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Scaling microfluidic 3D printing for hydrogels Melnick, Ryan Andrew 2020

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Scaling Microfluidic 3D Printing for HydrogelsbyRyan Andrew MelnickBASc., Chemical Engineering, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Chemical and Biological Engineering)The University of British Columbia(Vancouver)April 2020c© Ryan Andrew Melnick, 2020The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the thesis entitled:Scaling Microfluidic 3D Printing for Hydrogelssubmitted by Ryan Andrew Melnick in partial fulfillment of the requirements for the degree ofMaster of Applied Science in Chemical and Biological Engineering.Examining Committee:Mark Martinez, Mechanical EngineeringSupervisorEmily Cranston, Chemical and Biological EngineeringSupervisory Committee MemberDana Grecov, Mechanical EngineeringSupervisory Committee MemberiiAbstractReactive multilayer flow of alginate and calcium chloride was studied for the purpose of printinghydrogel structures. Particle image velociometery was used to capture the non-monotonic ve-locity profile of our three fluid layer printing process. Showing a separation of velocity profilesbetween fluid layers. Stability was studied under various flow regimes and reagent concentra-tions, where an unstable flow consisted of non-axisymmetric waves. Stable flow was found forall studied flow regimes at 0.75% alginate and 1.00% CaCl2. Stability decreased with increasingCaCl2 or alginate concentrations. Dimensions of the printed hydrogel structures were controlledvia regulating fluid layer flow rates. Printed structures were within the range of 7.4-10.8 mmouter diameter and 4.8-9.6 mm inner diameter. Time dependency of our printing process was ex-amined by cycling between two stable flow regimes, demonstrating the hydrogel can be sculptedby flow rates alone. PMMA particles were encapsulated within an alginate hydrogel using ourcontinuous printing process, producing capsules at 1.3 cm/s but not without variation in capsulesize and position. It was uncertain whether this inconsistency is due to timing issues in ourrotating pumps or physical mechanisms preventing more uniform capsule production.iiiLay SummaryMicro scale devices utilizing a controlled deposition of fluids are used to print user designedshapes and patterns in three dimensions. This can be accomplished with a variety of materials.These microfluidic printers are often used to create 3D structures for applications in medicineand material science. Often used by these printers are hydrogels which hold attractive propertiesof biocompatibility, mechanical strength, and elasticity, making them suitable for interfacingwith organs or growing mediums. An issue with microfluidic printing devices are their lowthroughput, primarily due to fluid instability at larger flow rates. This work aims to address thisissue by forming larger scale hydrogel structures by utilizing fluid rheology and flow control ina custom printing device. This is demonstrated by controlling dimensions of the printed materialand sculpting it into capsules. Stability of the fluid flow is also analyzed to determine underwhich parameters stable printing can be achieved.ivPrefaceThis dissertation is ultimately based on the experimental apparatus in Chapter 3 designed byJ. Mackenzie and M. Martinez. The rheology data in Chapter 3, and the alginate thicknessmodel in Chapter 4 (detailed in Appendix A.1), was also contributed by J. Mackenzie. All otherunreferenced work is by the author R. Melnick.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Vascular Tissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Sculpting and Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Approach, Scaling a Micro-fluidic Printer . . . . . . . . . . . . . . . . . . . . 32 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Research Questions and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Microfluidic 3D Printers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Chemical Cross-linking, Alginate Reaction . . . . . . . . . . . . . . . . . . . 72.4 Stability in Multi-layer Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.5 Visco-plastic Lubrication (VPL) . . . . . . . . . . . . . . . . . . . . . . . . . 112.6 Sculpting and Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Measurement of the Flow Field . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Diameter Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.4 Characterization of Alginate Hydrogel . . . . . . . . . . . . . . . . . . . . . . 253.5 Spatial Temporal Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6 Stability Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.7 Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28vi4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Forming Hydrogel Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Stability Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.3 Control of Hydrogel Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . 374.4 Sculpting Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.5 Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.1 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.2 Supporting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57viiList of TablesTable 3.1 Herschel-Bulkley coefficients (K) of dilute mixtures of alginate or Carbopool(c1) with a reacting agent (c2). The L2-norm of each fitting was below 0.01 ata sample size of N ∼ 300 [1]. . . . . . . . . . . . . . . . . . . . . . . . . . 25Table 4.1 Effect of increasing total flow rate on radial position, where WT is wall thick-ness. U1/U2 = U3/U2 = 10 at 0.75% alginate and 2% CaCl2. . . . . . . . . . 40Table A.1 Inner and outer diameter measurements of ID/OD Map of 0.75% Alginateand 1.00% CaCl2 shown in Figure 4.4. . . . . . . . . . . . . . . . . . . . . 57Table A.2 Data used to calculate the standard deviation of ID and OD measurements.Data collected using 0.75% alginate and 1.00% CaCl2. Reported standarddeviation is reported as the largest STD of the Q1/QT and Q3/QT data sets. . 58viiiList of FiguresFigure 2.1 a) Three layer flow geometery, b) Encapsulation of core medium. . . . . . 6Figure 2.2 Egg box model. Calcium cations represented by circles, or ’eggs’, and algi-nate strands form a kinked network [2]. . . . . . . . . . . . . . . . . . . . 9Figure 3.1 Wall mounted experimental apparatus used to print hydrogel structures. . . 18Figure 3.2 Glass reactor consisting of three concentric fluid layers, 95 cm in length and54 cm from z = 0 to the outlet. Hydrogel diameter measured ∼ 20 cm frominlet. Diameters of layers (mm) [Q1Dia, Q2Dia, Q3Dia] = [3, 8, 12] . . . . . . 19Figure 3.3 Benchmark PIV of flow field. Feed is distilled water seeded with PSP (QT =96 mL/min). Particles tracked with SpeedSense camera (Dantec Dynamics).Black lines indicate the velocity profile at their relative position. (a) Gradientrepresents the magnitude of the fluid velocity. (b) Gradient represents theradial velocity (Ur) of the fluid. . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 3.4 Tilt is corrected in Matlab by rotation of each frame by a measured angle(α) to the vertical. Overlaid lines across the reactors edge measure the slope,from which α is calculated. . . . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.5 (a) Each pixel value is averaged across all frames of video, highlighting theinterface position. (b) The average column pixel value from image (a) isplotted. This identifies the average interface position by the resulting peaks.The highest pixel intensity of the plot correlates to the ID position, while theabsolute gradient of the plot correlates to the OD position. . . . . . . . . . 24Figure 3.6 Yield stress of alginate hydrogel solutions [1]. . . . . . . . . . . . . . . . . 26Figure 3.7 Spatial temporal diagrams of reactor at z ∼20 cm. (a) stable flow at 1%alginate, 4% CaCl2. (b) unstable flow at 1.5% alginate, 4% CaCl2. . . . . . 27Figure 3.8 (a) Radial position measured at three locations y1, y2, and y3 spanning a20 mm vertical distance. 4Y31 and 4Y21 measures the hydrogel curvatureand is used to define stability. (b) Plot of 4 Y31 and 4 Y21, providing aquantitative measure of stability for a given flow regime. . . . . . . . . . . 28Figure 3.9 Time dependant flow rates for fluid encapsulation. Each profile is definedby Hold Time (HT ), Ramp Time (RT ), Constant Time (CT ), and4. . . . . 29Figure 3.10 (a) Encapsulation flow regime produces capsules connected by alginate hy-drogel. (b) Steady state flow regime produces a hydrogel tube structure. . . 30ixFigure 4.1 PIV images of reactor fed under conditions: 0.25% alginate, 1.00% CaCl2,and QT = 132 mL/min, U1/U2 = 2.6, U3/U2 = 2.5. Black lines indicate thevelocity profile at the relative position. Gradients are normalized to the crit-ical velocity Uc = QT /piR2 (a) Gradient represents the magnitude of the fluidvelocity. (b) Gradient represents the radial velocity (Ur) of the fluid. . . . . 33Figure 4.2 Coil of water filled alginate hydrogel tube. . . . . . . . . . . . . . . . . . . 33Figure 4.3 Stability maps of extrusion printing, QT = 150 mL/min. Hydrogel curvatureexceeding 1 mm over a 20 mm vertical distance is marked unstable. (a) 1.0%Alg, 2.0% CaCl2, (b) 1.0% Alg, 4.0% CaCl2, (c) 1.5% Alg, 2.0% CaCl2, (d)1.5% Alg, 4.0% CaCl2. Complete stability was obtained under 0.75% Algand 4% CaCl2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.4 Alginate hydrogel dimensions for 0.75% alginate, 1.00% CaCl2, and QT =150 ml/min. Each data point represents one trial where the outer diameter(a), inner diameter (b), and wall thickness (c) are all measured. (d) is pre-dicted wall thickness assuming fully developed one dimensional flow, for-mulated by Mackenzie [1], ∆P/L indicates normalized pressure drop. Gra-dients of these figures are normalized to the inner diameter of the reactor DP= 12 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 4.5 Time dependant sculpting of the outer hydrogel surface of two cases. CaseI where flow rates [Q1/QT , Q3/QT ] are toggled between [0.2, 0.5] and [0.2,0.3] with RU = RD = 5sec. And Case II, where flow rates [Q1/QT , Q3/QT ]are toggled between [0.3, 0.4] and [0.3, 0.6] with RU = RD = 4sec. A con-stant total flow rate of 150 mL/min was used, matching the measurements inFigure 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.6 Time dependant sculpting between the two flow regimes shown in Figure4.5 with constant total flux of QT = 150 ml/min. (a) Case I: A long cycletime between [Q1/QT , Q3/QT ] = (0.2, 0.3)→ (0.2, 0.5). (b) Case II: A shortcycle time between [Q1/QT , Q3/QT ] = (0.3, 0.4)→ (0.3, 0.6). . . . . . . . 41Figure 4.7 (a) Capsules of encapsulated 0.1% xanthan gum. (b) Optical coherence to-mography image of encapsulated 0.1% xanthan gum containing 0.0004%PMMA particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 4.8 (a) Spatial temporal diagram of 1% alginate, 0.3% xanthan, 1% CaCl2. (b)Intensity plot of capsule position from the top spatial temporal diagram, plotlines taken from position z = 17.0 cm and z = 24.3 cm. . . . . . . . . . . . 44Figure A.1 Schematic of the theoretical approach. The inlet flux for each layer is definedas Q1, Q2, Q3 and the dimensions of the printed body are defined as h1, h2, h3. 57Figure A.2 Stability measurements (largest 4Y31) of each data point comprising a Sta-bility Map. Some points were clearly stable, these 4 Y31 are omitted. (a)1.0% Alginate, 2.0% CaCl2, (b) 1.0% Alginate, 4.0% CaCl2, (c) 1.5% Algi-nate, 2.0% CaCl2, (d) 1.5% Alginate, 4.0% CaCl2. . . . . . . . . . . . . . 59xFigure A.3 Stability plots examples. Each measures curvature of the hydrogels outerdiameter (∆Y), a flat plot represents stable flow. (a) [U1/U2, U3/U2] = (10, 1),1.00% Alginate, 4.00% CaCl2, (b) [U1/U2, U3/U2] = (10, 5), 1.50% Alginate,2.00% CaCl2, (c) [U1/U2, U3/U2] = (15, 1), 1.00% Alginate, 2.00% CaCl2,(d) [U1/U2, U3/U2] = (15, 5), 1.50% Alginate, 4.00% CaCl2. . . . . . . . . 60xiAcknowledgmentsI would like to thank my supervisors Mark Martinez and Jordan Mackenzie for all of their guid-ance and assistance. Their patience is greatly appreciated. And to all my friends at the Pulp andPaper Centre.RYAN A. MELNICKThe University of British ColumbiaApril 2020xiiChapter 1IntroductionMicrofluidic 3D printing devices consist of slow, multilayered, flow where a viscous fluid is de-posited onto a surface. This deposit is used to build structures layer by layer, accomplishing ahigh degree of spatial resolution. These devices have been studied for small scale applicationsin tissue engineering, bioprinting, and cell encapsulation [3]. Producing large structures suchas arteries, skin tissue, or internal organs is slow due to the rate of material deposition, present-ing challenges if these processes are to be made into larger scale production. A commerciallysuccessful bio-printing process would need to be scalable in order to meet the large demand fororgan transplantation [4].1.1 Vascular TissuesA popular structure to fabricate using bioprinting techniques are vascular tissues, possibly be-cause they are structurally simple compared to other organs, but also because there is a largedemand for vascular transplants. In the US 500,000 vascular grafts are used for bypass surgeryeach year [5]. These are used to treat diseases such as atherosclerosis or coronary artery occlu-sion. The use of synthetic or tissue engineered grafts can be appealing here because autologousgrafts can have limited availability, require additional surgery, and have a 30% 10-yr failure rate[5]. Current engineered tissues have been found suitable for larger arteries (> 6 mm) such as the1thoracic aorta, abdominal aorta, and iliac artery [5]. If synthetic or tissue engineered grafts be-come increasingly viable, production of these tissues is critical to meet demand and lower costs.Developing a scalable process to bioprint vascular tissues could have a wide spread impact onthe availability of vascular surgeries.Current alternatives to 3D printing vascular tissues are free form assembly techniques. Exam-ples include growing cell sheets and wrapping them around a mandrel [6]. A felt manufacturingmethod, where a dual cylinder chamber system allows tubing material to be set and freeze driedin a tubular scaffold [7]. And electro spinning, which produces thread that is spun around a tubemandrel [8, 9]. However, these require careful and manual manipulation, presenting challengeswhen moving to mass production. Making 3D printing more appealing.1.2 Sculpting and EncapsulationThe physical properties of fibres and microfibres can be manipulated by sculpting its cross sec-tional area. Affecting material properties such as packing density, adherence, coefficient of fric-tion, rigidity, and wicking [10]. Sculpting is normally accomplished by using a dye or channelgeometry that forms the cross section. In the case of non-Newtonian fluids, sculpting has beenaccomplished using flow control and utilizing a fluids’ yield stress. A sufficiently large stress isapplied to the fluid interface to yield the material. Lowering the stress causes the fluid to returnto a plug flow state. This freezes the deformation interface into the fluids outer surface. Precisecontrol of flow rates and channel geometery can be used to sculpt uniquely desired shapes. Ap-plications of sculpted fibres include filtration and tissue engineering [11, 12]. Sculpting has evenbeen applied to large scale non Newtonian fluids, such as the transport of oil in pipelines [13].These methods are used for precise control of droplet formation, as the application of small scaledroplets’ offer compartments for working with single cells or micro dose environments [14]. Todemonstrate sculpting using our printer, we will form patterns within the hydrogel material aswell as encapsulate the core fluid.2Cell encapsulation is an attractive application of microfluidic printing that requires the carefulformation of a membrane. Cells are encapsulated within a semi permeable membrane that isimplanted into a host. The purpose is to treat diseases based on stem cells’ ability to producetherapeutic proteins or restore tissue function [15]. Embedding the cells within a semi perme-able and biocompatible membrane serves to protect them from the hosts’ immune system andother environmental conditions [16]. Clinical applications using encapsulated embryonic stemcells have been performed with various capsule materials, including alginate [17–24]. Currenttechniques in printing these capsules often require additional steps or slow production rates [3].In addition, current challenges are designing capsules with tailored permeability for differentcell types and application, maintaining capsule mechanical integrity, and minimizing the hostimmune response [25].There exists a need to manufacture encapsulated cells for clinical research at uniform shape andsize, at high through put, and with high reproducibility [26]. Current manufacturing methodsencase cells in a solid hydrogel bead using spray drying, spray cooling, extrusion, fluidized bed,coacervation, or emulsification. These methods can involve conditions that damage cells, such ashigh pressure, high temperature, or organic solvents [27, 28]. Solid cores can also result in a lackof control in positioning cells within the microbead. Cells aggregating to the surface of the beadcan result in a host immune response leading to inadequate immune protection [29, 30]. Liquidcores have the potential to create a micro environment that can be tailored to resemble phys-iological conditions that would support cell proliferation while maintaining a protective shell.Micro fluidic printing of liquid cores structures has previously been demonstrated [31], using achemical reaction to form the alginate hydrogel shell.1.3 Approach, Scaling a Micro-fluidic PrinterCurrent microfluidic 3D printers rely on creeping flow, the result of weak advective forces andlarge viscous forces. This slow stable flow of fluid allows for material layers to be deposited3with precision at small scale. In this work, we attempt to scale up this printing method to higherflow rates that will allow for larger structures and higher production rates. The challenge is thatflow becomes increasingly unstable as a result of increasing inertial forces. We attempt to usevisco-elastic and yield stress fluid properties to stabilize this flow. Alginic acid will be reactedwith a calcium chloride solution in a multilayered flow to produce a hydrogel structure. We willcharacterize stability so that we can understand the conditions and mechanisms which facilitatestable flow. This provides a boundary in which we can effectively use this printing method.Then we will demonstrate control using process inputs to set dimensions of the hydrogel as wellas sculpting it using time dependant flow rates. Lastly, we will encapsulate seeded particles todemonstrate how this printing technique can be used in capsule production.4Chapter 2Background2.1 Research Questions and ObjectivesMicro-fluidc 3D printing methods [32–36] have many advantages over free form methods [37–43] that include ease of use, rapid prototyping, and a high control of spatial dimensions [32].Attempts to scale up these methods for increased production has been largely unaddressed. Thiswork presents a technique for a higher production extrusion printer, using hydrogel. A three lay-ered channel flow fed by aqueous alginate and calcium chloride solutions are used to form twostructures (Figure 2.1). A continuous hollow tube and capsules. Dimensions are controlled viathe flow rates of each segregated fluid layer. Chemical reaction occurs at the fluid-fluid interfacesbetween fluids, gelating the middle layer of alginate. This process can be used to encapsulate,entrapping a seeded viscous core fluid in a continuous process. We aim to answer a few keyquestions. What are the processing bounds for this printer, meaning under what flow rates andreagent concentrations do we achieve stable production. Can we achieve precise control overthe end product dimensions. And can we encapsulate a seeded core fluid, producing uniformcapsules.5(b)Figure 2.1: a) Three layer flow geometery, b) Encapsulation of core medium.2.2 Microfluidic 3D PrintersAdditive manufacturing (3D printing) techniques deposits material onto a 2D surface while ei-ther a depositing needle, or platform, moves to draw each cross section of a structure. Tra-ditional 3D printing use metals, plastics, or polymers as printing materials where as bioprint-ing use living cells or biocompatible agents. Common bioprinting technologies include inkjet,micro-extrusion, and laser assisted printing. Features differentiating these methods are spacialresolution, cell viability, and allowable printing materials [44]. The work of this paper focuseson micro-extrusion, which dispenses controlled volumes of liquid in a continuous fashion by aprinting head. Micro-extrusion processes rely on viscous fluids to deposit material for accuracy,this unfortunately results in a high shear stress at the nozzle which can harm or kill cells. Becauseof this a lower cell viability is attributed to an increase in extrusion pressure [45]. The extrusionitself is normally pneumatic or mechanical, such as a piston or screw. And the resolution caneasily be changed by swapping nozzle sizes.Shim et al [46] used a multi nozzle system to bioprint dual cell-laden structures resembling os-teochondral tissue. Osteoblasts and chondrocytes retained their initial position in the scaffoldand proliferated up to 7 days after being dispensed. Cells suspensions were dosed using bothalginate hydrogel and polycaprolactone in combination to improve mechanical strength. Zhang6et al [47] using a coaxial nozzle configuration was able to print semi permeable vessel like mi-cro channels, which possess the mechanical integrity to support fluid transport. The hydrogelwas extruded via an inner tube surrounded by an outer cross linking fluid that reacts, creating ahollow filament. Cartilage progenitor cells encapsulated within this hydrogel maintained a cellviability of 95.1% 7 days after fabrication. The direct fabrication method of extrusion eliminatesadditional post processing but is limited to certain materials because of its fast gelation require-ment [48].Hydrodynamic focusing, or flow focusing, is when two laminar fluids of different flow rates runparallel in the same direction. The sheath (surrounding) fluid flows faster than the core fluidcausing its cross section to narrow due to extensional stresses imposed by the sheath fluid. Di-ameter of this core stream is dictated by the core fluids’ rheology and the flow rate ratio of thetwo streams. Using this technique gives control of the resolution of the printer head, opposed toa single fluid within a wall interface. Microfluidic pumps able to dictate the flow ratio in timeallows a single printing head to print with a range of resolutions. Reducing the need or frequencyin which a different size printer head needs to be used for a given structure. Flow focusing canalso be used to control the nano structure of the depositing material. As the sheath fluid acceler-ates and narrows the core fluid, any nano fibres or polymer begin to align parallel to the directionof flow. Karl et al. demonstrated the use of flow focusing to hydrodynamically align cellulosenano fibrils (CNF) [49]. Mechanical properties of the resulting filaments were proportional tothe alignment of CNF, with higher alignment providing greater tensile strength. Flow focusinghas the potential to control the nano structure of polymers and filaments through the use of flowrate ratio of the sheath and core fluids.2.3 Chemical Cross-linking, Alginate ReactionThe reaction considered in this work is that between a linear polysaccharide known as algi-nate and calcium chloride. Alginate is a polymer extracted from brown seaweed that has foundbiomedical uses due to its favourable properties of biocomptability. In addition, the mechanical7properties of the product of reaction contributes to stabilizing our printing process, which willbe later addressed. The calcium ions in solution react with alginate to form a viscoelastic hydro-gel, as in Equation 2.1. The alginate hydrogel forms a hydrophilic network of polymer chainsthat creates a scaffold that is able to support cellular growth. Providing void space for an extracellular matrix to develop and a free supply of nutrients. These hydrogels have been used inapplications of wound dressings and drug delivery mechanisms because of their permeability,elasticity, and mechanical strength [50, 51].2n(−RCOOH)+CaCl2→ n(−RCO−Ca−OCR−)gel +2nHCl (2.1)With a solution of alginate in the presence of calcium, the cation is capable of bonding withthe carboxyl groups located in either of the two monosaccharides that comprise alginate, α-L-guluronic acid and β -D-mannuronic acid. As each calcium is able to form an ionic bondto multiple carboxyl groups, a cross linked network is formed. The egg box model is used todescribe this network, where ions are packed into a surrounding network of buckled chains,shown in Figure 2.2 as a two dimensional structure. A three dimensional configuration formssheets with similar ion free tails. In the case of alginate, the sequence of the two monosaccharidesthat comprise alginate dictate which elements form the egg box and which are the free tails. Theegg box applies to other charged polysaccharides as well, such as gellan gum and κ-carrageanan.Once a bridge is formed between a cation and an alginate strand, the polysaccharide readilyaligns to form a dimer structure that will accept subsequent cations. This structure doesn’tnecessarily represent the most stable configuration, but the high activation energy of reopening,or separating polymer chains, traps the ions in place. The strength of the hydrogel material isdetermined by the density distribution across fibres. Or the packing of ions (or ’eggs’) withinthe chain network. The mechanical strength of the final product of this reaction is influenced byalginates’ molecular weight, concentration ratio of alginate vs calcium, and any non gelling ions[52].8Figure 2.2: Egg box model. Calcium cations represented by circles, or ’eggs’, and alginatestrands form a kinked network [2].The alginate-calcium reaction is fast and diffusion limited [53]. This is important for a highthroughput printer that needs to establish mechanical integrity of the depositing material, at leastenough to support its own weight before any post processing steps. In the case of forming sphereand tube structures, the calcium ions contact alginate at an interface. This creates a movinggel front as the cross linking ions propagates throughout the polymer layer until fully reacted.The time extent of reaction therefore depends on the calcium’s diffusive properties. The rateof diffusion decreases with higher viscosity and lower calcium concentration [52, 53]. Basedon this work and provided the thickness of our alginate layer of 2 mm, a complete reaction isexpected to occur on the order minutes.2.4 Stability in Multi-layer FlowTo achieve stable multilayered flow between miscible fluids, micro fluidic printers establish aslow viscous flow inside a narrow tube or channel [54]. The resulting low Reynolds num-ber means viscous stresses dominate over advective inertial forces [55]. This maintains thereversibility of the flow as there is no or little dissipation of fluid, keeping fluid layers stratified.High inertial forces are strong enough to cause interfacial instabilities in multilayered flows, re-sulting in mixing [56, 57]. This presents a challenge in 3D printers that utilize fluids. The multilayered flow of immiscible Newtonian fluids has been well studied at a range of Reynolds num-bers due to its application in the transport of oil [56]. However, less is known about the misciblecounter part in regard to what the fluid properties and flow rates support a stable stratified flow.9Fluid properties, such as viscosity or density, can also trigger instabilities if they exist in sharpgradients at the interface. This can occur even at low Reynolds flow [58]. In the Stokes regime,Talon and Meiburg demonstrate that for miscible flows with viscosity stratification, instabilitiesdevelop as a result of diffusive effects. Ern et al. [59] reports similar results studying the sta-bility of Couette flows with large viscosity differences. As fluid properties vary between layers,stability criteria becomes more complex. The effect of chemical reaction is important to ourstudy as fluid rheology is coupled with the reaction between CaCl2 and alginate, but also be-cause extrusion based printers rely on chemical cross-linking. Stability of low inertia parallelreactive flows have been experimentally studied by Burghelea and Frigaard [60] where workingfluids consisted of Carbopol (ph ∼3) and NaOH (pH ∼11) solutions of similar viscosity. Theneutralizing reaction between these fluids causes a viscosity change in the Carbopol solution atthe interface, which developed hydrodynamic instability resulting in mixing of the two fluids.Instability was attributed to a strong vorticity near the interface that supplies unreacted fluid andcauses further mixing. Complexity of the results in this study made it difficult to attribute a clearrelationship between channel geometry and flow speed, to stability.Prior work on stability of high Reynolds, multilayered, flows show a non trivial dependence onfluid viscosities. Selvam et al [55] finds fluid viscosity differences result in a critical viscosityratio. Below this ratio the flow is stable, for ratios above this critical viscosity ratio the flowis unstable provided the flow exceeds some critical Reynolds number. In addition to viscosity,the fluids’ orientation plays a role in stability. Interface stability was dependant on whether theviscous fluid occupies the core or sheath fluid in the case of two fluid flows. A viscous coreis found to be stable at larger Reynolds numbers compared to when it occupies the lubricatinglayer [55]. Selvam et al. also observes a non monotonic effect of diffusion at high Reynolds flowof viscosity stratified flows by varying the Peclet and Schmidt numbers. Suggesting that someoptimal level of diffusion exists to support stable flow, similar to that of viscosity. In addition,Selvam et al studies how the thickness of the fluid-fluid interface contributes to stability. In the10case of miscible core annular flows such as in extrusion printing, instability is observed at thin-ner interface thickness’s. With regard to density, differences among layers in horizontal flowscan be destabilizing with a lighter fluid on the bottom. However in vertical flows the effects ofdensity differences on stability are less clear [61]. The orientation of our reactor is positionedvertically with gravity, parallel to streamlines, minimizing stresses on the interface due to densitydifferences. The working fluids used in this study are also of similar density values, thus densityeffects in our case are considered negligible.Numerical simulations by Mackenzie [1] examine the stability of larger Re number flows onmultilayered fluids. Accomplished by simulating the effects of yields stress, viscosity ratio, andreaction rate by the effect of Reynolds, Bingham, Peclet, and Damkolher dimensionless num-bers. Stabilizing effects of viscosity ratio is attributed to a drop in the local Reynolds number(Re∼10) at the fluid-fluid interface. Increasing Re → 3500 is unstable even at large viscosityratios. Introduction of a yield stress under the same conditions stabilizes multi-layered flow witha Bn = 2200, corresponding to a yield stress of 200 Pa. Yield stress alone is unable to removalsome small inter-facial perturbations but demonstrates a positive effect toward stable flow. Sim-ulations of chemical reaction feature two equal viscosity fluids which produce a viscous gellayer, with viscosity that varies linearly with composition. This represents the extrusion based3D printing method as it relies on fast chemical reaction to form a depositing material, in ourcase a viso-elastic hydrogel. Under inertia, a slow reaction rate relative to advection results inunstable flow. Increasing the reaction (Da ≈ 104) a stable flow is obtained from the formation ofa gel layer that reduces the local Re number. Demonstrating that the reaction must be quick toallow sufficient time for a gel layer to develop.2.5 Visco-plastic Lubrication (VPL)Frigaard et al. [62] has demonstrated that stable high Reynolds core annular flows can beachieved by surrounding the core fluid with a yield stress fluid, referred to as VPL. A yieldstress causes a fluid to have two distinct flow regimes, when shear stress remains below the11yield stress the fluid follows a plug flow or rigid body motion. Second, if shear stresses becomegreater than the yield stress then it deforms non-linearly as a viscous fluid. An unyielded fluid ata liquid interface creates a plug that is able to prevent the growth of interfacial instabilities, pro-vided the interface stresses remain less the yield stress. An unyielding plug is able to resist sheardeformation and resist perturbations that would otherwise result in mixing. However, destabi-lizing affects can still be observed once the core flow becomes sufficiently large. A stable flowtransitions into wave like amplitudes that become frozen into the interface of the unyielded plugregion of the lubricating fluid. These waves translate along the pipe flow with constant shape.Increasing the core flow further breaks the plug regions surrounding the core and mixing occurs.Numerical studies introducing axis symmetric perturbations find that disturbances deforming orbreaking the plug flow remains localized at the interface [63]. The initial disturbance of a stableflow results in a rapid decay of the waveform as the unyielded plug reforms, even if the plug wasbroken.Entry level and start up effects of VPL flow were simulated by Frigaard et al [63]. Initial in-jection of a Newtonian fluid surrounded by a yield stress fluid results in a destabilized movingfront characterized by recirculating vortices. The front does not destabilized the flow behind it,and is simply advected from the pipe leaving stable flow. Interface radii was also studied and theresponse to pertubations at an increasing Re number. Observed was an increase in interface radiileads to a break of the unyielded interface at lower pertubations, leading to mixing of the fluids.This results indicates flow geometery plays a supporting factor in stability. As the fully devel-oped radii position of the interface can depend on many parameters that include inlet geometery,Re, and fluid rheology. Further investigation would be required to understand the magnitude thatinterface position and inlet geometery plays in stable flow using VPL.Sarmadi et al. [13, 64, 65] studied the application of VPL on the transport of heavy oils inpipelines. Lubricating layers are used to reduce pumping pressure by moving the high shearrates from the oil in pipelines to a less viscous fluid layer. The interface stability of the layers12are still susceptible to temperature and perturbations from start up, shut down, or transient flows.Sarmadi et al. used a third layer of unyielding viscoplastic fluid between the heavy oil and thelubricating fluid to address these perturbations. Examining the feasibility of these triple layerflows by varying viscosity ratios, flow ratios, eccentricity, and core radius. Critical parametersincluded the estimate of a minimal yield stress required by the unyielding fluid, which could bemet by known polymer gels at relatively low concentrations.It was discovered that as the viscosity ratio increased, the critical yield stress needed to maintaina rigid layer also increases. But this increase was small when m 1, which is already needed forreducing pressure drop in the pipeline. The purpose of using a lubricating fluid. An increase inRe leads to an increase in critical yield stress as would be expected. The inlet manifold creatingthe fluid geometry consisted of a longer core-middle wall, than the middle-outer fluid wall. Thisallowed for the unyielding fluid and lubricating fluids to develop more before interacting withthe core interface. This longer development length reduced the occurrence of non-uniformities.Compared to a more unstable flow when the core-middle fluid layers are allowed to develop morebefore interacting with the outer lubricant layer. Demonstrating a significant effect of geometryon stability of Non-Newtonian multilayer flow. Further investigation into entrance and start upeffects are desired. As the flows computed were sensitive to the manifold design. Sarmadi andFrigaard [66] further examines the stability of VPL in pipelines. Stable core annular flows areshown in regimes where they are typically unstable, without VPL. However, density differencesbetween the unyeilding fluid and the core fluid need to small. And application of three layerVPL should be restricted to moderately sized pipelines, as higher inertia can still lead towardunstable turbulent flow.Buoyancy forces acting on the core oil were balanced by generating a pressure in the lubricatinglayer. Achieved by sculpting the unyielding layer into a structure, relying on its rigid body mo-tion. Shaping of the unyielding layer was demonstrated by time dependant control of each fluidlayers’ flow rate. This type of flow control is analogous to the co-extrusion of polymers, where13multiple polymers forced through a die are shaped by channel geometry and flow rates. Thismethod of sculpting was found to work sufficiently for structures of long wavelengths, meaningslow variations in flow rates. This means the desired sawtooth pattern, for generating a radialpressure, was approximated by rounding of the corners. Forming sharp edges using flow controlwas not found to be practical.2.6 Sculpting and EncapsulationAt low Reynolds flow, the fabrication of complex shaped microfibres has often been accom-plished by utilizing microfluidic channels and relying on surface tension to minimize the interfa-cial energy between fluids, producing a uniform cross section. The difference in surface tensions,or spreading coefficient, of the working fluids dictate the formation of jet streams under thesetypes of mirco environments. Control of the spreading coefficients can be used to manipulatethese jet streams into microfibers [67]. Multiphase flows are converged into a narrow channeloften accompanied by an additional liquid template. The inert liquid template acts to form theouter boundary of the microfibre. Various shapes using surface tension, flow rate, and microchannels can be produced such as asymmetric hollow fibers and microbelts. The shape is thenset in situ by reaction such as photopolymerization. A challenge in production of shaped mi-crofibres is accurate control of multiphase flows and rheology of multiple fluids. An alternativemethod of producing microfibres uses single phase flow that relies on shaped micro channels toform the cross sectional shape [68]. These micro scale dyes or modified channels are fabricatedusing plastic or glass capillaries, directly moulding the microfibre. However, structures are notable to be sculpted in the longitudinal direction which is required for droplet formation or en-capsulation. Control of uniform droplets can be done using the same tools of micro channelsand surface tension [69]. These methods are still susceptible to instabilities and limitations existdue to complexity of devices and lack flexibility when performed with fixed channel geometries.Nelson et al. [70] uses an alternative method of using a yield stress fluid as a template to suspendmoulded immiscible droplets. Avoiding common flow instabilities. Stationary droplets can then14be manipulated or injected with additional compounds while being held in place for an indef-inite period of time. The stress ratio between the yield stress of the suspending fluid bath andthe stress that droplets exerts on the fluid bath, dictates the droplet formation. A much greateryield stress of the bath results in a continuous thread during the injection step, instead of discretedroplets.Living cells are encapsulated for the primarily use of drug delivery by local implantation. Cellscapable of secreting therapeutic proteins, are surrounded by a membrane to form a capsule thatcan be surgically implanted. Allowing for a prolonged dose of desired proteins at a targetedsite. A hydrogels’ nanoporous material allows for a rapid diffusion of small secreted proteinsand antibodies. The encapsulation also helps to isolate the entrapped cells from the hosts im-mune system. Encapsulation techniques has been demonstrated by treating diabetic animalsusing pancreatic islet [71], hormone or protein deficient diseases [72], and cancer therapy [73].Delivery rates of the therapeutic compound can be controlled by the degree of cross linking inthe hydrogel, chemical concentration, or degradation of the capsule wall [74]. The potential ofcell therapies are direct synthesis of these proteins using the already existing mechanisms in thecells.Production of capsules in excess of 300 µm are commonly fabricated by extruding a mixtureof alginate and islets from a nozzle where pulsating air, vibration, mechanical, or electrostaticpotential facilitates the break-off of individual droplets [75]. Droplets are immediately gellatedusing one of multiple methods, although commonly used are a bath of cross linking solutioncontaining Ca+2, Ba+2, or other ionic solutions. The resulting solid core hydrogel capsule willideally contain an even dispersion of islets, however current challenges include uniformly dis-tributing these cells [76]. These techniques can provide high production rates given the capsulessimplicity. A modification to the solid core capsules are liquid core capsules, which can be pre-pared in a similar fashion. A modified nozzle, or channel junction, is used to dispense a core fluidduring droplet formation [31, 77]. Forming uniform wall thickness’s, proper volumes of fluid,15and maintaining uniform shape increases the difficulty in manufacturing. Mechanical integrityof the capsule membrane becomes critical as to not puncture the capsule. The added benefit ofliquid cores, are that they can provide an additional level of control in drug delivery. By dictatingthe thickness of the surrounding capsule wall, the delivery rate can be manipulated. The liquidcomposition can also be configured independently from the membrane of the capsule, in orderto support cell proliferation.16Chapter 3Experimental Methods3.1 ApparatusOur apparatus is centered around a custom made glass reactor which takes three separate fluidlayers and merges them into a single multi layered pipe flow. Our system is wall mounted suchthat the fluid flow is oriented with gravity to reduce gravitational effects on stability (Figure 3.1).Rotating pumps (Micropump Inc.) and a syringe pump (KD Scientific) supplies all the fluid tothe reactor. Flow rates are controlled via Labview, this allows control of all our componentsthrough a single user interface. Supply tanks, pumps, and the reactor are connected by a 1/8”ID plastic tubing (Tygon S3). A collection vessel is placed under the reactor to collect all theoutflow. A movable platform, via an actuator (Zaber Technologies), supports multiple mountablecameras and a RayPower 5000 laser sheet (Dantec Dynamics). The actuator allows us precisecontrol over the vertical position of the camera and laser. The laser sheet is aimed directly at thereactor and 90 degrees to the cameras’ view. This supports a technique, later discussed, namedparticle image velocimetery (PIV).17Syringe PumpCollection VesselReactorLaser SheetActuatorRotating PumpsFigure 3.1: Wall mounted experimental apparatus used to print hydrogel structures.The reactor itself is made of a series of concentric cylinders (Figure 3.2). Two concentric pipeswithin the main body of the reactor separates fluid flow into three distinct layers. The inner twopipes extend a limited distance into the reactor and are open at the end. This opening defines theinlet condition where the three fluid layers meet. Here, the separated layers come into contactwhere a gelating reaction occurs at the fluid interfaces. The length of these pipes are long enoughto allow the flow in each layer to fully develop. The core fluid layer (Q1) and the outer fluidlayer (Q3) are both delivered to the reactor by the rotating pumps, the middle fluid layer (Q2) issupplied by the syringe pump. The solution supplied to Q2 is an aqueous alginate solution, usingmedium viscosity alginic acid sodium salt made by MP Biomedicals LLC. The collection vesseland reactor are filled with distilled water prior to running the extrusion process. Fluid suppliedto Q1 and Q3 varies but is either distilled water, an aqueous CaCl2 solution made from calciumchloride dihydrate by Sigma-Aldrich, or an aqueous xanthan gum solution. The xanthan gum isa simple grocery market grade powder made by Now Healthy Foods.18Figure 3.2: Glass reactor consisting of three concentric fluid layers, 95 cm in length and 54cm from z = 0 to the outlet. Hydrogel diameter measured ∼ 20 cm from inlet.Diameters of layers (mm) [Q1Dia, Q2Dia, Q3Dia] = [3, 8, 12]3.2 Measurement of the Flow FieldParticle image velocimetery is an optical method for flow visualization. It is used to measurefluid velocities over a spatial domain and can provide valuable insights into the governing fluidmechanics of a system. All fluid within a system is seeded with tracking particles which are smallenough that they have minimal or no affect on the surrounding fluid. Therefore, these particlesare assumed to follow the fluid streamlines. The ability for a particle to accurately follow fluidstreamlines is characterized by Stokes number (equation 3.1). Stokes number is defined as theratio of the characteristic time of a particle to the characteristic time of the flow. u is the fluidvelocity at far field, l is the characteristic dimension of an object in the flow path, and t is therelaxation time of the particle. For stokes flow the characteristic relaxation time is representedby equation 3.2, where µ is dynamic viscosity of the fluid, ρ is particle density, and d is particlediameter. For large Stokes numbers the particle trajectory is dominated by the particles inertia,19where a low Stokes number means the particles behaviour is dominated by the fluid flow.Stk =tul(3.1)t =ρd218µ(3.2)For Stk  1 particles can detach from the flow, reducing tracing accuracy, particularly whenthere is a large change in momentum. For Stk 1 the particles are accepted to follow stream-lines closely, and an accuracy error of 1% is achieved for stokes numbers less then 0.1 [78].Calculating the stokes number of our flow field at QT = 150 mL/min and assuming a characteris-tic length the same size of our seeded particles, the Stokes number is 0.414. Our PIV images arecaptured using the SpeedSense Lab 3.10 camera, 20 µm polyamid seeding particles (PSP), andincluded software, all purchased from Dantec Dynamics. All fluids supplied to the reactor areseeded with 0.026% (m/m) PSP. Tracking particles are embedded within the alginate may be ableto disrupt the packing arrangement of the egg box model and therefore influence its mechanicalproperties. However the PSP concentration to the calcium ion concentration (1.00-4.00%) is twoorders of magnitude less. We can realistically assume with PSP’s low concentration and particlesize that the hydrogel latex is not significantly affected.Tracking particles are illuminated by the laser sheet that is aimed 90 degrees to our camerasfields of view. Over a period of several seconds the SpeedSense camera picks up the movingparticles and tracks them. Software records average particle velocity and position, generating agrid of vector data that is then used to display the data, showing the flow field. Due to the lengthand required focus of the camera, the full reactor cannot be imaged by the SpeedSense cameraat once. Recording of the flow field must be done piecewise. To capture full PIV images thefollowing procedure is used. The SpeedSense camera, mounted on the movable platform, is firstpositioned facing the reactors inlet. Particle data is recorded at this position. The actuator then20lowers the camera 9.6 cm for recording of the next image. This vertical distance is less than thecameras field of view, providing approximately 14% overlap between the images. Once particlevelocity and position data is recorded at the lower position, the camera is then again loweredthe same 9.6 cm. This process is repeated several times, capturing a series of vector data whichspan the flow field of the reactor. A mask is required to be applied over the glass reactors wallsfor each data set in order to remove particle reflections. All data is exported and processed inMatlab. A final vector map is created by stitching together the series of images using a crosscorrelation function. A cross correlation measures the similarity of two images. Applied to thesection of overlap between the images, this allows us to align each image and remove the over-lap. Figure 3.3 shows the resulting PIV images our reactor, fed with distilled water in all layers.The velocity gradient is normalized to the characteristic velocity of the reactor (Equation 3.3)where R is the reactors inner radius and QT is the total flow rate.Uc =QTpiR2(3.3)The black lines represent the velocity profile at that vertical position. The Q1 flow rate in thiscase is much greater than Q2 or Q3 and is reflected in the intial profile just after the inlet. As allthree layers only contain water, the profile develops into a typical parabolic profile. Some radialvelocity is observed at the inlet due to pressure differences and inlet geometry, which quicklysubsides.21a) b)Figure 3.3: Benchmark PIV of flow field. Feed is distilled water seeded with PSP (QT =96 mL/min). Particles tracked with SpeedSense camera (Dantec Dynamics).Black lines indicate the velocity profile at their relative position. (a) Gradientrepresents the magnitude of the fluid velocity. (b) Gradient represents the radialvelocity (Ur) of the fluid.3.3 Diameter MeasurementInner diameter (ID) and outer diameter (OD) of the alginate hydrogel are measured during extru-sion using a color video camera. Direct measurement following the extrusion process is likely tointroduce error due to swelling of the hydrogel and presents challenges if the full profile of thetube is to be taken into account. Therefore, measurement using a camera and a pixel length scaleallows for a more detailed analysis. The true dimension of the hydrogel are likely to be off bya small systematic error due to any swelling or subsequent stresses on the hydrogel. This couldpossibly be taken into account by taking mechanical measurements of the hydrogel and apply-ing a correlation factor to estimate the average true dimensions. Direct measurements would benecessary for before testing any mechanical properties.22Hydrogel is illuminated via the laser sheet aimed at the center of the reactor, highlighting theinterface between the alginate and CaCl2 layers. It was tested that the laser does not need tobe exactly centred to clearly identify the interface position. The beam width is wide enoughto fully encompass the extruded material. The most important factor was light intensity to getan accurate reading. The color camera, positioned on the mount, records video for a minimum30 seconds at z = ∼20 cm from the inlet during a stable flow regime. This distance allows forimmediate entrance effects to subside. The average diameter of the tubing is calculated fromthis video sample by the following. Video is imported into Matlab for analysis and any tilt dueto camera position is first corrected. This is done by measuring the angle made by the reactors’edge to the vertical (α) and rotating each frame such that α → 0 (Figure 3.4). α is calculatedfrom the slope of a line, which is manually overlaid across the reactors’ straight edge. Followingtilt correction, the pixel values are averaged across all frames taken from the video sample. Thiscreates a single image that represents the average hydrogel position over all frames (Figure 3.5).This method requires stable video samples (minimal radial movement of the hydrogel) in orderto produce a quality image with defined interface positions. Every column of pixels in this re-sulting image has an average pixel value. Averaging each column of pixels into a single intensityvalue creates a single array that is then plotted. The higher intensity value at the interfaces pro-duces a peak in the plot, identifying the average interface position. Peaks of this plot identify theID position. The absolute gradient of the plot identifies the OD position. The length/pixel of theimage is required for scale, which is calculated knowing the reactors diameter (DP = 12 mm) andmanually selecting the DP position from the time averaged averaged frame. Performing repeatedmeasurements on samples produces an error less than the width of the pixel length taken fromthe cameras mounted position. Thus, the error associated with this method is the length scale ofa pixel, +/- 0.4 mm.23Figure 3.4: Tilt is corrected in Matlab by rotation of each frame by a measured angle (α)to the vertical. Overlaid lines across the reactors edge measure the slope, fromwhich α is calculated.a)6 4 2 0 2 4 6b)6 4 2 0 2 4 6Intensity (ID)Abs Intensity Gradient (OD)ODODIDIDFigure 3.5: (a) Each pixel value is averaged across all frames of video, highlighting the in-terface position. (b) The average column pixel value from image (a) is plotted.This identifies the average interface position by the resulting peaks. The high-est pixel intensity of the plot correlates to the ID position, while the absolutegradient of the plot correlates to the OD position.243.4 Characterization of Alginate HydrogelAqueous suspensions of medium-viscosity alginic acid sodium salt and CaCl2 constitutes ourworking fluids. Mackenzie [1] has characterized the rheology of the alginate hydrogel usinga rheometer with roughened parallel plates (AR2000, TA Instruments). Carbopool contactedwith NaOH and nano-fibrillated cellulose was also done in this work. Table 3.1 shows the yieldstress and Hershel-Bulkley coefficients of these fluids. This demonstrates the sensitivity of thehydrogels yield stress to calcium, also showing a non linear relationship to the cation. Figure 3.6shows the Hershel-Bulkley models fitted to the rheology measurements in Table 3.1. They showthe alginate yield stress increases non-monotonically with the addition of the gelating agent.Indicating the potential of an optimal ratio of our reagents for hydrogel strength. This could beattributed to the decrease in pH within the dispersion after alginate is fully reacted.Mixture c2/c1 c1 (w/w)% τy (Pa) K (Pa · sn) nCaCl2/Alginate 0 0.25 0 0.01 0.98CaCl2/Alginate 0.06 0.25 0.05 0.13 0.68CaCl2/Alginate 0.09 0.25 0.4 0.42 0.60CaCl2/Alginate 0.17 0.25 0.2 0.32 0.56Table 3.1: Herschel-Bulkley coefficients (K) of dilute mixtures of alginate or Carbopool(c1) with a reacting agent (c2). The L2-norm of each fitting was below 0.01 at asample size of N ∼ 300 [1].25Figure 3.6: Yield stress of alginate hydrogel solutions [1].3.5 Spatial Temporal PlotsSpatial temporal diagrams are used here to represent the flow regime in a single image, con-structed using a similar technique when measuring diameter. These images display the changein interface position over time and gives a better representation of a stable regime. Two spa-tial temporal diagrams representing stable and unstable regimes are shown in Figure 3.7. Thevertical axis of these plots represent the spatial dimension, in our case radius. The horizontalaxis represents time, meaning that each position on the time axis represents a single frame. Theprocess of creating the spatial temporal diagrams is explained as follows. First, video is taken at∼20 cm below the reactors inlet and is imported into Matlab for analysis. A fixed line or crosssection is chosen in the video from which each frame will be drawn (i.e. z = 15.1 cm). Thisline is used to construct the spatial diagram frame by frame. The pixels from this cross sectionis plotted as the first column of the spatial temporal diagram as t = 0. This cross section is keptconstant as the video advances to the next frame in sequence. Pixels from the new frame at thesame cross section is plotted as the next step in time (i.e. t = 0.03). Repeating this process foreach frame of video completes the diagram. Interface position can also be measured directlyfrom the spatial temporal image.26a) b)Figure 3.7: Spatial temporal diagrams of reactor at z ∼20 cm. (a) stable flow at 1% algi-nate, 4% CaCl2. (b) unstable flow at 1.5% alginate, 4% CaCl2.A second approach can be taken in constructing spatial temporal diagrams which produces aline image, converting the physical stability into a wave signal such as those demonstrated byOlce [79]. This methods allows the estimation of properties like frequency, amplitude, and wavevelocity which is used to characterise shaping of the interface. Once this can be achieved, thismethod will be used to analyse the consistency and control in sculpting the hydrogel.3.6 Stability CriteriaTo establish which conditions result in a stable flow regime, a quantitative measure of stabilityis first required. An unstable regime results in a permanent deformation of the material and pre-vents any control over sculpting of the material. Mixing instability is not a concern due to theyeild stress and elastic properties of the material, instead instability manifests itself as the occur-rence of amplitudes and wave structures. Therefore we choose to define stability as relating tothe curvature of the hydrogel during the extrusion process.Video samples are captured as previous, taken∼20 cm below the reactors inlet and imported intoMatlab for analysis. The length/pixel scale of image is determined by manually identifying thewall positions of the reactor in the first frame, which has a known diameter of 12 mm. A verticaldistance of 20 mm is then identified using the known length scale. We quantify curvature bymeasuring the outer diameter at three locations spanning this 20 mm vertical distance, labelledy1, y2, and y3 in Figure 3.8a. OD measurement is performed in the exact same method as for27Figure 3.5, by finding the peaks of the absolute gradient. The difference in OD position (4Y21and4Y31) are then calculated. These values directly quantify curvature. Plotting4Y over timeproduces a ’stability plot’ displayed in Figure 3.8b. The greater 4Y31 and 4Y21, the greater thecurvature. By comparison of video samples, their resulting stability plots, and any permanentdeformation in the final material, a threshold of 1 mm was chosen (8% of reactor’s diameter).Trials not exceeding this value means no permanent deformation/kinking was observed in thefinal product. A curvature exceeding this value over this 20 mm vertical distance is consideredunstable.a) b)Figure 3.8: (a) Radial position measured at three locations y1, y2, and y3 spanning a 20mm vertical distance. 4Y31 and 4Y21 measures the hydrogel curvature and isused to define stability. (b) Plot of 4 Y31 and 4 Y21, providing a quantitativemeasure of stability for a given flow regime.3.7 EncapsulationEncapsulation is achieved through periodic changes in flow rates, Figure 3.9 represents onecycle. The core flow (Q1) toggles on and off following the same ramp time (RT ) of that of Q2.This injects fluid from Q1 into the capsule. As Q1 turns off the ID will ideally goes to zero,28allowing the capsule to close. Q2 is further defined by the hold time (HT ), the time betweenformation of each capsule, and constant time (CT ), the duration of time which the capsule isbeing formed. The flow rate of Q2 aims to allow enough alginate to surround the core fluidsuch that the capsule is thick enough to withstand breaking. The Q3 profile is calculated topreserve a constant total flux (QT ). This process produces a line of capsules connected by analginate hydrogel string (Figure 3.10). This allows our reactor to transition from tube productionto capsules purely through control of the feed pumps.HT RT CTFigure 3.9: Time dependant flow rates for fluid encapsulation. Each profile is defined byHold Time (HT ), Ramp Time (RT ), Constant Time (CT ), and4.29Figure 3.10: (a) Encapsulation flow regime produces capsules connected by alginate hy-drogel. (b) Steady state flow regime produces a hydrogel tube structure.30Chapter 4Results and Discussion4.1 Forming Hydrogel TubesUnder stable steady state conditions, our reactor is feed with 0.25% alginate (Q2) and 1.00%CaCl2 solution (Q1 & Q3). As each fluid passes through the reactor, a cross linking reactionoccurs at the fluid-fluid interfaces at the inlet condition. Each layer is seeded with 0.026% (w/w)PSP particles such that PIV is performed, producing Figure 4.1. The higher pressure of thecore in Figure 4.1a results in an expansion of the inner diameter and a flattening of its velocityprofile. The velocity profile over the full radius of the reactor is non monotonic, characteristicof unstable flow in stratified fluids. However, a symmetric segregation is achieved indicted bythe distinct change in velocity gradients between each layer. The alginate velocity profile isflat showing plug like flow. The alginate resists shear flow, forming a parabolic profile in theouter and core layers, similar to what would be observed in typical Poiseuille flow. The reactiondevelops as calcium diffuse through Q2 from the salt solutions at both interfaces starting at theinlet condition. And as demonstrated by the quick development of the segregated velocity profilenear z/R = 0, the partially formed hydrogel layer is still capable of establishing stable stratifiedfluid layers. It is known to only be partially formed, at least for the first several length scales(z/R), as the time scale for a fully reacted layer is expected to be on the order of minutes, based31on work by Sindre et al. on the rate of alginate hydrogel formation [53].The alginate layer is still subject to elongational stresses which can be observed through a slightreduction in the thickness of the alginate layer. Figure 4.1b shows a strong radial flow at the inletoccurring at the moment of interaction between layers. This phenomenon may be a combinationof mass exchange due to osmotic pressure, as well entrance effects due to differences in fluidvelocities. These quickly subsides as the rapid reaction between CaCl2 and alginate occurs,forming a visco-plastic hydrogel that resists deformation. The hydrogel acts to dampen thetransfer of shear force across it, it’s also feasible that the transfer of body force between layers isreduced by viscous damping. It was also noticed that the cylinders of our reactor are not perfectlyconcentric. The velocity profile in the outer layer is slightly faster on the right side indicating arightward shift in the alignment of the inner cylinder. This effect could possibly impact results,although it is most likely minor. Figure 4.2 is the end product of the reaction. A hollow andelastic hydrogel tube, shown filled with water and capped at both ends. Strong enough to bemanipulated while containing fluid without tear. No punctures or leaks are discovered followinga trial with a stable regime.32a) b)Figure 4.1: PIV images of reactor fed under conditions: 0.25% alginate, 1.00% CaCl2, andQT = 132 mL/min, U1/U2 = 2.6, U3/U2 = 2.5. Black lines indicate the velocityprofile at the relative position. Gradients are normalized to the critical velocityUc = QT /piR2 (a) Gradient represents the magnitude of the fluid velocity. (b)Gradient represents the radial velocity (Ur) of the fluid.Figure 4.2: Coil of water filled alginate hydrogel tube.334.2 Stability MapsFor given alginate and CaCl2 concentrations, interfacial stability is dependant on the forces act-ing on that interface. In our case, there are two interfaces to consider. The alginate-water inter-face between layers 1 and 2 (Q12), and between fluid layers 2 and 3 (Q32). The fluid on eitherside of these two interfaces apply shear stress and inertial forces which act to destabilize the in-terface. Usually observed through deformation, mixing, or wave like perturbations. To simplifyour analysis we only consider the balance of forces on a given interface. Meaning in the caseof interface Q12, the most significant fluid layers affecting its stability are Q1 and Q2. Here, weassume the interface stability is only affected by the fluid layers directly acting on that interface.By not considering the effect which Q3 has on interface Q12 and that Q1 has on interface Q32, weare able to reduce the number of parameters to a manageable amount. We must already considerreagent concentration because of its effect on rheology, examining the effect all fluid layers in-dependently becomes an arduous task.The average shear and inertial forces acting on an interface by a single fluid layer will be pro-portional to its fluid velocity. Therefore, we consider interface stability as it relates to the fluidvelocity ratios U1/U2 and U3/U2. Starting with our conservation of mass equation (Equation 4.1),we normalize with respect to Q2. Where Ai and Ui is the cross sectional area and velocity of eachlayer. For a given choice of velocity ratios and QT we have a fully defined system. Additionally,with the choice of velocity ratio instead of flow rate ratio, we remove dependency on our reactorsgeometry.∑Qi = QT (4.1)U1A1U2A2+1+U3A3U2A2=QTQ2(4.2)From this simple model, our system is defined for a constant total flux and two flow rate ratios.34Stability maps (Figure 4.3) are constructed using these constraints, allowing us to experimen-tally determined where our system achieves stable flow at various alginate and calcium chlorideconcentrations. All flow rate parameters are calculated from Equation 4.2 with a constant totalflux QT = 150 mL/min. Stability is measured at each condition using the previously discussedmeasurement of curvature. Where if the curvature exceeds our threshold the flow is marked un-stable. Stability regions are drawn to illustrate these regimes. Areas of no data are due to thelimitations of our rotating pumps. Where flow rates become too low to be considered reliable ortoo high in that they exceed the pumps maximum flow rate.35a) b)c) d)Figure 4.3: Stability maps of extrusion printing, QT = 150 mL/min. Hydrogel curvatureexceeding 1 mm over a 20 mm vertical distance is marked unstable. (a) 1.0%Alg, 2.0% CaCl2, (b) 1.0% Alg, 4.0% CaCl2, (c) 1.5% Alg, 2.0% CaCl2, (d)1.5% Alg, 4.0% CaCl2. Complete stability was obtained under 0.75% Alg and4% CaCl2.Increasing the CaCl2 concentration from map (a) to (b) or from map (c) to (d), increases thearea of unstable flow. This is to be expected in the presence of osmotic pressure, due to the saltgradient that exists between the salt solution and alginate layer, which is comprised of mostlywater. Osmotic pressure acts on the water within the alginate layer, applying an outward radialforce. When unbalanced, this pressure would explain the unstable wave patterns at higher CaCl2concentrations. Inhomogeneity in the alginate or local gradients in the salt concentration on36the hydrogel surface leads to its deformation. This results in various wave amplitudes in thestructure as a result of the hydrogels elastic properties. If a significant flux of water were ableto move freely from the alginate layer into the salt water layer, this could possibly balance thesalt gradient reducing the osmotic pressure and stabilize the hydrogel. The flux of water movingthrough the alginate layer can reasonably be expected to follow Darcy’s Law.q =− kµ∇P (4.3)Where q is the discharge per unit area, k the intrinsic permeability of the medium, µ dynamicviscosity of the fluid, and ∇P is the pressure gradient. If osmotic pressure is the driving forceof water through the hydrogel, then the flux of water would be proportional to the porosity ofthe hydrogel. It is reasonable to expect that increasing the thickness and/or cross linking ofa hydrogel will impede the flow of water though the medium. The effect of diffusing Ca+2ions into the alginate could also affect the salt gradient. However, the rate which calcium ionsdiffusive into alginate is slow in comparison to the time scale of our reactor [53], therefore itis reasonable to assume this will not have any appreciable effect on osmotic pressure. The easeof water to flow through hydrogels have been expressed before as a friction coefficient [80],although no measure of alginate hydrogel friction coefficient was found.It is important to note that the value chosen for the stability threshold is subjective. The choiceof this threshold affects the regions seen in these maps. However, varying the threshold andobserving the effect on stability regions did not reduce its complexity or reveal any new trends.4.3 Control of Hydrogel DimensionsRadial position of the inner and outer interface of alginate tubing is dependant on each layers’flow rate Qi. As discussed earlier in Section 4.2, the quantity of interest here is flow rate (orvelocity) ratios. At constant total flux QT = 150 mL/min, radial dimensions were measured forvarious flow rate ratios under steady state conditions. ID and OD measurements were taken 2037cm below the inlet of the reactor, these data points shown in Figure 4.4 are indicated by theblack markers. A gradient is used to interpolate between these data points, the ID and OD arealso normalized to the reactors’ diameter. The diagonal of the measured data points representslines of constant Q2/QT , i.e. a constant alginate flow rate. The wall thickness figure is generatedfrom the difference in the ID and OD maps. Indicating the wall thickness is largely independentof the outer flow rate at a constant total flux. The relationship in Figure 4.4 also shows the innerdiameter weakly depends on the flow rate of the outer layer, however this is not the case with theouter diameter, suggesting that it is possible to independently sculpt the outer diameter. Repeatedmeasurements were performed to estimate error, the largest standard deviation in interface po-sition was found to be 0.4 mm. Figure 4.4 illustrates a model prediction of hydrogel thickness,details in Appendix A.1. Both the model and experimental results show a similar relationships ofwall thickness the flow rates Qi. A constant total flow rate is held in Figure 4.4 due to the effectof inertia on radial position. To demonstrate this, Table 4.1 indicates the total flow rate increasedat a constant velocity ratios of U1/U2 = 10, U3/U2 = 2.5 at 0.75% alginate and 2% CaCl2. Wediscovered that inertial forces affect the radial position and the thickness of the hydrogel. Thisdoes not indicate whether stability is affected by the interface position, but it does give reason tohold a constant total flow rate when comparing stability of different flow regimes.38a) b)c) d)Figure 4.4: Alginate hydrogel dimensions for 0.75% alginate, 1.00% CaCl2, and QT =150 ml/min. Each data point represents one trial where the outer diameter (a),inner diameter (b), and wall thickness (c) are all measured. (d) is predictedwall thickness assuming fully developed one dimensional flow, formulated byMackenzie [1], ∆P/L indicates normalized pressure drop. Gradients of thesefigures are normalized to the inner diameter of the reactor DP = 12 mm.39QT (mL/min) ID (mm) OD (mm) WT (mm)80 6.7 8.8 1.05150 7.5 9.1 0.80300 7.9 9.4 0.75Table 4.1: Effect of increasing total flow rate on radial position, where WT is wall thick-ness. U1/U2 = U3/U2 = 10 at 0.75% alginate and 2% CaCl2.4.4 Sculpting LayersUnder steady state conditions we can predict the inner and outer diameters using Figure 4.4. Butin order to sculpt the hydrogel material it is important to examine any time dependant effectsfrom changing flow rates. This was accomplished by measuring interface position while oscil-lating between two different data points on Figure 4.4 at two different time scales. This is showngraphically in Figure 4.5. As the pathway of these oscillations experience a gradient on the ODmap but not on the ID map, this suggests it is possible to sculpt the outer diameter while hold-ing the inner diameter constant. Ideally, the dimensions from our time dependant measurementsshould closely match the steady state case without time dependant effects.The red and blue lines of Figure 4.6 represent the upper and lower bounds of the steady stateOD, meaning these lines represent the data points shown in Figure 4.5. Comparing the timedependant measurement to these lines is comparing the time dependant case to the steady statecase. The cycles are consistent both in shape and in their peaks. The gradual incline seen be-tween cycles are due to the Ramp Up and Ramp Down times. As the ID of Case I and CaseII fluctuate in a range of approximately 1 mm and 0.5 mm, the ability to sculpt the interfaceindependently of the other appears difficult. However, these fluctuations may be explained bytiming errors incurred during these experiments. A small timing delay was often noticed in ourtwo rotating pumps when initiating the ramp up function, possibly explaining the cycles in theID. But given the error in diameter measurement, this is not confirmed. The inner diameter of40Case I did not return to a consistent peak as in Case II, where it has a slow gradual upward slope.Possibly indicating it needs more time to reach steady state between cycles. Interestingly, theshorter cycle time reached steady state between cycles when the longer cycle did not.Figure 4.5: Time dependant sculpting of the outer hydrogel surface of two cases. Case Iwhere flow rates [Q1/QT , Q3/QT ] are toggled between [0.2, 0.5] and [0.2, 0.3]with RU = RD = 5sec. And Case II, where flow rates [Q1/QT , Q3/QT ] aretoggled between [0.3, 0.4] and [0.3, 0.6] with RU = RD = 4sec. A constanttotal flow rate of 150 mL/min was used, matching the measurements in Figure4.4a)Case Ib)Case IIFigure 4.6: Time dependant sculpting between the two flow regimes shown in Figure 4.5with constant total flux of QT = 150 ml/min. (a) Case I: A long cycle timebetween [Q1/QT , Q3/QT ] = (0.2, 0.3)→ (0.2, 0.5). (b) Case II: A short cycletime between [Q1/QT , Q3/QT ] = (0.3, 0.4)→ (0.3, 0.6).414.5 EncapsulationAutomated control of fluid layer flow rates allow encapsulation of the core fluid resulting in astring of connected capsules. Each capsule is formed at the inlet as the core fluid injects mate-rial into a surrounding alginate layer. The core flow then tapers off to zero, and the outer flowramps up. Radial pressure from the outer fluid layer closes the inner diameter. The cross linkingreaction takes place while the inner alginate walls are in contact, provided sufficient time for thereaction to take place, sealing the capsule. This process repeats itself for each capsule. Using0.75% alginate and 1.00% CaCl2 solution in the outer layer, we successfully encapsulated 0.1%xanthan gum solution as the core fluid (Figure 4.7). The result is a continuous, uninterruptedhydrogel string connected by capsules containing xanthan. Xanthan was used to demonstrateencapsulation can be achieved without using a cross linking solution as the core fluid, relyingonly on the diffusion of calcium ions from the outer hydrogel interface. Encapsulation of wateras the core was also attempted, but was unsuccessful. The viscosity of xanthan was required sothat the core fluid could be deformed into the desired shape by exerting a high pressure from Q3.Allowing the alginate inner diameter to close while the core retained its shape. The response ofa non viscous core fluid like water, resulted in an excretion of the core fluid out of the alginatetube by the high Q3 pressure. To demonstrate that we are able of seeding cells into capsules, weencapsulated xanthum gum containing 0.0004% PMMA particles. Optical coherence tomogra-phy of the seeded capsules (Figure 4.7) shows the scattered particles underneath a solid alginatelayer.Figure 4.8 is a spatial temporal plot of the encapsulation of a xanthan solution. Each white streakis a capsule as it advects through the reactor. The horizontal spacing between each line repre-sents the distance between capsules. Thus, non uniform spacing shows inconsistent timing inthe formation of each capsule. The differences in the width of the streaks, representing the sizeof each capsule, demonstrates the differences in spatial dimensions. The slope of these streaksrepresent capsule velocity, as the horizontal axis represents time and the vertical axis represents42distance. Average capsule velocity of Figure 4.8 is determined by identifying the ∆t of eachstreak by pixel intensity over a constant ∆Z. The average capsule velocity is found to be 1.3cm/s, however this has little importance in controlling the capsules spatial dimensions.A plot of pixel intensity in Figure 4.8 is constructed from the spatial temporal image. Horizon-tal lines of pixels at z = 17.0 cm and z = 24.3 cm are plotted, creating a wave signal (Figure4.8 b). These two plots are initially out of phase due to the slope of the image, so they havebeen shifted such that the plots overlap. The image is also zoomed, showing only a few cycles,to increase clarity. Exactly overlapping peaks would indicate the capsules are frozen in placeafter formation and advects perfectly through the reactor, however we see some variance. Thechanges in wavelength and width could be reversible changes due to the pulsating flow rates orcould be due to low mechanical strength of the alginate. The standard deviation in peak positionis +/-0.99 cm and the distance between each capsule range has a range of 3.48-7.39 cm. Visu-ally, it can be seen that the capsules are inconsistent in both shape and position. This could be aresult of timing issues with our pumps or programming. Possible mechanisms that could preventconsistent capsule formation are osmotic pressure or inertia. Meaning that small local gradientsof inhomogeneity in reagent concentration could potentially have large effects on local materialproperties, such as strength or elasticity.a) b)Figure 4.7: (a) Capsules of encapsulated 0.1% xanthan gum. (b) Optical coherence tomog-raphy image of encapsulated 0.1% xanthan gum containing 0.0004% PMMAparticles.43a) b)Figure 4.8: (a) Spatial temporal diagram of 1% alginate, 0.3% xanthan, 1% CaCl2. (b)Intensity plot of capsule position from the top spatial temporal diagram, plotlines taken from position z = 17.0 cm and z = 24.3 cm.44Chapter 5Summary and ConclusionsThree layered flow at Re 1 was established using alginate and CaCl2 solutions as the workingfluids. Flow rates of each layer was used to induce different flow conditions in order to examinestability criteria. The stability behaviour was complex in relation to the reagents concentrationsand fluid layer flow rates, this is in part due to the hydrogels’ rheology being a function of reagentconcentrations. Increasing the absolute amount of either calcium or alginate was found to in-crease instability. The most significant factors are attributed to the rheology of the viscoelasticalginate hydrogel, produced from calcium ions gelating the alginic acid, is the osmotic pressureas a result of the salt gradient across fluid layers. No instability was observed at a concentrationof 0.75% alginate and 1.00% CaCl2 under our conditions. Dimensions of the hydrogel werefound to be a function of velocity ratios under a constant total flow rate and reagent concentra-tion. It was demonstrated that control of the inner and outer diameters of the hydrogel could beachieved through control of each layers flow rate. These dimensions were not independent ofinertial forces, or total flow rate, as increasing the total flow resulted in a thinning of the wallthickness. Changing between flow conditions in time showed similar results to measuring thehydrogel dimensions at steady state. Showing a low dependence on time scale when sculptingthe hydrogel using flow rates. To demonstrate the ability of sculpting, we successfully encapsu-lated PMMA particles within the core layer, surrounded by a hydrogel membrane. The product45was a string of capsules connected by a purely alginate strand. Measuring the position of eachcapsule resulted in a range in capsule position of 3.48-7.39 cm. Capsules were observed to havevariation in both shape and position. Which may be attributed to timing issues with pumps orprogramming. It is not conclusive whether there are physical mechanisms preventing consistentand uniform production of capsules.The original research question posed were, what are the processing bounds for this printer device,can precise control over spatial dimensions be obtained, and are we able to encapsulate thecore fluid forming uniform capsules? The processing bounds for this device was found to beunconditionally stable under QT = 150 mL/min, 0.75% alginate, and 1.00% CaCl2. Conditionalstability was found at increasing alginate or CaCl2 concentrations as per our stability maps.Homogeneous alginate hydrogel tubing was produced at desired dimensions using flow ratecontrol. Standard deviation in controlling tubing diameter was found to be 0.4 mm, which is3.3% of the 12 mm pipe diameter.5.1 Future WorkMeasurements of cell viability are needed to quantity the effect of shear during encapsulation,some loss is always expected due to the extrusion process alone. The speed in which capsulesare formed could be optimized between greater production and viable cell count. Further work isrequired to produce more spherical and uniform capsules as our results show. Different reactionmechanisms or mediums could be investigated to improve our results. Different cell mediums(core fluid) could have a significant effect on capsule formation such as mechanical strength,uniformity, or affect migration of the cells. As the range of our pumps did not allow for lowerflow rates (<10 mL/min), this would likely improve capsule formation and cell viability due tolower shear. Diameter measurements of hydrogel tubes were taken within the reactor so anyswelling following production was not accounted for in the final product. This relationshipwould be critical for accurate manufacturing. A greater amount of physical characterisation is46required to determine what reagent concentrations provide optimal properties such as elasticity,tensile strength, or permeability.47Bibliography[1] Jordan Mackenzie. Unknown title, 2019. Unpublished post doctorate research of J.Mackenzie at the University of British Columbia. → pages viii, ix, x, 11, 25, 26, 39[2] Gregor T. Grant, Edwin R. Morris, David A. Rees, Peter J. C. Smith, and David Thom.Biological interactions between polysaccharides and divalent cations: The egg-box model.FEBS Letters, 32(1):195–198, 1973. → pages ix, 9[3] Duo An, Alan Chiu, James A Flanders, Wei Song, Dahua Shou, Yen-Chun Lu, Lars GGrunnet, Louise Winkel, Camilla Ingvorsen, Nicolaj Strøyer Christophersen, et al.Designing a retrievable and scalable cell encapsulation device for potential treatment oftype 1 diabetes. Proceedings of the National Academy of Sciences, 115(2):E263–E272,2018. → pages 1, 3[4] Farhan Zafar, Chesney Castleberry, Muhammad S. Khan, Vivek Mehta, Roosevelt Bryant,Angela Lorts, Ivan Wilmot, John L. Jefferies, Clifford Chin, and David L.S. Morales.Pediatric heart transplant waiting list mortality in the era of ventricular assist devices. TheJournal of Heart and Lung Transplantation, 34(1):82 – 88, 2015. MINI-THEME ISSUE:LUNG TRANSPLANTATION. → page 1[5] Song Li, Debanti Sengupta, and Shu Chien. Vascular tissue engineering: from in vitro toin situ. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 6(1):61–76,2014. → pages 1, 2[6] H. Kerdjoudj, F. Boulmedais, N. Berthelemy, H. Mjahed, H. Louis, P. Schaaf, J. C.Voegel, and P. Menu. Cellularized alginate sheets for blood vessel reconstruction. SoftMatter, 7:3621–3626, 2011. → page 2[7] Jason D. Roh, Gregory N. Nelson, Matthew P. Brennan, Tamar L. Mirensky, Tai Yi,Tyrone F. Hazlett, George Tellides, Albert J. Sinusas, Jordan S. Pober, W.M. Saltzman,Themis R. Kyriakides, and Christopher K. Breuer. Small-diameter biodegradablescaffolds for functional vascular tissue engineering in the mouse model. Biomaterials,29(10):1454 – 1463, 2008. → page 2[8] Xiaohui Zhang, Xiuli Wang, Vinny Keshav, Xiaoqin Wang, Jacqueline T Johanas, Gary GLeisk, and David L Kaplan. Dynamic culture conditions to generate silk-basedtissue-engineered vascular grafts. Biomaterials, 30(19):3213–3223, 2009. → page 248[9] Yanming Wang, Haigang Shi, Jing Qiao, Ye Tian, Man Wu, Wei Zhang, Yuan Lin,Zhongwei Niu, and Yong Huang. Electrospun tubular scaffold with circumferentiallyaligned nanofibers for regulating smooth muscle cell growth. ACS applied materials andinterfaces, 6(4):2958–2962, 2014. → page 2[10] Janine K. Nunes, Chueh-Yu Wu, Hamed Amini, Keegan Owsley, Dino Di Carlo, andHoward A. Stone. Fabricating shaped microfibers with inertial microfluidics. AdvancedMaterials, 26(22):3712–3717, 2014. → page 2[11] Marcus A. Hunt, Tomonori Saito, Rebecca H. Brown, Amar S. Kumbhar, Amit K. Naskar,TN (United States) Oak Ridge National Lab. (ORNL), Oak Ridge, HighTemperature Materials Laboratory, and Center for Nanophase Materials Sciences.Patterned functional carbon fibers from polyethylene. Advanced Materials,24(18):2386–2389, 2012. → page 2[12] Edward Kang, Yoon Y. Choi, Su-Kyoung Chae, Jin-Hee Moon, Joon-Young Chang, andSang-Hoon Lee. Microfluidic spinning of flat alginate fibers with grooves forcell-aligning scaffolds. Advanced Materials, 24(31):4271–4277, 2012. → page 2[13] Parisa Sarmadi, Sarah Hormozi, and Ian A. Frigaard. Flow development and interfacesculpting in stable lubricated pipeline transport. Journal of Non-Newtonian FluidMechanics, 261:60–80, 2018. → pages 2, 12[14] A. B. Theberge, F. Courtois, Y. Schaerli, M. Fischlechner, C. Abell, F. Hollfelder, andW. T. S. Huck. Microdroplets in microfluidics: An evolving platform for discoveries inchemistry and biology. Angewandte Chemie. International Edition, 49(34):5846–5868,2010. → page 2[15] Maryam Hashemi and Fatemeh Kalalinia. Application of encapsulation technology instem cell therapy. Life Sciences, 143:139 – 146, 2015. → page 3[16] Denise Freimark, PP Pino-Grace, Sebastian Pohl, Christian Weber, Christine Wallrapp,Peter Geigle, R Portner, and Peter Czermak. Use of encapsulated stem cells to overcomethe bottleneck of cell availability for cell therapy approaches. Transfusion Medicine andHemotherapy, 37(2):66–73, 2010. → page 3[17] Y. Naaldijk, M. Staude, V. Fedorova, and A. Stolzing. Effect of different freezing ratesduring cryopreservation of rat mesenchymal stem cells using combinations ofhydroxyethyl starch and dimethylsulfoxide. BMC BIOTECHNOLOGY, 12(1):49–49,2012. → page 3[18] Wei Seong Toh, Eng Hin Lee, Xi-Min Guo, Jerry KY Chan, Chen Hua Yeow, Andre BChoo, and Tong Cao. Cartilage repair using hyaluronan hydrogel-encapsulated humanembryonic stem cell-derived chondrogenic cells. Biomaterials, 31(27):6968–6980, 2010.[19] Kiwon Ban, Hun-Jun Park, Sangsung Kim, Adinarayana Andukuri, Kyu-Won Cho,Jung Wook Hwang, Ho Jin Cha, Sang Yoon Kim, Woan-Sang Kim, Ho-Wook Jun, and49Young-Sup Yoon. Cell therapy with embryonic stem cell-derived cardiomyocytesencapsulated in injectable nanomatrix gel enhances cell engraftment and promotes cardiacrepair. ACS Nano, 8(10):10815–10825, 2014. PMID: 25210842.[20] Phan Kim Ngoc, Pham Van Phuc, Truong Hai Nhung, Duong Thanh Thuy, and NguyenThi Minh Nguyet. Improving the efficacy of type 1 diabetes therapy by transplantation ofimmunoisolated insulin-producing cells. Human cell, 24(2):86–95, 2011.[21] Laura A. Smith, Xiaohua Liu, Jiang Hu, and Peter X. Ma. The enhancement of humanembryonic stem cell osteogenic differentiation with nano-fibrous scaffolding.Biomaterials, 31(21):5526 – 5535, 2010.[22] Tim Maguire, Alexander E. Davidovich, Eric J. Wallenstein, Eric Novik, Nripen Sharma,Henrik Pedersen, Ioannis P. Androulakis, Rene Schloss, and Martin Yarmush. Control ofhepatic differentiation via cellular aggregation in an alginate microenvironment.Biotechnology and Bioengineering, 98(3):631–644, 2007.[23] Anna M.B. Heile, Christine Wallrapp, Petra M. Klinge, Amir Samii, Moustapha Kassem,Gerald Silverberg, and Thomas Brinker. Cerebral transplantation of encapsulatedmesenchymal stem cells improves cellular pathology after experimental traumatic braininjury. Neuroscience Letters, 463(3):176 – 181, 2009.[24] Nan Wang, Gary Adams, Lee Buttery, Franco H Falcone, and Snow Stolnik. Alginateencapsulation technology supports embryonic stem cells differentiation intoinsulin-producing cells. Journal of biotechnology, 144(4):304–312, 2009. → page 3[25] Hasan Uludag, Paul De Vos, and Patrick A Tresco. Technology of mammalian cellencapsulation. Advanced drug delivery reviews, 42(1-2):29–64, 2000. → page 3[26] Jean-Michel Rabanel, Xavier Banquy, Hamza Zouaoui, Mohamed Mokhtar, and PatriceHildgen. Progress technology in microencapsulation methods for cell therapy.Biotechnology progress, 25(4):946–963, 2009. → page 3[27] Stefania Mazzitelli, Lorenzo Capretto, Federico Quinci, Roberta Piva, and ClaudioNastruzzi. Preparation of cell-encapsulation devices in confined microenvironment.Advanced drug delivery reviews, 65(11-12):1533–1555, 2013. → page 3[28] Jennifer Burgain, Claire Gaiani, Michel Linder, and Joel Scher. Encapsulation ofprobiotic living cells: From laboratory scale to industrial applications. Journal of foodengineering, 104(4):467–483, 2011. → page 3[29] Duy Khiem Nguyen, Young Min Son, and Nae-Eung Lee. Hydrogel encapsulation of cellsin core–shell microcapsules for cell delivery. Advanced Healthcare Materials,4(10):1537–1544, 2015. → page 3[30] Minglin Ma, Alan Chiu, Gaurav Sahay, Joshua C. Doloff, Nimit Dholakia, Raj Thakrar,Joshua Cohen, Arturo Vegas, Delai Chen, Kaitlin M. Bratlie, Tram Dang, Roger L. York,Jennifer Hollister-Lock, Gordon C. Weir, and Daniel G. Anderson. Core–shell hydrogel50microcapsules for improved islets encapsulation. Advanced Healthcare Materials,2(5):667–672, 2013. → page 3[31] A Blaeser, DF Duarte Campos, M Kopf, M Weber, and H Fischer. Assembly ofthin-walled, cell-laden hydrogel conduits inflated with perfluorocarbon. RSC Advances,4(87):46460–46469, 2014. → pages 3, 15[32] Savas Tasoglu and Utkan Demirci. Bioprinting for stem cell research. Trends inbiotechnology, 31(1):10–19, 2013. → page 5[33] Daniel Therriault, Scott R White, and Jennifer A Lewis. Chaotic mixing inthree-dimensional microvascular networks fabricated by direct-write assembly. Naturematerials, 2(4):265, 2003.[34] Vladimir Mironov, Richard P Visconti, Vladimir Kasyanov, Gabor Forgacs, Christopher JDrake, and Roger R Markwald. Organ printing: tissue spheroids as building blocks.Biomaterials, 30(12):2164–2174, 2009.[35] James E Smay, Joseph Cesarano, and Jennifer A Lewis. Colloidal inks for directedassembly of 3-d periodic structures. Langmuir, 18(14):5429–5437, 2002.[36] Pallab Datta, Bugra Ayan, and Ibrahim T Ozbolat. Bioprinting for vascular andvascularized tissue biofabrication. Acta biomaterialia, 51:1–20, 2017. → page 5[37] Yanan Du, Majid Ghodousi, Hao Qi, Nikhil Haas, Wenqian Xiao, and AliKhademhosseini. Sequential assembly of cell-laden hydrogel constructs to engineervascular-like microchannels. Biotechnology and bioengineering, 108(7):1693–1703,2011. → page 5[38] Lindsey K Fiddes, Neta Raz, Suthan Srigunapalan, Ethan Tumarkan, Craig A Simmons,Aaron R Wheeler, and Eugenia Kumacheva. A circular cross-section pdms microfluidicssystem for replication of cardiovascular flow conditions. Biomaterials,31(13):3459–3464, 2010.[39] Yibo Ling, Jamie Rubin, Yuting Deng, Catherine Huang, Utkan Demirci, Jeffrey M Karp,and Ali Khademhosseini. A cell-laden microfluidic hydrogel. Lab on a Chip,7(6):756–762, 2007.[40] Jeffrey T Borenstein, H Terai, Kevin R King, EJ Weinberg, MR Kaazempur-Mofrad, andJP Vacanti. Microfabrication technology for vascularized tissue engineering. Biomedicalmicrodevices, 4(3):167–175, 2002.[41] Sergey S Shevkoplyas, Sean C Gifford, Tatsuro Yoshida, and Mark W Bitensky. Prototypeof an in vitro model of the microcirculation. Microvascular research, 65(2):132–136,2003.[42] Janelle R Anderson, Daniel T Chiu, Rebecca J Jackman, Oksana Cherniavskaya, J CooperMcDonald, Hongkai Wu, Sue H Whitesides, and George M Whitesides. Fabrication of51topologically complex three-dimensional microfluidic systems in pdms by rapidprototyping. Analytical chemistry, 72(14):3158–3164, 2000.[43] KR Stevens, MD Ungrin, RE Schwartz, S Ng, B Carvalho, KS Christine, RR Chaturvedi,CY Li, PW Zandstra, CS Chen, et al. Invert molding for scalable control of tissuemicroarchitecture. Nature communications, 4:1847, 2013. → page 5[44] SV Murphy and A. Atala. 3d bioprinting of tissues and organs. NATUREBIOTECHNOLOGY, 32(8):773–785, 2014. → page 6[45] Bryan A. Nerger, P-T Brun, and Celeste M. Nelson. Microextrusion printing cell-ladennetworks of type i collagen with patterned fiber alignment and geometry. Soft matter,15(28):5728–5738, 2019. → page 6[46] Jin-Hyung Shim, Jung-Seob Lee, Jong Y. Kim, and Dong-Woo Cho. Bioprinting of amechanically enhanced three-dimensional dual cell-laden construct for osteochondraltissue engineering using a multi-head tissue/organ building system. Journal ofMicromechanics and Microengineering, 22(8):85014, 2012. → page 6[47] Yahui Zhang, Yin Yu, Howard Chen, and Ibrahim T. Ozbolat. Characterization ofprintable cellular micro-fluidic channels for tissue engineering. Biofabrication,5(2):025004–025004, 2013. → page 7[48] Amer B. Dababneh and Ibrahim T. Ozbolat. Bioprinting technology: A currentstate-of-the-art review. Journal of Manufacturing Science and Engineering,136(6):61016, 2014. → page 7[49] Karl M. O. Ha˚kansson, Andreas B. Fall, Fredrik Lundell, Shun Yu, Christina Krywka,Stephan V. Roth, Gonzalo Santoro, Mathias Kvick, Lisa Prahl Wittberg, Lars Wa˚gberg,L. D. So¨derberg, Wallenberg Wood Science Center, Centra, Fiberteknologi, Skolanfo¨r kemivetenskap (CHE), FLOW Linne´ Flow Center, Skolan fo¨r teknikvetenskap (SCI),Mekanik, Fiber och polymerteknologi, and KTH. Hydrodynamic alignment and assemblyof nanofibrils resulting in strong cellulose filaments. Nature communications, 5(1):4018,2014. → page 7[50] Blessing A. Aderibigbe, Buhle Buyana, Blessing Aderibigbe, and Buhle Buyana.Alginate in wound dressings. Pharmaceutics, 10(2):42, 2018. → page 8[51] Jinchen Sun and Huaping Tan. Alginate-based biomaterials for regenerative medicineapplications. Materials (Basel, Switzerland), 6(4):1285–1309, 2013. → page 8[52] Arne Mikkelsen and Arnljot Elgsaeter. Density distribution of calcium-induced alginategels. a numerical study. Biopolymers, 36(1):17–41, 1995. → pages 8, 9[53] Sindre H Bjornoy, Stefan Mandaric, David C Bassett, Andreas KO AAslund, Seniz Ucar,Jens-Petter Andreassen, Berit L Strand, and Pawel Sikorski. Gelling kinetics and in situmineralization of alginate hydrogels: a correlative spatiotemporal characterizationtoolbox. Acta biomaterialia, 44:243–253, 2016. → pages 9, 32, 3752[54] Darryl A. Boyd, Adam R. Shields, Peter B. Howell, and Frances S. Ligler. Design andfabrication of uniquely shaped thiol–ene microfibers using a two-stage hydrodynamicfocusing design. Lab Chip, 13:3105–3110, 2013. → page 9[55] Balakrishnan Selvam, S Merk, Rama Govindarajan, and E Meiburg. Stability of misciblecore annular flows with viscosity stratification. Journal of Fluid Mechanics, 592:23–49,2007. → pages 9, 10[56] D. D. Joseph, R. Bai, K. P. Chen, and Y. Y. Renardy. Core-annular flows. Annual Reviewof Fluid Mechanics, 29(1):65–90, 1997. → page 9[57] Charles E. Hickox. Instability due to viscosity and density stratification in axisymmetricpipe flow. Physics of Fluids, 14(2):251–262, 1971. → page 9[58] L. Talon and E. Meiburg. Plane poiseuille flow of miscible layers with differentviscosities: instabilities in the stokes flow regime. Journal of Fluid Mechanics,686:484–506, 2011. → page 10[59] Patricia Ern, Francois Charru, and Paolo Luchini. Stability analysis of a shear flow withstrongly stratified viscosity. Journal of Fluid Mechanics, 496:295–312, 2003. → page 10[60] Teodor I. Burghelea and Ian A. Frigaard. Unstable parallel flows triggered by a fastchemical reaction. Journal of Non-Newtonian Fluid Mechanics, 166(9):500–514, 2011.→ page 10[61] E. Lajuenesse, J. Martain, N. Rakotomalala, D. Salin, and Y. C. Yortsos. Miscibledisplacement in a hele-shaw cell at high rates. Journal of Fluid Mechanics, 398:299–319,1999. → page 11[62] S. Hormozi, D. M. Martinez, and I. A. Frigaard. Stable core-annular flows of viscoelasticfluids using the visco-plastic lubrication technique. Journal of Non-Newtonian FluidMechanics, 166(23):1356–1368, 2011. → page 11[63] S. Hormozi, K. Wielage-Burchard, and I. A. Frigaard. Entry, start up and stability effectsin visco-plastically lubricated pipe flows. Journal of Fluid Mechanics, 673:432–467,2011. → page 12[64] Parisa Sarmadi, Sarah Hormozi, and Ian A. Frigaard. Triple-layer configuration for stablehigh-speed lubricated pipeline transport. Physical Review Fluids, 2(4), 2017. → page 12[65] Parisa Sarmadi and Ian A. Frigaard. Inertial effects in triple-layer core-annular pipelineflow. Physics of Fluids, 31(10):103102, 2019. → page 12[66] Parisa Sarmadi and Ian A. Frigaard. Stable core-annular horizontal flows in inaccessibledomains via a triple-layer configuration. Chemical Engineering Science: X, 3:100028,2019. → page 1353[67] Chang-Hyung Choi, Hyunmin Yi, Sora Hwang, David A. Weitz, and Chang-Soo Lee.Microfluidic fabrication of complex-shaped microfibers by liquid template-aidedmultiphase microflow. Lab on a chip, 11(8):1477, 2011. → page 14[68] Wei Liu, Zhengnan Xu, Lixiang Sun, Peng Guo, Changfeng Zeng, Chongqing Wang, andLixiong Zhang. Polymerization-induced phase separation fabrication: A versatilemicrofluidic technique to prepare microfibers with various cross sectional shapes andstructures. Chemical Engineering Journal, 315:25–34, 2017. → page 14[69] Thomas Cubaud and Thomas G. Mason. Capillary threads and viscous droplets in squaremicrochannels. Physics of Fluids, 20(5):053302–053302–11, 2008. → page 14[70] Arif Z. Nelson, Binu Kundukad, Wai K. Wong, Saif A. Khan, and Patrick S. Doyle.Embedded droplet printing in yield-stress fluids. Proceedings of the National Academy ofSciences of the United States of America, 117(11):5671–5679, 2020. → page 14[71] Paul de Vos, Chris G. van Hoogmoed, Jacoba van Zanten, S. Netter, Jan H. Strubbe, andHenk J. Busscher. Long-term biocompatibility, chemistry, and function ofmicroencapsulated pancreatic islets. Biomaterials, 24(2):305–312, 2003. → page 15[72] A. Al-Hendy, G. Hortelano, G. S. Tannenbaum, and P. L. Chang. Growth retardation–anunexpected outcome from growth hormone gene therapy in normal mice withmicroencapsulated myoblasts. Human gene therapy, 7(1):61, 1996. → page 15[73] Anthony Atala, Toshiaki Abe, Peter M. Black, Rona S. Carroll, Nicholas T. Seyfried,Marcelle Machluf, Ian F. Dunn, Jianhong Zhu, and Tatsuhiro Joki. Continuous release ofendostatin from microencapsulated engineered cells for tumor therapy. NatureBiotechnology, 19(1):35–39, 2001. → page 15[74] Kuen Yong Lee and David J Mooney. Alginate: properties and biomedical applications.Progress in polymer science, 37(1):106–126, 2012. → page 15[75] Ulf Pru¨sse, Luca Bilancetti, Marek Bucˇko, Branko Bugarski, Jozef Bukowski, PeterGemeiner, Dorota Lewin´ska, Verica Manojlovic, Benjamin Massart, Claudio Nastruzzi,Viktor Nedovic, Denis Poncelet, Swen Siebenhaar, Lucien Tobler, Azzurra Tosi, AlicaVikartovska´, and Klaus-Dieter Vorlop. Comparison of different technologies for alginatebeads production. Chemical Papers, 62(4):364–374, 2008. → page 15[76] Heiko Zimmermann, Stephen G. Shirley, and Ulrich Zimmermann. Alginate-basedencapsulation of cells: Past, present, and future. Current Diabetes Reports, 7(4):314–320,2007. → page 15[77] Choong Kim, Kang S. Lee, Young E. Kim, Kyu-Jung Lee, Soo H. Lee, Tae S. Kim, andJi Y. Kang. Rapid exchange of oil-phase in microencapsulation chip to enhance cellviability. Lab on a chip, 9(9):1294, 2009. → page 15[78] Cameron Tropea, Alexander L. Yarin, John F. Foss, SpringerLink ebooks Engineering,and Ebook Central. Springer handbook of experimental fluid mechanics. Springer, Berlin,2007. → page 2054[79] M. d’Olce, J Martin, N Rakotomalala, D Salin, L Talon, et al. Convective/absoluteinstability in miscible core-annular flow. part 1: Experiments. Journal of FluidMechanics, 618:305–322, 2009. → page 27[80] Masayuki Tokita and Toyoichi Tanaka. Friction coefficient of polymer networks of gels.The Journal of Chemical Physics, 95(6):4613–4619, 1991. → page 3755Appendix ASupporting MaterialsA.1 Theoretical ModelFor the theoretical work in Figure 4.4, hydrogel ID and OD position. We estimate the dimen-sions of the printed body by assuming the flow field to be one-dimensional, fully developed andunder creeping flow conditions. Under the assumption that the hydrogel layer is unyielded, theequations of motion reduce toµ1∂ 2u1∂y2=∂P∂x[u1(0) = 0, u1(h1) =Up](A.1)∂τ∂y=∂P∂x[τ(h1) =−µ1 ∂u1∂y ), τ(h1 +h2) =−µ3∂u3∂y](A.2)µ3∂ 2u3∂y2=∂P∂x[u3(h1 +h2) =Up, u3(H) = 0], (A.3)where Up is the plug velocity of the sculpted hydrogel layer. See Figure A.1, the mass balanceequations for the problem readQ1 =∫ h10u1(y)dy (A.4)Q2 = h2Up (A.5)Q3 =∫ Hh1+h2u3(y)dy. (A.6)Since Q is set experimentally, we solve the system iteratively by1. Assuming a value of the pressure gradient ∂P/∂x and interface position h1 and h3,562. Solving the system of Eqs. (A.1) – (A.3)3. Correcting the approximation for ∂P/∂x, h1 and h3, using Newton’s method, until Eqs. (A.4)– (A.6) are satisfied within a tolerance of 10−10.Figure A.1: Schematic of the theoretical approach. The inlet flux for each layer is definedas Q1, Q2, Q3 and the dimensions of the printed body are defined as h1, h2, h3.A.2 Supporting DataQ1/QT Q3/QT ID (mm) OD (mm)0.3 0.6 7.62 8.540.5 0.4 8.43 9.090.1 0.8 6.39 8.090.3 0.4 7.58 9.800.5 0.2 9.12 10.240.1 0.2 4.48 11.120.1 0.6 5.05 9.340.7 0.2 9.38 10.050.1 0.4 5.01 10.240.3 0.2 6.89 10.820.2 0.7 7.02 7.870.4 0.5 8.06 8.920.6 0.3 8.63 9.200.2 0.3 6.23 10.500.2 0.5 6.51 9.050.4 0.3 8.44 10.27Table A.1: Inner and outer diameter measurements of ID/OD Map of 0.75% Alginate and1.00% CaCl2 shown in Figure 4.4.57Q1/QT Q3/QT ID (mm) OD (mm)0.2 0.5 6.51 9.050.2 0.5 7.09 9.690.2 0.5 6.36 9.490.4 0.3 8.44 10.270.4 0.3 8.35 10.360.4 0.3 8.10 10.210.3 0.4 7.58 9.800.3 0.4 7.49 9.890.3 0.4 7.75 10.06Table A.2: Data used to calculate the standard deviation of ID and OD measurements. Datacollected using 0.75% alginate and 1.00% CaCl2. Reported standard deviationis reported as the largest STD of the Q1/QT and Q3/QT data sets.58a) b)c) d)Figure A.2: Stability measurements (largest4Y31) of each data point comprising a Stabil-ity Map. Some points were clearly stable, these 4 Y31 are omitted. (a) 1.0%Alginate, 2.0% CaCl2, (b) 1.0% Alginate, 4.0% CaCl2, (c) 1.5% Alginate,2.0% CaCl2, (d) 1.5% Alginate, 4.0% CaCl2.59a) b)c) d)Figure A.3: Stability plots examples. Each measures curvature of the hydrogels outer di-ameter (∆Y), a flat plot represents stable flow. (a) [U1/U2, U3/U2] = (10, 1),1.00% Alginate, 4.00% CaCl2, (b) [U1/U2, U3/U2] = (10, 5), 1.50% Alginate,2.00% CaCl2, (c) [U1/U2, U3/U2] = (15, 1), 1.00% Alginate, 2.00% CaCl2, (d)[U1/U2, U3/U2] = (15, 5), 1.50% Alginate, 4.00% CaCl2.60

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