/2025).[28] Damon G. K. Aboud and Anne-Marie Kietzig. âSplashing Threshold of ObliqueDroplet Impacts on Surfaces of Various Wettabilityâ. en. In: Langmuir 31.36(Sept. 2015), pp. 10100â10111. doi: 10.1021/acs.langmuir.5b02447. url: https://pubs.acs.org/doi/10.1021/acs.langmuir.5b02447 (visited on 10/01/2025).[29] Alireza Bordbar et al. âMaximum Spreading and Rebound of a Droplet Impactingonto a Spherical Surface at Low Weber Numbersâ. en. In: Langmuir 34.1762(May 2018), pp. 5149â5158. doi: 10.1021/acs.langmuir.8b00625. url: https://pubs.acs.org/doi/10.1021/acs.langmuir.8b00625 (visited on 10/01/2025).[30] Que Kong et al. âThe surface morphology and dynamic impact properties withrebounding and splashing of water droplet on phase separation and breathfigure assisted electrospinning filmsâ. en. In: Designed Monomers and Polymers24.1 (Jan. 2021), pp. 164â174. doi: 10 .1080/15685551.2021.1930670. url:https://www.tandfonline.com/doi/full/10.1080/15685551.2021.1930670 (visitedon 10/01/2025).[31] Tongwei Zhang, Jie Wu, and Xingjian Lin. âScaling laws for the droplet re-bound with lateral motion after impacting on heterogeneous surfacesâ. en. In:International Journal of Multiphase Flow 148 (Mar. 2022), p. 103960. doi:10.1016/j.ijmultiphaseflow.2021.103960. url: https://linkinghub.elsevier.com/retrieve/pii/S0301932221003566 (visited on 10/01/2025).[32] Laura Campo-Deaño and Christian Clasen. âThe slow retraction method (SRM)for the determination of ultra-short relaxation times in capillary breakup ex-tensional rheometry experimentsâ. en. In: Journal of Non-Newtonian Fluid Me-chanics 165.23-24 (Dec. 2010), pp. 1688â1699. doi: 10.1016/j.jnnfm.2010.09.007.url: https://linkinghub.elsevier.com/retrieve/pii/S0377025710002508 (visitedon 10/01/2025).[33] Jelena Dinic et al. âExtensional Relaxation Times of Dilute, Aqueous PolymerSolutionsâ. en. In: ACS Macro Letters 4.7 (July 2015), pp. 804â808. doi: 10.1021/acsmacrolett.5b00393. url: https://pubs.acs.org/doi/10.1021/acsmacrolett.5b00393 (visited on 10/01/2025).[34] Patrícia C. Sousa et al. âMeasurement of relaxation times in extensional flow ofweakly viscoelastic polymer solutionsâ. en. In: Rheologica Acta 56.1 (Jan. 2017),pp. 11â20. doi: 10.1007/s00397-016-0980-1. url: http://link.springer.com/10.1007/s00397-016-0980-1 (visited on 10/01/2025).63[35] Leidy Nallely Jimenez et al. âExtensional Relaxation Time, Pinch-Off Dynam-ics, and Printability of Semidilute Polyelectrolyte Solutionsâ. en. In: Macro-molecules 51.14 (July 2018), pp. 5191â5208. doi: 10.1021/acs.macromol.8b00148.url: https://pubs.acs.org/doi/10.1021/acs.macromol.8b00148 (visited on10/01/2025).[36] Christopher J.S. Petrie. âExtensional viscosity: A critical discussionâ. en. In:Journal of Non-Newtonian Fluid Mechanics 137.1-3 (Aug. 2006), pp. 15â23. doi:10.1016/j.jnnfm.2006.01.011. url: https://linkinghub.elsevier.com/retrieve/pii/S0377025706000371 (visited on 10/01/2025).[37] A.S. Lubansky et al. âAn approximate solution to flow through a contraction forhigh Trouton ratio fluidsâ. en. In: Journal of Non-Newtonian Fluid Mechanics144.2-3 (July 2007), pp. 87â97. doi: 10 . 1016 / j . jnnfm . 2007 . 04 . 002. url:https://linkinghub.elsevier.com/retrieve/pii/S0377025707000845 (visited on10/01/2025).[38] Minghuan Xu et al. âInfluence of p H, salt ions, and binary mixtures of differentmolecular weights on the extensional rheology of polyethylene oxideâ. en. In:Journal of Rheology 66.5 (Sept. 2022), pp. 881â893. doi: 10.1122/8.0000467.url: https://pubs.aip.org/jor/article/66/5/881/2846194/Influence-of-pH-salt-ions-and-binary-mixtures-of (visited on 09/16/2025).[39] Randy L. Vander Wal, Gordon M. Berger, and Steven D. Mozes. âThe splash/non-splash boundary upon a dry surface and thin fluid filmâ. en. In: Experiments inFluids 40.1 (Jan. 2006). Publisher: Springer Science and Business Media LLC,pp. 53â59. doi: 10.1007/s00348-005-0045-1. url: http://link.springer.com/10.1007/s00348-005-0045-1 (visited on 07/18/2025).[40] Ruobing Wang et al. âImpacts of polymer/surfactant interactions on spray driftâ.en. In: Colloids and Surfaces A: Physicochemical and Engineering Aspects 500(July 2016). Publisher: Elsevier BV, pp. 88â97. doi: 10.1016/j.colsurfa.2016.6403.056. url: https://linkinghub.elsevier.com/retrieve/pii/S0927775716301972(visited on 07/20/2025).[41] Hassouna Bahrouni et al. âEffect of sprayer parameters and wind speed onspray retention and soil deposits of pesticides: Case of artichoke cultivarâ. en.In: Plant Protection Science 57.4 (Sept. 2021). Publisher: Czech Academy ofAgricultural Sciences, pp. 333â343. doi: 10.17221/29/2021-pps. url: http://pps.agriculturejournals.cz/doi/10.17221/29/2021-PPS.html (visited on07/20/2025).[42] M.C Butler Ellis, C.R Tuck, and P.C.H Miller. âHow surface tension of surfactantsolutions influences the characteristics of sprays produced by hydraulic nozzlesused for pesticide applicationâ. en. In: Colloids and Surfaces A: Physicochem-ical and Engineering Aspects 180.3 (May 2001), pp. 267â276. doi: 10.1016/S0927-7757(00)00776-7. url: https://linkinghub.elsevier.com/retrieve/pii/S0927775700007767 (visited on 07/29/2025).[43] Bavand Keshavarz et al. âLigament Mediated Fragmentation of ViscoelasticLiquidsâ. en. In: Physical Review Letters 117.15 (Oct. 2016), p. 154502. doi:10.1103/PhysRevLett.117.154502. url: https://link.aps.org/doi/10.1103/PhysRevLett.117.154502 (visited on 07/29/2025).[44] C. Josserand and S.T. Thoroddsen. âDrop Impact on a Solid Surfaceâ. en.In: Annual Review of Fluid Mechanics 48.1 (Jan. 2016). Publisher: AnnualReviews, pp. 365â391. doi: 10.1146/annurev-fluid-122414-034401. url: https://www.annualreviews.org/doi/10.1146/annurev-fluid-122414-034401 (visited on07/18/2025).[45] M. A. Delele et al. âPredicting the dynamic impact behaviour of spray dropletson flat plant surfacesâ. en. In: Soft Matter 12.34 (2016). Publisher: RoyalSociety of Chemistry (RSC), pp. 7195â7211. doi: 10.1039/c6sm00933f. url:https://xlink.rsc.org/?DOI=C6SM00933F (visited on 07/23/2025).65[46] Xiaoguang Zhang and Osman A. Basaran. âDynamic Surface Tension Effectsin Impact of a Drop with a Solid Surfaceâ. en. In: Journal of Colloid andInterface Science 187.1 (Mar. 1997). Publisher: Elsevier BV, pp. 166â178. doi:10.1006/jcis.1996.4668. url: https://linkinghub.elsevier.com/retrieve/pii/S0021979796946688 (visited on 07/20/2025).[47] Vance Bergeron. âDesigning intelligent fluids for controlling spray applicationsâ.en. In: Comptes Rendus. Physique 4.2 (Mar. 2003). Publisher: Cellule MathDoc/-Centre Mersenne, pp. 211â219. doi: 10.1016/s1631-0705(03)00043-4. url: https://comptes- rendus.academie- sciences.fr/physique/articles/10.1016/S1631-0705(03)00043-4/ (visited on 07/20/2025).[48] Christophe Clanet et al. âMaximal deformation of an impacting dropâ. en. In:Journal of Fluid Mechanics 517 (Sept. 2004). Publisher: Cambridge UniversityPress (CUP), pp. 199â208. doi: 10 . 1017 / s0022112004000904. url: https ://www.cambridge.org/core/product/identifier/S0022112004000904/type/journal_article (visited on 07/20/2025).[49] Mounir Aytouna et al. âImpact dynamics of surfactant laden drops: dynamicsurface tension effectsâ. en. In: Experiments in Fluids 48.1 (Jan. 2010). Publisher:Springer Science and Business Media LLC, pp. 49â57. doi: 10.1007/s00348-009-0703-9. url: http://link.springer.com/10.1007/s00348-009-0703-9 (visited on07/20/2025).[50] Lydéric Bocquet and Eric Lauga. âA smooth future?â en. In: Nature Materials10.5 (May 2011). Publisher: Springer Science and Business Media LLC, pp. 334â337. doi: 10.1038/nmat2994. url: https://www.nature.com/articles/nmat2994(visited on 07/20/2025).[51] Xu Deng et al. âLiquid Drops Impacting Superamphiphobic Coatingsâ. en. In:Langmuir 29.25 (June 2013). Publisher: American Chemical Society (ACS),66pp. 7847â7856. doi: 10.1021/la401120j. url: https://pubs.acs.org/doi/10.1021/la401120j (visited on 07/20/2025).[52] Nick Laan et al. âMaximum Diameter of Impacting Liquid Dropletsâ. en. In:Physical Review Applied 2.4 (Oct. 2014). Publisher: American Physical Society(APS). doi: 10.1103/physrevapplied.2.044018. url: https://link.aps.org/doi/10.1103/PhysRevApplied.2.044018 (visited on 07/20/2025).[53] Sungchan Yun. âReducing the Bounce Height during Truncated Spherical DropImpact on a Solid Surfaceâ. en. In: Langmuir 34.25 (June 2018). Publisher:American Chemical Society (ACS), pp. 7465â7471. doi: 10.1021/acs.langmuir.8b01355. url: https://pubs.acs.org/doi/10.1021/acs.langmuir.8b01355 (visitedon 07/20/2025).[54] Maher Damak et al. âDynamics of an impacting emulsion dropletâ. en. In:Science Advances 8.11 (Mar. 2022). Publisher: American Association for theAdvancement of Science (AAAS). doi: 10.1126/sciadv.abl7160. url: https://www.science.org/doi/10.1126/sciadv.abl7160 (visited on 07/20/2025).[55] Eunsang Lee and Florian Müller-Plathe. âEffect of Polymer on the ContactLine Friction of a Capillary Bridgeâ. en. In: Macromolecules 55.7 (Apr. 2022).Publisher: American Chemical Society (ACS), pp. 2649â2658. doi: 10.1021/acs.macromol.1c02539. url: https://pubs.acs.org/doi/10.1021/acs.macromol.1c02539 (visited on 07/20/2025).[56] Jinlong Song et al. âLarge-Area Fabrication of Droplet Pancake Bouncing Surfaceand Control of Bouncing Stateâ. en. In: ACS Nano 11.9 (Sept. 2017), pp. 9259â9267. doi: 10.1021/acsnano.7b04494. url: https://pubs.acs.org/doi/10.1021/acsnano.7b04494 (visited on 07/29/2025).[57] R.E. Gaskin, K.D. Steele, and W.A. Forster. âCharacterising plant surfacesfor spray adhesion and retentionâ. en. In: New Zealand Plant Protection 58(Aug. 2005). Publisher: New Zealand Plant Protection Society, pp. 179â183. doi:6710.30843/nzpp.2005.58.4244. url: https://nzpps.org/_journal/index.php/nzpp/article/view/4244 (visited on 07/23/2025).[58] D. R. Beacham, O. K. Matar, and R. V. Craster. âSurfactant-Enhanced RapidSpreading of Drops on Solid Surfacesâ. en. In: Langmuir 25.24 (Dec. 2009),pp. 14174â14181. doi: 10.1021/la9019469. url: https://pubs.acs.org/doi/10.1021/la9019469 (visited on 08/14/2025).[59] Hans De Ruiter et al. âInfluence of Surfactants and Plant Species on Leaf Reten-tion of Spray Solutionsâ. en. In: Weed Science 38.6 (Nov. 1990). Publisher: Cam-bridge University Press (CUP), pp. 567â572. doi: 10.1017/s004317450005150x.url: https://www.cambridge.org/core/product/identifier/S004317450005150X/type/journal_article (visited on 07/23/2025).[60] F. Dan Hess and Chester L. Foy. âInteraction of Surfactants with Plant Cuticles1â.en. In: Weed Technology 14.4 (Oct. 2000). Publisher: Cambridge University Press(CUP), pp. 807â813. doi: 10.1614/0890-037x(2000)014[0807:ioswpc]2.0.co;2.url: http://www.bioone.org/doi/abs/10.1614/0890-037X%282000%29014%5B0807%3AIOSWPC%5D2.0.CO%3B2 (visited on 07/23/2025).[61] W.A. Forster, G.N. Mercer, and W.C. Schou. âSpray droplet impaction modelsand their use within AGDISP software to predict retentionâ. en. In: New ZealandPlant Protection 65 (Jan. 2012). Publisher: New Zealand Plant Protection Society,pp. 85â92. doi: 10.30843/nzpp.2012.65.5393. url: https://nzpps.org/_journal/index.php/nzpp/article/view/5393 (visited on 07/20/2025).[62] W.A. Forster et al. âEffect of target wettability on spray droplet adhesionretention spreading and coverage artificial collectors versus plant surfacesâ.en. In: New Zealand Plant Protection 67 (Jan. 2014). Publisher: New ZealandPlant Protection Society, pp. 284â291. doi: 10.30843/nzpp.2014.67.5727. url:https://nzpps.org/_journal/index.php/nzpp/article/view/5727 (visited on07/20/2025).68[63] M Smith and V Bertola. âThe anti-rebound effect of flexible polymers onimpacting dropsâ. en. In: (2010).[64] Minghuan Xu et al. âQuantifying the effect of extensional rheology on theretention of agricultural spraysâ. en. In: Physics of Fluids 33.3 (Mar. 2021),p. 032107. doi: 10.1063/5.0038391. url: https://pubs.aip.org/pof/article/33/3/032107/1063919/Quantifying-the-effect-of-extensional-rheology-on (visited on07/29/2025).[65] Vance Bergeron et al. âControlling droplet deposition with polymer additivesâ.In: Nature 405 (2000), pp. 772â775. doi: 10.1038/35015525.[66] J. A. Odell, A. Keller, and Y. Rabin. âFlow-induced scission of isolated macro-moleculesâ. en. In: The Journal of Chemical Physics 88.6 (Mar. 1988), pp. 4022â4028. doi: 10.1063/1.453855. url: https://pubs.aip.org/jcp/article/88/6/4022/95051/Flow-induced-scission-of-isolated (visited on 07/29/2025).[67] Jeffrey A. Odell et al. âDegradation of polymer solutions in extensional flowsâ. en.In:Macromolecules 23.12 (June 1990), pp. 3092â3103. doi: 10.1021/ma00214a011.url: https : / / pubs . acs . org / doi / abs / 10 . 1021 /ma00214a011 (visited on07/29/2025).[68] Mary M. Caruso et al. âMechanically-Induced Chemical Changes in PolymericMaterialsâ. en. In: Chemical Reviews 109.11 (Nov. 2009), pp. 5755â5798. doi:10.1021/cr9001353. url: https://pubs.acs.org/doi/10.1021/cr9001353 (visitedon 07/29/2025).[69] Frédéric Bossard et al. âInfluence of dispersion procedure on rheological prop-erties of aqueous solutions of high molecular weight PEOâ. en. In: RheologicaActa 49.5 (May 2010), pp. 529â540. doi: 10.1007/s00397-009-0402-8. url:http://link.springer.com/10.1007/s00397-009-0402-8 (visited on 07/29/2025).69[70] F. E. Bailey and J. V. Koleske. âChapter 4 â Solution Properties of Poly(EthyleneOxide)â. In: Poly(ethylene oxide). F. E. Bailey and J. V. Koleske. AcademicPress, 1976, pp. 29â86.[71] Arnaldo R. DâAlmeida and Marcos L. Dias. âComparative study of shear degra-dation of carboxymethylcellulose and poly(ethylene oxide) in aqueous solutionâ.In: Polymer Degradation and Stability 56.3 (1997), pp. 331â337. doi: https://doi.org/10.1016/S0141-3910(96)00187-5.[72] Emanuele Cerruto et al. âModelling Spray Pressure Effects on Droplet SizeDistribution from Agricultural Nozzlesâ. en. In: Applied Sciences 11.19 (Oct.2021), p. 9283. doi: 10.3390/app11199283. url: https://www.mdpi.com/2076-3417/11/19/9283 (visited on 08/30/2025).[73] Madan Sapkota, Simerjeet Virk, and Glen Rains. âSpray Deposition and QualityAssessment at Varying Ground Speeds for an Agricultural Sprayer with andwithout a Rate Controllerâ. en. In: AgriEngineering 5.1 (Mar. 2023), pp. 506â519. doi: 10.3390/agriengineering5010033. url: https://www.mdpi.com/2624-7402/5/1/33 (visited on 09/01/2025).[74] Malcolm A Faers et al. âSuspension Concentrate crop protection formulation de-sign and performance for low spray volume and UAS spray applicationâ. en. In: Pest Management Science 80.2(Feb. 2024), pp. 220â234. doi: 10.1002/ps.7707. url: https://onlinelibrary.wiley.com/doi/10.1002/ps.7707 (visited on 08/28/2025).[75] Carina D. V. Martínez Narváez, Thomas Mazur, and Vivek Sharma. âDynamicsand extensional rheology of polymerâsurfactant association complexesâ. en. In:Soft Matter 17.25 (2021), pp. 6116â6126. doi: 10.1039/D1SM00335F. url:https://xlink.rsc.org/?DOI=D1SM00335F (visited on 08/28/2025).[76] Michael Gradzielski. âPolymerâsurfactant interaction for controlling the rheologi-cal properties of aqueous surfactant solutionsâ. en. In: Current Opinion in Colloid70& Interface Science 63 (Feb. 2023), p. 101662. doi: 10.1016/j.cocis.2022.101662.url: https://linkinghub.elsevier.com/retrieve/pii/S1359029422001017 (visitedon 08/28/2025).[77] Manorama Panda and Mohammad Kamil. âPolymer-Amphiphile Interactions:An Overviewâ. en. In: Eurasian Chemico-Technological Journal 19.2 (June 2017),pp. 99â113. doi: 10.18321/ectj643. url: https://ect-journal.kz/index.php/ectj/article/view/118 (visited on 08/28/2025).[78] Antoine Gaillard, Rick Sijs, and Daniel Bonn. âWhat determines the dropsize in sprays of polymer solutions?â en. In: Journal of Non-Newtonian FluidMechanics 305 (July 2022), p. 104813. doi: 10.1016/j.jnnfm.2022.104813. url:https://linkinghub.elsevier.com/retrieve/pii/S0377025722000581 (visited on08/28/2025).[79] Pascal De Sainte Claire. âDegradation of PEO in the Solid State: A TheoreticalKinetic Modelâ. en. In: Macromolecules 42.10 (May 2009), pp. 3469â3482. doi:10.1021/ma802469u. url: https://pubs.acs.org/doi/10.1021/ma802469u (visitedon 09/02/2025).[80] S.F. Laermer and P.F. Zambetti. âAlpha-Tocopherol (Vitamin E)âthe NaturalAntioxidant for Polyolefinsâ. en. In: Journal of Plastic Film & Sheeting 8.3 (July1992), pp. 228â248. doi: 10.1177/875608799200800306. url: https://journals.sagepub.com/doi/10.1177/875608799200800306 (visited on 09/02/2025).[81] C. Wolf, C. Macho, and K. Lederer. âAccelerated ageing experiments withcrosslinked and conventional ultra-high molecular weight polyethylene (UHMW-PE) stabilised with -tocopherol for total joint arthroplastyâ. en. In: Journal ofMaterials Science: Materials in Medicine 17.12 (Dec. 2006), pp. 1333â1340. doi:10.1007/s10856-006-0608-6. url: http://link.springer.com/10.1007/s10856-006-0608-6 (visited on 09/02/2025).71
Thesis/Dissertation
eng
Chemical and Biological Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Frostad, John M.
Evaluating the impact of extensional rheology on agricultural spray retention
Text