@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Engineering, School of (Okanagan)"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCO"@en ; dcterms:creator "Bhattacharjee, Biddut"@en ; dcterms:issued "2012-10-02T16:01:59Z"@en, "2012"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """This thesis focuses on the symmetric and asymmetric splitting of droplets, which is a prominent fluidic operation in a digital microfluidic system (DMFS). The prerequisite part of the investigation of droplet splitting is to understand the electrowetting-on-dielectric (EWOD) based droplet actuation. This thesis demonstrates that not only the EWOD actuation is a self-feedback system - implying that the actuation force depends on the position of the droplet, but also the size of the droplet affects the magnitude of actuation force. However, a sensing mechanism is essential for complex operations, e.g. dispensing and splitting. One contribution of this thesis is a novel method of sensing the droplet position that requires connections to the two adjacent electrodes in the lower plate only. For the fabrication of prototype DMFS, a new polymeric material, cyanoethyl pullulan (CEP), is proposed as the dielectric layer resulting in a simple and low-cost fabrication of DMFS. The required voltage for droplet manipulation is drastically reduced owing to high relative permittivity of CEP. Droplet splitting is investigated both numerically and experimentally. Numerical investigation of droplet splitting in FLOW-3D®, a commercial computational fluid dynamics software, revealed that the strength of viscous forces relative to the surface tension force determines the success of splitting. For successful asymmetric splitting, performed by applying voltages of unequal magnitude to left-hand and right-hand sides of the droplet, there exists a minimum voltage for the low-voltage side that guarantees splitting. This minimum voltage increases if the aspect ratio (i.e., diameter to height) of the droplet is reduced while keeping the diameter of the droplet constant. Investigation of the asymmetric splitting with different ratios of applied voltage revealed that the ratio between the volumes of accumulated liquid on either sides increases with voltage ratio. The feasibility of asymmetric splitting as well as the effects of different ratios of applied voltages were studied in prototype DMFS. The results verify the existence of a minimum voltage for successful splitting. The ratio between the volumes of the sister droplets increases with that of the applied voltages. Moreover, the general characteristics of flow-rates and liquid accumulation were found to be similar to those in simulations."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/43314?expand=metadata"@en ; skos:note "STUDY OF DROPLET SPLITTING IN AN ELECTROWETTING BASED DIGITAL MICROFLUIDIC SYSTEM by BIDDUT BHATTACHARJEE B.Sc., Bangladesh University of Engineering & Technology, 2004 M.Sc., Bangladesh University of Engineering & Technology, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Applied Science) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) September 2012 © Biddut Bhattacharjee, 2012 ii Abstract This thesis focuses on the symmetric and asymmetric splitting of droplets, which is a prominent fluidic operation in a digital microfluidic system (DMFS). The prerequisite part of the investigation of droplet splitting is to understand the electrowetting-on-dielectric (EWOD) based droplet actuation. This thesis demonstrates that not only the EWOD actuation is a self-feedback system - implying that the actuation force depends on the position of the droplet, but also the size of the droplet affects the magnitude of actuation force. However, a sensing mechanism is essential for complex operations, e.g. dispensing and splitting. One contribution of this thesis is a novel method of sensing the droplet position that requires connections to the two adjacent electrodes in the lower plate only. For the fabrication of prototype DMFS, a new polymeric material, cyanoethyl pullulan (CEP), is proposed as the dielectric layer resulting in a simple and low-cost fabrication of DMFS. The required voltage for droplet manipulation is drastically reduced owing to high relative permittivity of CEP. Droplet splitting is investigated both numerically and experimentally. Numerical investigation of droplet splitting in FLOW-3D ® , a commercial computational fluid dynamics software, revealed that the strength of viscous forces relative to the surface tension force determines the success of splitting. For successful asymmetric splitting, performed by applying voltages of unequal magnitude to left-hand and right-hand sides of the droplet, there exists a minimum voltage for the low-voltage side that guarantees splitting. This minimum voltage increases if the aspect ratio (i.e., diameter to height) of the droplet is reduced while keeping the diameter of the droplet constant. Investigation of the asymmetric splitting with different ratios of applied voltage revealed that the ratio between the volumes of accumulated liquid on either sides increases with voltage ratio. The feasibility of asymmetric splitting as well as the effects of different ratios of applied voltages were studied in prototype DMFS. The results verify the existence of a minimum voltage for successful splitting. The ratio between the volumes of the sister droplets increases with that of the applied voltages. Moreover, the general characteristics of flow-rates and liquid accumulation were found to be similar to those in simulations. iii Preface This thesis presents the results of research conducted in the Advanced Control and Intelligent Systems (ACIS) laboratory at the Okanagan School of Engineering, UBC, under the supervision of Dr. Homayoun Najjaran. Part of the thesis has been published in peer reviewed journals and conferences. The highlights of contributions of this thesis are as follows: The simulation results of Section 1 of Chapter 2 were published in two journals ( a Bhattacharjee and Najjaran 2010, b Bhattacharjee and Najjaran 2010). The droplet dynamic system was modelled by considering the droplet as a rigid body and incorporating the empirical functions for the resistive forces. A simple controller and generic actuation and sensing mechanisms were also considered for the control of droplet position between two adjacent electrodes. Results show the relative strength of different resistive forces, transient and steady- state response in relation to controller gain and geometrical parameters. My responsibility was to investigate the modelling, computer simulation and manuscript preparation. Another contribution of this thesis is a novel method of droplet position sensing by measuring the capacitance between two coplanar electrodes. An analytical model of coplanar capacitance given by a quadratic function of the droplet position is proposed and verified by both numerical and experimental results, presented in Section 2 of Chapter 2. This new sensing method can be easily incorporated in feedback control of droplet operations from simple motion to complex splitting. Results of Section 3 of Chapter 2 were published in a conference ( c Bhattacharjee and Najjaran 2009) and my task was to analyse the EWOD-actuated droplet, develop simulation model of droplet motion, process and organize simulation results and prepare the manuscript. Under the assumption of a cylindrical conductive droplet, the EWOD-actuated droplet was demonstrated as a self-feedback system where the magnitude and direction of the generated actuation force depends on the position of the droplet with respect to the energized electrode. Moreover, the profile of actuation force also depends on the size of the droplet. Results in terms of transition time for the droplet from one electrode to the next as a function of electrode size, dielectric thickness and dielectric constant were also presented. The results of the last section of Chapter 2 were published in another conference ( d Bhattacharjee and Najjaran 2010). I was responsible for researching the material, fabricating the device and setting up instruments for measurement and writing the manuscript. The dielectric material, cyanoethyl pullulan, reported in this paper possesses high dielectric constant and can be iv deposited using a spin-coater only. Thus, digital microfluidic devices, which are fabricated using this new material, can be operated at significantly lower voltages than the values commonly reported in the literature. One of the major contributions of this thesis is the extensive study of the coupled electrohydrodynamics of symmetric and asymmetric splitting of droplets through CFD simulations ( e Bhattacharjee and Najjaran 2011). Results shown in Chapter 3 elucidate the distribution of electric field, charges, pressure and velocities during symmetric splitting. The relative strength of viscous shear with surface tension force determines the result of splitting. For a given size of the droplet, material properties and geometry, there exists a voltage level below which splitting is infeasible. Identification of the key parameters in determining the success of asymmetric splitting and the extent to which each of the parameters influence the splitting process is another major contribution of this thesis and is presented in Chapter 4. There exists a minimum required voltage for the low voltage side in asymmetric splitting for a given electrode size and aspect ratio of the droplet. The required voltage increases with increasing droplet height while the electrode size remains constant. For a given geometry and droplet aspect ratio, the ratio between the flow-rates to the right-hand and left-hand sides increases with the ratio between the applied voltages till the breakup of the neck. The final contribution of this thesis is the experimental investigation of asymmetric splitting. The results, as presented in Chapter 5, verify the characteristic pattern of exponentially decaying liquid flow-rates and capillary numbers. The ratio between the volumes of sister droplets resulting from asymmetric splitting increases with that of the applied voltages. Moreover, the volume ratio is greater for higher base voltages on the low voltage side. List of Publications Bhattacharjee B. and Najjaran H., 2012, “Droplet sensing by measuring the capacitance between coplanar electrodes in a digital microfluidic system”, Lab on a Chip (Accepted) Bhattacharjee B. and Najjaran H., 2010, “Simulation of droplet position control in digital microfluidics systems”, Journal of Dynamic System, Measurement and Control, 132, 014501. Bhattacharjee B. and Najjaran H., 2010, “Droplet position control in digital microfluidic systems”, Biomedical Microdevices, 12 ,115-124. Bhattacharjee B. and Najjaran H., 2011, “Modeling and simulation of unequal droplet splitting in electrowetting based digital microfluidics”, ASME ICNMM, Edmonton. v Bhattacharjee B. and Najjaran H., 2011, “Low-cost, low-voltage microfluidic biochip based on electrowetting actuation of droplets”, Proceedings of Microtechnologies in Medicine and Biology, Lucerne, Switzerland. Bhattacharjee B. and Najjaran H., 2010, “Effects of the properties of dielectric materials on the fabrication and operation of digital microfluidic systems”, Proceedings of ASME IMECE, Vancouver. Bhattacharjee B. and Najjaran H., 2009, “Size dependant droplet actuation in Digital Microfluidic system”, Proceedings of SPIE conference on Micro- Nanotechnology Sensors, Systems and Application, Orlando, 7318. vi Table of Contents Abstract .......................................................................................................................................... ii Preface .......................................................................................................................................... iii Table of Contents .......................................................................................................................... vi List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... ix Acknowledgements ....................................................................................................................... xv Dedication ................................................................................................................................... xvi CHAPTER 1 INTRODUCTION ..................................................................................................... 1 1.1 Motivation .......................................................................................................... 1 1.2 Objectives .......................................................................................................... 3 1.3 Literature review ................................................................................................. 4 1.3.1 Droplet actuation ...................................................................................... 4 1.3.2 DMFS design and fabrication ................................................................... 8 1.3.3 Hydrodynamics of droplet motion ......................................................... 10 1.3.4 Electromechanical fundamentals of EWOD ........................................... 11 1.3.5 Electro-hydrodynamics of digital microfluidics ..................................... 13 1.3.6 Microfluidic operations ........................................................................... 14 1.3.7 Feedback control in DMFS .................................................................... 15 1.3.8 Bioassay applications .............................................................................. 17 1.4 Thesis outline ................................................................................................... 21 CHAPTER 2 DIGITAL MICROFLUIDICS - OPERATIONS AND ENHANCEMENTS ......... 22 2.1 Droplet translocation and control ..................................................................... 22 2.1.1 Dynamics and control of droplet motion ................................................ 22 2.1.2 Detailed model of droplet dynamic system ............................................ 26 2.1.3 Simulation results and discussion .......................................................... 29 2.2 Droplet sensing ................................................................................................. 37 2.2.1 Coplanar capacitance ............................................................................. 37 2.2.2 Numerical investigation ......................................................................... 38 2.2.3 Experimental .......................................................................................... 42 2.2.3.1 Sensing electronics .................................................................... 42 2.2.3.2 Results ....................................................................................... 43 vii 2.3 EWOD droplet actuation .................................................................................. 50 2.3.1 EWOD force .......................................................................................... 50 2.3.2 Simulation results ................................................................................... 56 2.4 Investigation of the effects of dielectric material ............................................. 64 2.4.1 Materials and fabrication......................................................................... 64 2.4.2 Experimental results ............................................................................... 65 2.4.2.1 Contact angle .............................................................................. 65 2.4.2.2 Droplet actuation ....................................................................... 67 CHAPTER 3 SYMMETRIC SPLITTING: SIMULATION ........................................................ 70 3.1 Computational fluid dynamics in droplet splitting ........................................... 70 3.2 Simulation model .............................................................................................. 73 3.3 Symmetric splitting of droplets ........................................................................ 75 3.3.1 General theory ......................................................................................... 75 3.3.2 Electro-hydrodynamic response .............................................................. 77 3.3.3 Successful and unsuccessful splitting ..................................................... 81 CHAPTER 4 ASYMMETRIC SPLITTING: SIMULATION ...................................................... 89 4.1 Preliminary concepts of asymmetric splitting .................................................. 89 4.1.1 Minimum voltage ................................................................................... 90 4.1.2 Voltage ratio and aspect ratio ................................................................. 94 4.2 Variation of droplet aspect ratio ...................................................................... 99 4.3 Variation of voltage ratio ............................................................................... 109 CHAPTER 5 EXPERIMENTS ................................................................................................... 117 5.1 Fabrication ..................................................................................................... 117 5.2 Experimental setup ........................................................................................ 119 5.3 Symmetric splitting ........................................................................................ 122 5.4 Asymmetric splitting ..................................................................................... 126 5.4.1 Preliminary investigation ..................................................................... 126 5.4.2 Variation of voltage ratio ..................................................................... 128 CHAPTER 6 CONCLUSIONS AND FUTURE RESEARCH .................................................. 142 6.1 Conclusions .................................................................................................... 142 6.2 Future research .............................................................................................. 146 BIBLIOGRAPHY ....................................................................................................................... 148 viii List of Tables Table 2.1: The values of fluidic, geometrical and other parameters used in simulation .............. 30 Table 2.2: Simulation results for two different values of proportional gain ................................. 31 Table 2.3: The values of fluidic, geometrical and other parameters used in simulation of EWOD actuated droplet motion ................................................................................. 56 Table 3.1: Material properties and dimensions used in simulations ............................................ 73 Table 4.1: Properties of the droplet and the device used in study of aspect ratio variation and summary of results .................................................................................................... 100 Table 5.1: Voltages, droplet volume and splitting time for asymmetric splitting with constant left-side voltage of 49.5 Vrms ..................................................................................... 130 Table 5.2: Voltages, droplet volume and splitting time for asymmetric splitting with constant left-side voltage of 42.4 Vrms ..................................................................................... 137 ix List of Figures Figure 1.1: Droplet configuration for splitting (Cho et al. 2001) ................................................. 15 Figure 1.2: Schematic of the integrated EWOD-MALDI-MS device (Moon et al. 2006) ........... 19 Figure 2.1: Side-view of droplet motion showing the sources of resistance to motion ................ 23 Figure 2.2: Block diagram of the open loop droplet motion ........................................................ 24 Figure 2.3: Block diagram for the closed-loop control of droplet position from one cell to an adjacent cell .............................................................................................................. 24 Figure 2.4: The effect of transient response in droplet motion ..................................................... 26 Figure 2.5: The ‘Droplet’ subsystem using resistive forces proposed in the literature ................ 29 Figure 2.6: Simulation results showing droplet response to a step command .............................. 31 Figure 2.7: Simulation results showing droplet response (velocity) to a step command ............. 33 Figure 2.8: Resistive forces against droplet motion ..................................................................... 33 Figure 2.9: Resistive forces as fractions of total resistance .......................................................... 34 Figure 2.10: Rise time as a function of dimensionless L’ and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm ................................................................................. 35 Figure 2.11: Settling time as a function of dimensionless L' and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm ................................................................................. 36 Figure 2.12: Percentage overshoot as a function of dimensionless L’ and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm ............................................................... 36 Figure 2.13: Electric field lines, equivalent capacitances and overlapped areas; (i) Electric field lines formed between the coplanar electrodes, (ii) Equivalent parallel plate capacitances, (iii) Top view of the droplet showing areas of overlap on the two coplanar electrodes .................................................................................................. 37 Figure 2.14: Capacitance between coplanar electrodes for two droplet heights .......................... 40 Figure 2.15: Capacitance between coplanar electrodes for three inter-electrode gaps ................. 41 Figure 2.16: Maximum capacitance between coplanar electrodes in a DMFS with inter-electrode gap of 60 µm and droplet height of 80 µm ..................................... 41 Figure 2.17: Schematic diagram showing the capacitance measurement circuitry ....................... 42 Figure 2.18: Photograph of the experimental setup for capacitance measurement ...................... 43 Figure 2.19: Images of droplet at five different positions between the two adjacent coplanar electrodes connected to measure capacitance. Electrode size: 1.4 mm × 1.4 mm, Inter-electrode gap: 60 µm, Droplet height: 80 µm ................................................. 44 x Figure 2.20: Measured capacitance in a DMFS with 40 µm gap between the upper and lower plates ....................................................................................................................... 45 Figure 2.21: Measured capacitance in a DMFS with 80 µm gap between the upper and lower plates ....................................................................................................................... 46 Figure 2.22: Droplets of different volumes placed at the center of two coplanar. Electrode size: 1.4 mm × 1.4 mm, Inter-electrode gap: 60 µm, Droplet height: 80 µm .......... 47 Figure 2.23: Maximum capacitance measured when the droplet is at the midpoint between electrodes (1.4 mm 1.4 mm); Inter-electrode gap: 60 µm, Droplet height: 80 µm .. 48 Figure 2.24: Capacitance formed between the conductive droplet and the energized electrode ... 51 Figure 2.25: Sequential positions and the corresponding overlapped areas of a droplet (L/2600 o C) prohibits the integration of CMOS foundry technology and the use of polymer substrates. In an attempt to reduce the working temperature Li et al. (2008) used anodic Ta2O5 ( ) as the dielectric material and successful droplet movement was achieved at 14 V. Although the anodization of Tantalum could be performed at room temperature, this requires the special resource for sputtering Tantalum on the substrate. d Bhattacharjee and Najjaran (2010) reported the use of cyanoethyl pullulan (CEP), having high dielectric strength ( ), as the dielectric material and demonstrated that droplet actuations were possible at voltages as low as 20 V. The additional advantage of using CEP is that it can be deposited using a spin-coater only, obviating the need for any costly deposition setup needed for thermally/chemically grown dielectric layer. Chang et al. (2010) demonstrated droplet motion with a very low voltage of 3 V in an open DMFS where the dielectric layer was a 127 nm thick atomic layer deposition (ALD) aluminium oxide (Al2O3). Using polyvinyledene-fluoride- trifluoroethylene (PVDF-TrFE) as the dielectric material, Zhao et al. (2009) demonstrated that droplets can be successfully transported in an open EWOD device. 1.3.3 Hydrodynamics of droplet motion The response of a liquid droplet to an applied electric field is not fully understood yet. Besides, the generation, splitting and mixing of droplets actuated by EWOD are more complex than the transport of a droplet. Hence, a good understanding of the results of research on droplet hydrodynamics is essential in the development of an approximate model of fluidic operations. Investigation of the 3-D flow fields inside an EWOD-driven droplet has been studied by Lu et al. (2008). Micro particle image velocimetry (µPIV) data obtained for different horizontal planes of a moving water droplet containing red polystyrene beads revealed two internal circulations on either side of the vertical meridian plane. In order to capture the 3-D velocity field and circulations on vertical planes, the 2-D µPIV data were utilized along with the continuity equation. It was found that a strong downward flow exists near the activated electrode due to the electrowetting force. Although the flow pattern near the interface could not be revealed because of the interference of the curved surface, experiments show that reversible laminar flow results in little net displacement of particles when the droplet is moved back and forth. This implies that complex patterns of droplet motion results in better mixing of particles rather than linear back and 11 forth motion. A numerical model of the EWOD-driven droplet was developed by coupling the electrostatic force with the droplet hydrodynamics (Arzpeyma et al. 2007). The voltage dependent contact angle change was calculated from the Lippmann-Young equation where the input potential is obtained from solving the Laplace equation. The droplet shape and velocity were then obtained from the solution of Navier-Stokes equations. The results of simulation in terms of droplet velocity under different actuation voltages and electrode actuation frequencies were in agreement with those obtained from experiments. The EWOD force distribution along the droplet interface and the variations of the net force on the droplet were investigated by Baird et al. (2007). Their numerical scheme solved the potential distribution and charge densities on the droplet interface. The net force on the droplet obtained from integrating the charge densities matches closely with the predicted values obtained from analytical model. Results show that the EWOD force is stronger for dielectric materials with higher dielectric constants and is not affected by initial contact angles. The force distribution, however, depends on the curvature of the interface. Recently, Ahmadi et al. (2011) reported a volume-of-fluid method numerical modeling of the coupled electrohydrodynamics of droplet motion in an EWOD-based DMFS. Incorporating the empirical models of resistive forces from the filler fluid as well as from the contact line, numerical results were shown to be in good agreement with the experimental results. 1.3.4 Electromechanical fundamentals of EWOD The electromechanical interpretation of the EWOD-actuation of a liquid droplet allows one a generic approach to develop a lumped-parameter model of an electrofluidic system (Jones 2005, Jones 2009, Chatterjee et al. 2009). The electrohydrodynamics of a droplet driven by EWOD or DEP was studied by Zeng and Korsmeyer (2004) and Chakrabarty et al. (2010) from the continuum electromechanics point of view. It is argued that aqueous droplets, which are not perfectly conductive, undergo a transient process of delivering the charges to the droplet-insulator interface. When the transient time scale of electroquasistatic behaviour of the droplet is comparable to the hydrodynamic time scale, conductivity of the liquid should be taken into account. Furthermore, for liquids of relatively higher permittivity than the dielectric material between the droplet and electrodes, the droplet should be modeled as a leaky dielectric material. The traditional electrowetting theory centers on the idea that wettability dependent contact angle change acts as the driving force for the droplet motion. This interpretation fails to explain some of the characteristics of EWOD-driven droplet manipulation, for example the motion of dielectric liquid, low-surface tension liquid with no apparent change in contact angle, and the contact angle saturation (Chatterjee et al. 2006, Abdelgawad and Wheeler 2008). 12 Therefore, the electromechanical analysis of the EWOD-driven droplet motion aims at finding a reasonable explanation for such behaviours. Jones et al. (2003) and Jones (2009) studied the electromechanics of a generic liquid droplet by considering the lumped capacitance and conductance of the droplet, dielectric material and the surrounding medium. It is proposed that the EWOD and DEP are the low and high frequency limits of electromechanical response of the droplet, respectively. Below the critical frequency, given by , a deionized water droplet has no electric field developed inside it and the entire applied voltage is dropped across the dielectric layer. When ω >> ωc, the water droplet behaves like a dielectric and a certain fraction of the applied voltage is dropped across the droplet. A detailed analysis of frequency-dependent electrical actuation of liquid droplets has been done by Kumari et al. (2008). Under the assumption that the droplet retains a circular footprint, the energy minimization of the electrical network (composed of the droplet, activated electrode and the dielectric layer) yields a frequency dependent expression of the actuation force. For a droplet with given conductivity, the actuation force corresponds to that of EWOD-force when the driving frequency is low. The actuation force decreases with frequency and with a sufficiently high frequency the actuation force corresponds to that for a perfectly insulating liquid. Moreover, this behaviour is shifted towards higher frequency regions as the conductivity of the droplet liquid increases. Recently, Chatterjee et al. (2009) reported a comprehensive analysis of the droplet actuation by an AC voltage. Results verified that for a given gap between the top and bottom plates the liquid dielectric property becomes more and more pronounced as the frequency of the applied voltage is increased. As the frequency approaches the critical value, determined by the electrical properties of the liquid and dielectric layer, the DEP force on the droplet increases. However, the total actuation force reduces quickly beyond the critical frequency. When the voltage drop across the droplet exceeds that of dielectric layer, the DEP force becomes stronger than the electrowetting force. In addition, due to the dependence of conductance on the gap between two plates the total actuation force acting on the droplet increases when the gap is decreased. Recently, c Bhattacharjee & Najjaran (2009) showed that the EWOD actuation of a droplet can be modeled as a closed-loop system with an inherent unity feedback of droplet position. Electrode, dielectric and droplet are modeled as a capacitor with variable area as the droplet, considered as a conductor, moves over the dielectric layer. The EWOD force depends on the rate of change of droplet area over the actuated electrode, which in turn depends on the direction of motion and the position of the droplet between the actuated and previous electrode. Thus, EWOD actuation intrinsically utilizes the droplet position to generate sufficient force to 13 accelerate the droplet. When the droplet approaches the final position, the magnitude of force reduces automatically so the droplet decelerates. In case the droplet has sufficient momentum to exceed the final position, the EWOD force, according to the model, will act on the opposite side of the droplet in order to bring it back to the desired position. Moreover, it is also pointed out that the EWOD force and hence, the response of the droplet depends on the size of the droplet. 1.3.5 Electro-hydrodynamics of digital microfluidics The spatial distribution of electric potential in the space occupied by a droplet, its surrounding fluid and the dielectric layers is given by the Poisson equation under the electro- quasistatic assumption (Chakrabarty at al. 2010, Zeng and Korsmeyer 2004): (1.3) where is the applied potential to the control electrode, is the free charge per unit volume inside the droplet, is the relative permittivity, is the vacuum permittivity, i stands for the respective material. Initially the droplet may not have any free charge inside. However, if the droplet possesses finite conductivity, free charges can be transported according to the following charge conservation law: ( ) ( ) (1.4) where is the droplet conductivity, is the velocity field, ( ) is the divergence of current density in which is the electric field. This charge distribution in turn affects the potential distribution. However, free charges migrate towards the interface and accumulate there very fast if the transient time of charge distribution is much smaller than the hydrodynamic time scale for the liquid. Thus, a discontinuity in the electric field appears at the droplet-medium interface which is accounted for by the following boundary condition (Chakrabarty at al. 2010): ̂ ( ) (1.5) where is the surface charge density at the droplet-medium interface. The net macroscopic effect on the droplet is given by the following expression of electric force per unit of liquid volume: ( ) ( ). (1.6) The first term is the well-known Coulomb force on the induced free charges in the bulk of the liquid or at the interface. The second term is known as the DEP force originating from the polarization. The presence of electric field distorts the charge poles of individual molecules of the liquid and any other species present in the droplet. The resultant of all the forces on each of these 14 polarized particles is the net DEP force. This is the only driving force for a droplet with very low or no conductivity under electrical actuation. Since most liquids are incompressible and Newtonian in typical digital microfluidics applications, the hydrodynamics of a liquid droplet surrounded by another fluid medium is governed by the Navier-Stokes equations (Arzpeyma et al. 2007): [ ] (1.7) (1.8) where is the liquid density, is the time, is the Del operator, is the pressure, is the dynamic viscosity, is the gravitational acceleration, is the body force per unit of liquid volume. At the droplet-medium interface the following boundary conditions hold: ( ) ̂) ̂ ̂ (1.9) ( ) ̂) ̂ ( ) ̂ (1.10) where ( ) is the stress tensor, d and m stands for droplet and medium, ̂ and ̂ are the normal and tangential unit vectors at the interface, is the surface tension between droplet and medium, ̂( ̂ ) is the surface gradient operator. 1.3.6 Microfluidic operations Droplet generation, merging and splitting has been performed on an EWOD-based system demonstrating its capability of serving as a practical lab-on-a-chip where all the common microfluidic operations can be perfectly accomplished. Pollack et al. (2002) successfully performed droplet splitting and merging by controlling the pattern of energized electrodes. A droplet can be dispensed from the reservoir containing a large droplet by activating a number of electrodes along a direction which results in a liquid finger/protrusion. Subsequent deactivation of the intermediate electrodes and activation of the reservoir electrode pulls back the liquid from the neck and finally leaves a droplet on the terminal electrode after the neck is broken off. Cho et al. (2002) demonstrated the droplet generation method by arranging two extra electrodes orthogonally on both sides of the electrode where necking is expected to initiate. Instead of having an electrode for the reservoir, those two electrodes facilitate the neck initiation and break off. In another study involving droplet actuation with AC voltages of various frequencies, it was found that droplets can be moved at a speed of 25 cm/s when 150 Vac is applied. The latter was a significant improvement in droplet speed on a digital microfluidic system. Microscale mixing has also been successfully demonstrated in EWOD-based DMFS by merging two droplets and transporting the merged droplet along specified paths (Fowler et al. 2002, Ren et al. 2003, Paik et 15 al. 2003). Results show that the efficiency of active mixing depends on the number of rolls of the merged droplet as well as the merge and split strategy. Droplet splitting is a generic microfluidic operation which can affect the overall performance of a DMFS. The generation of a droplet from a reservoir can be regarded as a splitting process. Therefore, from the generation of a droplet of specified volume to the control of concentration of sample species, droplet splitting process plays the key role. Droplet splitting process has been physically and experimentally studied by Cho et al. (2001). Based on the study of the geometry of a droplet in splitting process, shown in Figure 1.1, taking into account the Lippmann-Young equation and the Laplace equation of pressure across the interface, it was shown that applied voltage is related to the radii of curvature of the deformed droplet. The required gap between two hydrophobic surfaces is calculated using the estimated values of the radii of curvature R1 and R2. A droplet cannot be split when the gap is larger than the calculated value. A required gap of 150 µm was calculated for the size of electrode and droplet, material properties used in the experiment. The above criterion for droplet splitting was verified by experiments conducted with channel gaps of 80 µm, 150 µm and 300 µm. Only the device with 80 µm gap was able to split a droplet. Recently, Clime et al. (2009) demonstrated splitting of a droplet containing magnetic beads in an electrowetting-based device. Figure 1.1: Droplet configuration for splitting (Cho et al. 2001). 1.3.7 Feedback control in DMFS Recently, the need for integration of feedback control system for reliable and accurate operation on droplets has been realized and several researchers have demonstrated the benefits of closed-loop controllers in DMFS. The notion of the feedback control of droplet motion was first proposed by Gong et al. (2004) for a cross-referencing based DMFS where the droplets are driven by the EWOD force. The system consisting of a droplet, the dielectric layer and the electrodes is modeled using a network of capacitors and resistors. The position of the droplet is monitored by measuring the voltage drop across an external resistor. The simple control algorithm first Energized electrodes R2 Undeformed droplet R 1 P 1 P 2 16 compares the measured voltage drop with a predefined/calibrated value and continues to apply the driving voltage to the target row and column electrodes as long as the measured voltage drop is smaller than the predefined value. In order to achieve high precision in droplet generation, Ren et al. (2004) proposed a control system which utilizes the capacitance feedback. The dispensed volume of a droplet can be approximated by its footprint area over the activated electrode where the footprint area can be measured using the capacitance between the droplet and electrode. The control algorithm implemented in LabVIEW ® monitors the capacitance which is measured in terms of the output frequency of a ring oscillator. When the generated droplet completely overlaps the electrode, the output of the ring oscillator reaches a cut-off value and the controller shuts off the flow of liquid by closing the valve of an external continuous flow system. The reproducibility of this method was evaluated by varying the droplet volume, viscosity and generation rate. The experimental results comply with the acceptable values of the prevailing parameters in typical biomedical applications. Gong and Kim (2006) used a PID controller for the generation of droplets to eliminate the external continuous flow source of liquid and achieve higher compactness for the DMFS. Measuring the capacitance of the system, composed of the droplet-in-progress and the electrode where the droplet is to be formed, and controlling the driving voltage of the electrodes on the creation site and reservoir, successful dispensing of droplets with higher accuracy and precision was demonstrated. Droplet capacitance was shown to be related to the type and amount of contents in the liquid and utilized in mixing and concentration control (Schertzer et al. 2010). Shih et al. (2010) demonstrated that the operation of a DMFS based on the detection of a droplet on a given electrode significantly increases the reliability of bio-assays. Recently, Miguel and Najjaran (2011) have demonstrated that position of a droplet, as it moves, between two adjacent electrodes can be estimated by measuring capacitance. It is noted that all the applications of capacitance sensing in a DMFS are based on measuring between the upper electrode and one of the square electrodes in the lower plate. This method is straightforward in a sense that the measured capacitance is linearly dependent on the droplet overlap area. A major drawback of this method is the inapplicability in a single plate DMFS, where the ground electrodes are incorporated into the lower plate. Even in a two plate DMFS, the engagement of the upper plate for sensing restricts the integration of any other functionality that requires access from above. Therefore, a sensing method avoiding the connection to the upper plate would greatly enhance the functionality of a DMFS. The introduction of a coplanar sensing approach as one of the contributions of this thesis is discussed in Chapter 2. 17 Armani et al. (2005a, 2005b) proposed a visual feedback control system for the EWOD based DMFS. The vision algorithm isolates the pixels corresponding to the liquid/vapour interface of the droplet and then determines the location of the interface by applying the Gaussian smoothing and standard Edge Detection technique. The requirement of an external fast vision system and complex computation for image processing of multiple droplets will make the system costly as well as non-portable. Therefore, it is apparent from the above literature review that an accurate in-situ electrical signal feedback control is necessary and appropriate to attain the accuracy and precision required for the microfluidic operations such as splitting and mixing performed in the DMFS. In an attempt to avoid bulky attachments for detection in DMFS, Luan et al. (2008) reported a DMFS with integrated InGaAs-based thin-film photodetectors distributed among the electrodes. Optical fiber-based droplet sensing was demonstrated by Wang et al. (2008) for feedback control of dielectrophoretic droplet dispensing. Recently, a general model of the closed-loop control system for droplet position between two adjacent cells in a DMFS has been presented ( c Bhattacharjee & Najjaran, 2009). The droplet dynamic system, modeled using the semi-empirical relations of resistances to motion (Ren et al. 2002, Bahadur and Garimella 2006), is simulated for a step command in position and transient characteristics are obtained and discussed. The transient and steady-state response i.e., rise time, settling time and percentage overshoot are used to calculate the operational parameters of a DMFS such as driving frequency as well as to identify the unwanted situations. The need and utility of a feedback control system for proper functioning of a DMFS are also identified. 1.3.8 Bioassay applications As mentioned in the previous paragraphs, there are a number of bio-analysis related applications that can benefit from asymmetric splitting of a droplet. For a DMFS, the particle separation and concentration control was first demonstrated by Cho and Kim (2003) by designing a separate set of electrodes for electrophoresis. Application of DC voltage between the electrodes facing a droplet can concentrate charged particles near the cathode or anode. With two oppositely charged particles in the droplet, both the cathode and the anode will attract particles of positive and negative charge, respectively. The EWOD driven splitting of the droplet, then, results in two droplets of equal volume but different concentration or different particles. Separation of negatively charged carboxylate modified latex and polystyrene particles using an electric field of 3.3 V/mm followed by the application of 60 Vac (10 kHz) resulted in droplets with mostly the desired particles. An efficient particle concentration and separation method was developed by Zhao et al. (2007) by designing the electrodes for the travelling-wave dielectrophoresis (twDEP) on the bottom plate and those for EWOD on the top plate. A droplet containing target particles 18 (e.g., aldehyde sulfate (AS) beads) is brought to the target location and the particles are concentrated to one side of the droplet. A subsequent splitting of the droplet into two equal size droplets results in one daughter droplet with almost all (98%, as reported) of the target particles. Results support that separation of different particles is also possible. A droplet containing two types of particles (AS and glass beads) was successfully split into two equal droplets with one having 97% of AS beads and the other having 77% of glass beads. However, the efficiency and speed of separation and concentration control through splitting is limited because with the reported methods the mother drop will be always halved. It can be noted that with the capability of splitting a droplet into two unequal droplets higher concentration of one type of particle and hence a better separation efficiency can be obtained in the smaller droplet. By modulating the applied signal and designing multiple strip electrodes within the array of usual square electrodes, the DEP manipulation of neuroblastoma cells and polystyrene beads has been successfully shown (Fan et al. 2008). Analysis of the system of droplet sandwiched between two plates, by considering as a network of resistors and capacitors, revealed that an electric field is established inside the droplet above a cut-off frequency of the applied signal. Since the width of a strip electrode is very low compared to a square electrode, the field inside the droplet is non-uniform. This non-uniform electric field has been utilized in separating the particles with positive or negative DEP depending on the proposed weighted Clausius-Mossotti factor. Moon et al. (2006) designed a multiplexed proteomic sample preparation device for high throughput Matrix Assisted Laser Desorption/Ionization Mass Spectrometry (MALDI-MS). Figure 1.2 shows the device that consists of electrode arrays of two different sizes with transition sites where the smaller electrodes denoted by × are inscribed within the larger electrodes. The sample containing both the protein and impurities are dispensed from the reservoir, transported to the transition site using the array of smaller electrode and left there to dry. A rinsing droplet is brought over the dried sample through the array of larger electrodes. The impurities are washed away by the rinsing droplet which is then disposed into the waste reservoir. The larger electrode at the transition site is designed to overcome the difficulty in moving a droplet past the smaller electrode containing the dried protein rendering the surface hydrophilic and rough. Next, the droplet containing the MALDI-MS reagent is delivered to the spot for further analysis. However, the requirement of two arrays of unequal electrodes imposes a burden of extra time and cost in the design and fabrication. As a result, it is greatly desirable to have a device with equal-sized electrodes in the array and dispensing a droplet of the proteomic sample having a footprint area smaller than the electrode area. The EWOD actuation cannot move a droplet smaller than the size of the electrode since certain amount of overlap on the adjacent electrode is required for 19 continuous motion. In contrast, a regular-sized droplet can be transported to the target location and a droplet smaller than the electrode can be generated by splitting the mother droplet into 1:x ratio by EWOD. Figure 1.2: Schematic of the integrated EWOD-MALDI-MS device (Moon et al. 2006). Clinical diagnostics of human physiological fluids, such as whole blood, serum, plasma, sweat, saliva, urine and tear, have been demonstrated on a EWOD-driven droplet-based lab-on-a- chip (Srinivasan et al. 2004). Glucose assay was performed on all the above mentioned fluids in a device integrated with reservoirs, transportation bus, detection spots and a mixing area. The results obtained agree with the reference measurements, except for the urine where interference by the uric acid affected the result. However, the glucose assay in a DMFS is performed with only a twofold dilution of the droplet containing the sample, while the bench-scale assay requires dilution factors greater than 100. With a 1:1 splitting process it will take many steps to achieve the desired dilution making the process time-consuming and susceptible to error. In a DMFS with the capability of higher dilution factors can be achieved faster than with a 1:1 splitting. The proposed method of splitting a droplet into a 1:x ratio is explained in Section IV. The compatibility and feasibility of EWOD-based microfluidic systems for polymerase chain reaction (PCR) has been investigated by researchers (Pollack et al. 2003). Pollack et al. (2003) observed that the PCR reagent can be successfully manipulated without cross- contamination through the oil medium or the solid surface. Chang et al. (2006) implemented the 20 PCR in an EWOD-based device incorporating a microheater and thermal sensor for feedback controlled thermal cycling. Droplets of cDNA samples and PCR reagent are generated, merged, mixed and transported to the PCR chamber. The final results of fluorescent signal are comparable to those obtained from a bench-scale device. It is noted that the process of PCR can be enhanced with an EWOD-based DMFS capable of diluting samples to arbitrary factors and of mixing samples fast and accurately. 21 1.4 Thesis outline This thesis is organized as follows: Chapter 1 presents the objectives of this research, the review of relevant literature and contributions of the research. Simulation results of droplet position control are presented in Chapter 2. A lumped parameter model of a moving droplet is developed based on the empirical theories of resistances. Results of multiple simulations considering a range of material properties and geometric parameters are discussed. Two dielectric materials possessing higher dielectric constants are investigated to reduce to the operational voltage and cost of fabrication. Experimental results of this investigation are also shown. Finally, a novel method of droplet sensing using only the control electrodes along with results is presented. In Chapter 3, the capabilities and limitations of computational fluid dynamics software packages in simulating liquid with free surface are evaluated. The general electrohydrodynamics of droplet splitting and the role of key parameters in determining the success of splitting are explained based on the simulation results obtained from FLOW-3D ® . The results of simulation based investigation of asymmetric splitting are presented in Chapter 4. The role of minimum voltage, droplet size and aspect ratio, viscous shear, surface tension and the ratio between applied voltages in determining necessary conditions for successful splitting are discussed. The required voltages for successful asymmetric splitting of droplets of various aspect ratios are determined and the parameters that characterize splitting such as flow rates, capillary numbers are presented. Finally, the simulation results of asymmetric splitting with different voltage ratios are discussed. Chapter 5 describes the design and fabrication of the digital microfluidic system as well as the experimental setup and the results of droplet splitting experiments. The minimum voltages required for both symmetric and asymmetric splitting of a droplet of deionized water in the fabricated device are identified. Experimental results in terms of volumetric flow rates and accumulated volume of liquid in asymmetric splitting with different voltage ratios are discussed. Finally, the sources of error in experiments and of variability in results are discussed. Chapter 6 presents the conclusions of this research along with opportunities for further research on the problem. 22 CHAPTER 2 DIGITAL MICROFLUIDICS – OPERATIONS AND ENHANCEMENTS Accurate and reliable operations in digital microfluidics require either a feedback control system having all the parameters tuned appropriately or extensive study of the open-loop droplet operations such as motion, dispensing and splitting. The open-loop dynamic system in digital microfluidics typically consists of a moving or deforming droplet and the actuation mechanism. A mechanism for sensing the position of a droplet and the volume of liquid is essential to control droplet operations in a closed-loop fashion. This chapter begins with the study of closed-loop control of droplet position assuming generic actuation and sensing mechanisms, and lumped parameter models of the opposing forces. Simulation results reveal the significant underlying relations between the droplet response and the parameters of the controller as well as the geometry. In the next section, a novel droplet sensing mechanism is proposed which not only facilitates the realization of closed-loop control of operations in digital microfluidics, but also eliminates the limitations of traditional droplet sensing methods. This new sensing method can potentially be used for closed-loop control of droplet splitting. Since EWOD-actuated droplet splitting is central to this thesis, understanding the fundamentals of EWOD is essential. Therefore, a lumped-parameter analysis of EWOD-actuated droplet motion is performed to identify the critical factors determining the effectiveness of EWOD. Since the magnitude of EWOD force is directly related to the dielectric properties of the insulating layer, a material with high dielectric constant, CEP, is investigated in terms of contact angle change as well as droplet actuation. Results, presented in the final section, prove that droplet operations can be reliably performed with significantly lower voltages in addition to the fact that DMFS can be quickly fabricated using an inexpensive equipment. 2.1 Droplet Translocation and Control 2.1.1 Dynamics and Control of Droplet Motion: In this study, a confined digital microfluidic system with a planar array of cells (electrodes) is considered. In this system, liquid droplets are submerged in a filler fluid (e.g., silicone oil) to prevent evaporation of droplets and to lubricate the solid surface at the contact line, and hence, to reduce the force of friction. Figure 2.1 shows the free body diagram of a 23 droplet moving from one cell to another in a confined DMFS. A greatly simplified model of the droplet motion in a DMFS can resemble a mass and damper system without the stiffness term. In this way, the displacement of the droplet is the output of the system and the driving force is the input to the system. In the present study, it is assumed that the driving force may be either a surface-force (e.g., electrowetting force) or a body-force (e.g., magnetic force), provided that the magnitude and direction of the force can be controlled. Figure 2.1: Side-view of droplet motion showing the sources of resistance to motion. Hence, if the total resistive force against droplet motion can be modeled as a viscous friction force, which is linearly related to droplet velocity, the dynamic equation of the droplet motion is given by: (2.1) where x is the displacement of droplet, m is the droplet mass, c is the coefficient of friction and Fdr is the driving force. Thus, the transfer function G(s) of this simplified DMFS is given by: ( ) ( ) ( ) (2.2) where X(s) and Fdr(s) are the Laplace transforms of the displacement and driving force respectively. The block diagram of droplet dynamic system is shown in Figure 2.2. Now, consider the droplet actuation mechanism is such that the position of the droplet between two adjacent cells is not intrinsically utilized to generate the magnitude and direction of the driving force. In absence of external feedback on position of the droplet, the above mentioned driving force cannot produce the desired final position of the droplet despite the fact that its magnitude and direction can be controlled. For instance, a pulse of driving force will result in droplet displacement as a function of the magnitude and duration of the pulse whereas a constant driving force will continue to move the droplet. This implies that the DMFS is an open loop system and there is no control over the final position of the droplet. It can be mentioned here that in an EWOD-based DMFS, the EWOD force is a function of the droplet position. Hence, the system inherently utilizes droplet position feedback and the droplet finally settles down on the destination cell. Droplet Top plate Bottom plate Fc Ff Fd Hydrophobic Layer Dielectric Layer Electrode U D L 24 Nevertheless, position feedback is necessary in EWOD-based DMFS for accurate actuation of successive electrodes and guaranteed transport of droplets. Feedback control is also necessary for the control of temperature and concentration as well as for operations like droplet creation. Figure 2.2: Block diagram of the open-loop droplet motion. Figure 2.3: Block diagram for the closed-loop control of droplet position from one cell to an adjacent cell. Hence, the feedback control of individual droplets is necessary for accurate positioning of the droplets and proper functioning of the DMFS. In a typical DMFS, a droplet can only be moved by one cell when actuated. To move a droplet from a starting cell to a destination cell along a path having multiple cells, the droplet needs to be actuated successively. The frequency of this successive actuation is defined as the droplet actuation frequency. The average droplet speed is defined as the total time taken by the droplet to travel the total distance between the start and destination cells. The study of transient response of a moving droplet in a feedback control system will be helpful in determining the actuation frequency and average droplet speed. Information on droplet position can help in detecting the malfunction of any particular bioassay operation (e.g. mixing) and the presence of faulty cells which are defined as the cells failing to actuate droplets further because of manufacturing flaws and degradation of materials. For example, if a droplet is stuck between two cells, this might indicate the presence of a faulty cell and the exact position of the droplet will be useful in identifying the faulty cell and thus saving those sample/reagent droplets which were programmed to use the cells now identified as faulty. Droplet position can be sensed by using the visual feedback from a camera which must be capable of working at a high frames per second and a reasonably good resolution to detect the interface of the droplet (Gong and Kim, 2006). However, this method requires a transparent plate in a closed system and a fast image processing for real-time applications. Alternatively, the position of a droplet can be sensed from the electrical signals, such as impedance, resonant 𝑚𝑠 𝑐𝑠 Fdr(s) X(s) + - 𝑚𝑠 𝑐𝑠 Fdr(s) X(s) K Xref(s) E(s) H(s) 25 frequency and capacitance (Armani et al. 2005). Sensing of an electrical signal requires integration of no additional device in EWOD-based DMFS or minimum additional device for a DMFS based on other droplet actuation principles. In an EWOD-based DMFS, the same electrodes can be used for both actuation and sensing the droplet. Electrical signals, generating from the system consisting of the electrodes, the droplet and the insulator, change in relation to the position of the droplet. Depending on the mechanism of position sensing, a transfer function may be present in the feedback path. The addition of a transfer function due to the position sensor in the feedback path will change the damping ratio (defined as the ratio of the damping coefficient of the system to its critical damping coefficient) and natural frequency of oscillation (defined as the frequency with which an undamped 2 nd order system oscillates when excited by a step input), but both the type and the order of the system will remain unchanged. Clearly, accurate and fast sensing of droplet position in DMFS is essential for closed-loop control. For the demonstration of the basics of the DMFS control system, it is assumed that a position sensor with unity feedback is available for the control system. The closed-loop control block diagram of the position of a droplet moving from its current cell to the adjacent cell is shown in Figure 2.3. The controller shown in Figure 2.3 is a simple proportional gain. It represents the model of the hardware that compares the actual position with command value and generates the driving force for the droplet according to the error signal. The closed-loop transfer function with unity feedback (H(s) =1) of this system is given by: ( ) ( ) ( ) ( )⁄ ( )⁄ (2.3) It is noted that the effect of position feedback and proportional gain is similar to adding stiffness to the original system. More precisely, a DMFS with position feedback will resemble a 2 nd order dynamic system represented by mass, spring and damper. Depending on the values of m, c and K, the dynamic response of the system can be evaluated in terms of percentage overshoot, rise-time and settling time that play an important role in the performance of a DMFS. For example, the percentage overshoot must be controlled to avoid unintentional mixing between two droplets. The later can be a common control problem since a droplet residing in one cell may also cover a certain portion of adjacent cells due to variation in the dispensed droplet volume from the reservoir. To understand the effect of overshoot on the bioassay operation let us consider two droplets A and B in the two dimensional array (7×5) of cells shown in Figure 2.4. Droplets A and B are commanded to move from cell (x6,y4) to cell (x5,y4) and from cell (x2,y4) to cell (x3,y4), respectively. In moving multiple droplets simultaneously, fluidic constraints must be maintained at all times in order to avoid unintentional merging of two or more droplets (Griffith 2005). The 26 fluidic constraints say that both the current and next destination cell of a droplet must have all the adjacent cells empty. Therefore, the two movements mentioned above are permissible as there will be one empty cell between the new positions of the two droplets which are shown by dotted circles. If the overshoots of the droplets are large enough, their front end may come into contact. This will lead to inaccurate results of the chemical/biological analyses involving droplets A and B if their mixing is prohibited. The rise-time and settling-time are also important in determining the average speed of droplet motion which in turn affects the overall throughput of the DMFS. In case of successive displacement of a droplet in one direction, which is the case for droplet C in Figure 2.4, the frequency of droplet actuation can be related to the rise-time in order to achieve maximum possible droplet speed for given values of other system parameters. When a droplet needs to change the direction of motion, as is the case for droplet A in Figure 2.4, it must be actuated only after the acceptable settling time has elapsed. If the droplet is actuated before acceptable settling time the droplet may have excessive inertia in the direction of motion. As the actuation force is applied in a transverse direction, the droplet may follow an unpredictable trajectory. This combined effect of droplet momentum in one direction and actuation force in a perpendicular direction can be avoided by actuating the droplet only after acceptable settling time. Thus, the droplet A in Figure 2.4 must be actuated to move from cell (x5,y4) to cell (x5,y5) only after the settling time has elapsed since it started from cell (x6,y4). Figure 2.4: The effect of transient response in droplet motion. 2.1.2 Detailed Model of Droplet Dynamic System: In developing the block diagrams and transfer functions of open-loop and closed-loop droplet position control systems it is assumed that the resistive force against droplet motion can be modeled by viscous damping where the resistive force is proportional to velocity. The coefficient of friction, c, used in the transfer functions in Equations 2.2 and 2.3, is the constant of proportionality. However, previous analytical and experimental study suggests that the resistance x6 B A y5 y4 y3 y2 y1 x1 x2 x3 x7 x4 x5 C 27 to droplet motion results from different sources. The three sources of resistance reported in the literature (Ren et al. 2002, Bahadur and Garimella 2006) are (i) viscous dissipation inside the droplet, (ii) viscous drag due to droplet moving through filler-fluid, and (iii) slippage of contact- line (between the droplet and hydrophobic surface). These resistive forces can be nonlinear functions of velocity and time-dependent due to the change in fluidic properties arising from microfluidic operations, cross-contamination and deterioration. These three sources of resistance are used to estimate the total resistance to droplet motion only and research on developing the exact model of the underlying physics is still ongoing. Moreover, uncertainties in droplet motion and positioning, resulting from surface imperfection and variations in dimensions of material layer introduced at the fabrication and assembly stage, cannot be modeled. The purpose of a closed-loop control of droplet position is to compensate for the imperfections in the device and the error in modeling. However, addition of such a controller to the DMFS will increase the cost significantly and the feasibility of having a controller should be studied considering the application of the DMFS. A general purpose DMFS where the precise positioning and tracking of individual droplets are not crucial may not have a closed-loop controller for droplet position. On the other hand, a DMFS has the potential to be used as a high throughput and highly sensitive lab- on-a-chip (e.g., in drug discovery) where the investment of a robust controller for droplet position can be economically justified. In this study, the models of the resistive forces proposed in the literature (Ren et al. 2002, Bahadur and Garimella 2006, Berthier et al. 2007, Chen and Hsieh 2006) are used to analyze and simulate the transient response of a droplet. The total plate shear force (assuming a parabolic velocity profile far from the liquid-liquid interface) is approximately modeled by (Bahadur and Garimella 2006, Yuh et al. 2006) ( ) ( ) (2.4) where, D is the spacing between the upper and lower plate, r, μd and U are the droplet radius, viscosity and velocity, respectively. This assumption may not represent the exact flow pattern inside the droplet, but considering the fact that in a typical DMFS the plate separation is much smaller compared to droplet diameter, the above model serves as a good approximation for lumped parameter study of droplet dynamics (Kuo et al. 2003). In addition, experiments on EWOD-based DMFS revealed that plate shear force accounts for a smaller fraction of the total resistive force (Ren et al. 2002). Under the assumption that droplet as a rigid body is moving through filler fluid, the viscous drag is estimated by ( )( ) (2.5) 28 where CD is the drag coefficient of a cylinder in a cross-flow and ρf is the density of filler fluid. In general, for low Reynolds number ( ) flows,CD is a function of , and for moderate Reynolds number flows ( ), CD remains relatively constant (Munson et al. 2008). The contact-line friction is modeled by ( ) (2.6) where ζ is the coefficient of contact-line friction defined in molecular kinetics and n varies from 0 to 2 (Chen and Hsieh 2006). The contact-line friction accounts for a larger fraction of the total friction force (Ren et al. 2002). Chen and Hsieh (2006) and Kuo et al. (2003) found that the model without considering contact-line friction overestimates the motion. Hence, an accurate model of the contact-line friction is necessary for the prediction of droplet dynamic behavior. In many studies, a linear relationship between the contact-line friction and droplet velocity could adequately verify experimental results (Ren et al. 2002, Chen and Hsieh 2006). In this paper, we also use the linear relationship in simulating droplet motion. It can noted that, for a certain range of Reynolds number ( ), CD can be a linear function of making the Ff linear with U. Under this special condition, the total resistive force to droplet motion will be a linear function of droplet velocity and an exact solution of the droplet response can be derived. The contact angle hysteresis, defined as the difference between the advancing and receding contact angle of a droplet in motion, is another factor that needs to be considered in order to model the droplet motion accurately. This implies that a portion of the driving force is used to overcome the contact angle hysteresis and below this threshold of force a droplet cannot be moved (Berthier et al. 2007). Thus, the equation of droplet motion, in a DMFS based on a general actuation mechanism, can be written as (2.7) where Fthresh is the threshold of driving force. Although equation 2.7 represents the approximate dynamic model of a droplet in a general DMFS, the exact model may have additional terms specific to the actuation method. For instance, the total actuation force on a droplet in an EWOD- based DMFS is the resultant of the force acting on the tri-phase contact-line and that acting on the interface between the droplet and medium. The total force depends on the conductance and permittivity of the droplet and the magnitude and frequency of the applied voltage. The deviation of the droplet from circular shape (i.e., reduction of contact-angle on the advancing side) due to the energy stored in the droplet-insulator interface and the effect of the release of that energy upon withdrawal of voltage may be neglected considering their weaker influences. As droplets in a typical DMFS flow with low , the scaling law suggests that the inertial effect of the droplet is 29 not dominant. However, consideration of droplet mass is not unusual for the analysis of transient and steady-state responses of a system modeled in terms of lumped parameters (Bahadur and Garimella 2006). The oversimplified model, derived by ignoring the droplet mass, may result in inaccurate estimation of parameters characterizing the dynamic response. For example, Kuo et al. (2003) have reported significant overshoot of a droplet driven by electrowetting force that can only be explained by the effect of the inertial force. The overshoot and the associated oscillations of the droplet result in a longer settling time. However, the calculated settling time using the droplet dynamic model without the mass term will result in a shorter time. The block diagram of the closed-loop control of the droplet position considering the detailed resistances to motion is similar to Figure 2.3 except that the transfer function is replaced by a subsystem called ‘Droplet’. Figure 2.5 shows the details of the subsystem ‘Droplet’ defined based on the nonlinear dynamics of droplet motion defined by equation 2.7. Figure 2.5: The ‘Droplet’ subsystem using resistive forces proposed in the literature. 2.1.3 Simulation Results and Discussion: The dynamic response of a droplet can be obtained numerically by solving the differential equation of motion. For the present study, the dynamic response of the closed-loop position control system is simulated using SIMULINK ® . It is assumed that the footprint of a droplet on both the top and bottom plate remains circular from the start to the end of motion and that the radius of the circular footprint is slightly greater (assumed 5%) than the half-length of a cell so that a droplet also overlaps the adjacent cells. Droplet mass, m, can be estimated by that of a cylinder with height equal to the plate spacing. Although the governing equation of droplet dx/dt Fc Fd Ff Contact l ine Viscous_droplet 1 X 1 s Integrator1 1 s IntegratorF_thresh f(u) Drag_FillerFluid f(u) f(u) 1/m 1 F_dr 30 motion is nonlinear, we make no attempt to design a controller for this system. Instead, this paper focuses on the necessity of feedback control and the effect of transient and steady-state responses on the performance of a DMFS. That is why a simple proportional controller is used in the simulation. The value of proportional gain can be adjusted to achieve desired transient response. Simulation is performed using ODE45 solver with a maximum step-size of 0.0001 and an absolute tolerance of 0.0001. The input to this system is a step command for position which is equal to the electrode pitch and is applied at the start of simulation. The position of the centre of the droplet is the output of the system. The geometric and fluidic parameters used in the simulation are summarized in Table 2.1. The droplet (water with 0.1 M KCl) and filler fluid (silicone oil) considered here are those used in the experiment performed by Pollack et al. (2002). The threshold driving force which is related to the contact angle hysteresis is taken to be 5×10 -6 N (Berthier et al. 2007). Table 2.1: The values of fluidic, geometrical and other parameters used in simulation. The results of simulation for two different values of proportional gain are shown in Figures 2.6-2.7 and are summarized in Table 2.2. The droplet response is similar to a typical 2 nd order system. For the given values of fluidic and geometric parameters the system behaves as an underdamped one with the proportional gains of 1 and 10. For this simulation, the rise time is defined as the time taken by the system to attain the command value for the first time. Thus, the simulated rise time can be considered as the earliest time a droplet (e.g., droplet C) can be Droplet viscosity, µd, (1 μL Water with 0.1M KCL) 1.9×10 -3 Pa.s Droplet density, ρd 1000 kg/m 3 Filler-fluid (Silicone oil) viscosity, μf 1.7×10 -3 Pa.s Filler-fluid density, ρf 760 kg/m 3 Electrode (cell) pitch, Lnom 1500×10 -6 m Plate spacing, Dnom 300×10 -6 m Surface-tension between droplet & filler, γLM 40×10 -3 N/m Coefficient of Drag, C 30 Contact-line friction coefficient, ζ 0.04 N.s/m2 Droplet radius, r (Assuming 5% overlap of adjacent electrodes) (L/2) + 0.05(L) Droplet mass, m; 1.77x10 -6 kg Threshold of driving force, Fthresh 5 μN 31 actuated to move from its current destination cell (e.g., cell (x5y2)) to the new destination cell (e.g., cell (x4y2)). For example, a rise time of 5.659 millisecond (for K = 1) implies that the actuation frequency cannot exceed 177 Hz resulting in a maximum obtainable average droplet speed of 26.55 cm/sec, where the average speed is calculated from dividing cell pitch by the rise time. The droplet speed thus calculated can be used in determining the transportation time for multiple droplets along different paths and consequently the assay completion time as well as optimal scheduling. Figure 2.6: Simulation results showing droplet response to a step command. Table 2.2: Simulation results for two different values of proportional gain. Proportional Gain (K) Rise time (ms) Peak time (ms) % Overshoot Settling time (ms) 1 5.649 7.349 5.27 12.719 10 1.565 2.145 8.71 6.275 The percentage overshoot indicates how close a droplet can get to a nearby droplet while they are not allowed to contact each other. A critical situation arises when two droplets approach 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (millisecond) D ro p le t p o s it io n ( m ill im e te r) K = 10 K = 1 32 each other, which is depicted in Figure 2.4 where droplets A and B are moved to their new cells simultaneously. From simulation with K = 10, a 8.71% (0.1306 mm) overshoot added to the normal 5% (0.075 mm) overlap results in a total overlap of 13.71% (0.2056 mm) of cell (x4,y4) for droplet A . An equal overlap of 13.71% on the left side of cell (x4,y4) is also caused at the same time by droplet B. Therefore, at the time of peak displacement (i.e., at 2.145 millisecond) of the two droplets, there is a gap of 1.09 mm (72.58% of L) between the advancing edges of the droplets A and B. This is safe as far as the unwanted contact between two droplets is concerned. Thus, simulation results provide information on critical parameters which are helpful in identifying unwanted situations within the DMFS. The settling times (defined as the time required for the response to remain within 2% of the steady-state value) obtained are 9.219 millisecond for K = 1 and 5.195 millisecond for K = 10. If the predetermined path of the droplet is such that there are changes in the direction along which it must move, then sufficient time should be allowed for the droplet to settle down in each destination cell before it is commanded again to move to the next destination cell along the path. The simulated settling time should be used as the period after which another actuation cycle can begin to move such a droplet (e.g., droplet A in Figure 2.4) from its current destination cell (e.g., cell (x5y4)) to an adjacent destination cell (e.g., cell (x5y5)). Thus, using the settling times obtained from simulation, the maximum allowable frequencies of actuating a droplet are found to be ~108 Hz and ~192 Hz for K = 1 and K = 10 respectively. The average speeds of a droplet are calculated by dividing the cell pitch by settling time and the speeds are found to be 16.3 cm/sec and 28.9 cm/sec for K = 1 and K = 10, respectively. 33 Figure 2.7: Simulation results showing droplet response (velocity) to a step command. Figure 2.8: Resistive forces against droplet motion. 0 2 4 6 8 10 12 14 16 18 20 -400 -200 0 200 400 600 800 1000 1200 1400 Time (millisecond) D ro p le t v e lo c it y ( m m /s e c ) K = 10 K = 1 0 2 4 6 8 10 12 14 16 18 20 -200 0 200 400 600 800 1000 Time (millisecond) R e s is ti v e f o rc e s ( m ic ro -N e w to n ) Fd Ff Fc 34 Figure 2.9: Resistive forces as fractions of total resistance. Figure 2.8 shows the variation of different resistive forces (for K = 1) as the droplet moves to the adjacent cell. Individual resistances as percentages of the total resistive force are shown in Figure 2.9. At very low velocity of the droplet contact-line friction is most dominant (71.85 %) and the drag force due to the filler-fluid is least significant (~0%). As the droplet attains speed, contributions of each of the resistive forces change greatly. After 1.13 milliseconds, the droplet velocity becomes maximal. At this point, the percentage contributions of resistance due to viscous shear, drag and contact-line are 5.67%, 79.88% and 14.46% respectively. The drag force dominates until the droplet reaches the adjacent cell. The contact-line friction starts to dominate again as the droplet speed decreases. The relation between the dynamic response of a droplet and geometric parameters of the DMFS has been studied. Simulations are performed by varying the electrode size, L (600 μm – 2000 μm), varying the gap between top and bottom plates, D (100 μm – 500 μm) and varying both L and D (200 μm – 600 μm) such that the L/D = 5. The rise time, settling time and percent overshoot are plotted against dimensionless L’ = L/Lmin and D’ = D/Dmin in Fig. 10, 11 and 12 respectively. It is assumed that the droplet radius is 5% greater than the size of the electrode and the droplet is in contact with both the top and bottom plate in each case of the simulation. The 0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 70 80 Time (millisecond) F ra c ti o n o f to ta l re s is ta n c e ( % ) Fd Ff Fc 35 total mass of the droplet and the resistance increase at greater rates with electrode size than with gap between two plates. Thus, the rise time increases at a faster rate with increasing L than with increasing D, shown in Figure 2.10. For similar reasons, the rise time increases at the fastest rate when both D and L are varied. Figure 2.11 shows that the settling time decreases at a higher rate with increasing L due to the fact that as the droplet becomes larger the response approaches that of a damped system. Interestingly, the settling time shows a local minimum for the range of values when both D and L are increased. This can be explained with the help of Figure 2.12 which shows that overshoot decreases at the fastest rate when both D and L are increased. With less overshoot and hence shorter duration of oscillations, the settling time decreases. With D>400 μm and L>2000 μm, the droplet response approaches that of a critically damped system and the settling time starts to increase again. Figure 2.10: Rise time as a function of dimensionless L’ and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm. 1 1.5 2 2.5 3 3.5 4 4.5 5 2 4 6 8 10 12 14 16 18 20 Dimensionless L' and D' R is e t im e ( m ill is e c o n d ) L varies, D = D nom D varies, L = L nom Both D & L vary, L/D = 5 36 Figure 2.11: Settling time as a function of dimensionless L’ and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm. Figure 2.12: Percentage overshoot as a function of dimensionless L’ and D’; L’=L/Lmin, D’=D/Dmin, Lnom=1500 μm, Dnom=300 μm. 1 1.5 2 2.5 3 3.5 4 4.5 5 5 10 15 20 25 30 35 40 45 50 55 Dimensionless L' and D' S e tt lin g t im e ( m ill is e c o n d ) L varies, D = D nom D varies, L= L nom Both D & L vary, L/D = 5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 20 25 30 35 40 Dimensionless L' and D' O v e rs h o o t, % L Varies , D=D nom D Varies , L=L nom Both D & L vary, L/D=5 37 2.2 Droplet sensing Traditional droplet position sensing utilizes both the upper and lower plates to measure the capacitance. This prohibits the integration of any other feature, which might add to the functionality of the DMFS, to the upper plate. The new method of capacitance measurement proposed here relies on the capacitance measurement between the electrodes only on the lower plate. 2.2.1 Coplanar capacitance A schematic of the side view of a droplet positioned between two electrodes is shown in Figure 2.13 (i). Electric field lines between the electrodes in the lower plate and the ground electrode in the upper plate are parallel over the entire area of the electrodes except in a small region near the midpoint. The equivalent parallel plate capacitances are shown in Figure 2.13 (ii). Figure 2.13: Electric field lines, equivalent capacitances and overlapped areas; (i) Electric field lines formed between the coplanar electrodes, (ii) Equivalent parallel plate capacitances, (iii) Top view of the droplet, showing areas of overlap on the two coplanar electrodes. CLD C RD C LS C RS C MD C MS A L AR G D Hydrophobic layer Electrode Dielectric layer Droplet (i) (ii) (iii) 38 Electric field lines originating from a small region of one electrode near the midpoint in the corresponding region of the other electrode. The equivalent capacitances due to these elliptic field lines inside the liquid and the solid dielectric layer, identified as and , are typically less than a picofarad. The total capacitance of the dielectric layer and the droplet between the two coplanar electrodes in lower plate is given by (2.8) where and are the equivalent capacitances due to the elliptic field lines in the droplet and the solid layer, respectively; is the equivalent capacitance of the series connected capacitances and ; is the equivalent relative permittivity of solid layers, is the relative permittivity of the solid layer, is the total thickness of the solid layers, is the height of the droplet; and are the areas of overlap on the right-side and left-side electrodes respectively. is given by ( ) ( )( ) (2.9) where is the overlap area on the right-side electrode normalized by the total area of overlap. Theoretically, the values of can range between 0 and 1, corresponding to the droplet positions at the centers of the left-side and the right-side electrodes. In practical situations, however, the droplet is usually large enough to have non-zero values of and at the initial and final position, and hence . The capacitance, , is a quadratic function of the area fraction, , and has the maximum value at corresponding to the droplet positioned at the midpoint between the two coplanar electrodes. As the droplet moves away from the midpoint towards either direction, the value of capacitance decreases. Equation (2.9) shows that varies linearly with the total overlap area on the coplanar electrodes. A larger droplet will form larger capacitance than a smaller droplet. It should be noted that due to the circular or elliptic shape, as observed in top-view, of the droplet, the total overlap area is not constant for the whole duration of translocation from one electrode to the adjacent one. The total overlap area remains constant except for the beginning and final parts of the travel distance equal to the length of initial droplet overlap on the adjacent electrodes. A droplet with smaller height generates higher capacitance since is inversely related to droplet height. 2.2.2 Numerical investigation Three dimensional finite element analyses were performed in COMSOL ® to investigate the variation of capacitance between two coplanar electrodes. Geometry of the model included 39 two electrodes, each 1.4 mm × 1.4 mm, the dielectric layer of thickness 1.23 µm and the droplet. These dimensions are chosen to represent those of a DMFS used in experiments. The inter- electrode gap is adjusted depending on the type of investigation. A portion of the electrode on each side of the two sensing electrodes is also incorporated so as to model the actual device more closely. Along the transverse direction, the dielectric layer is extended sufficiently beyond the droplet-air interface. In all simulations, the diameter of the cylindrical droplet of deionized water is 1.6 mm. The error in the capacitance due to the assumption of a 90 o contact angle is expected to be insignificant, since the dynamic contact angle during droplet motion typically varies from ~80 o to ~110 o . Since the thickness of the hydrophobic layer in typical designs is an order of magnitude lower than that of the dielectric layer in the lower plate, the hydrophobic layer is not modeled separately to avoid complexities in mesh generation. However, the relative permittivity of the dielectric layer is set equal to the equivalent permittivity calculated by considering the individual capacitances of cyanoethyl pullulan ( ) and Teflon ® connected in series. Moreover, the Teflon layer in the upper plate was neglected since the capacitance of this layer can also be considered as connected to the dielectric layer in series and the equivalent permittivity was assigned to the dielectric layer in the computational model. The capacitance between the coplanar electrodes is obtained by defining the governing physics as electrostatics and solving for the electric field distribution in the computational domain according to (2.10) where and are the permittivities of vacuum and material respectively, is the free charge per unit volume, and is the electric field and is the electric potential. The boundary conditions for the internal surfaces between two different materials are set to continuity of electric displacement field, . The coplanar electrodes for the computation of capacitance are defined as ports while the other electrodes are set to floating potentials. Likewise, the upper surfaces of the droplet and the surrounding medium are set to floating potentials implying that these surfaces attain virtually the same potential as that of the electrode in the upper plate. A zero charge boundary condition, defined as ̂ , is set for each of the outer surfaces of dielectric materials. The capacitance between coplanar electrodes is calculated according to (2.11) where is the potential difference between the electrodes and is the electrical energy stored in the domain. COMSOL ® calculates the stored energy according to | | (2.12) where denotes the entire computational domain in the model. 40 Capacitances were computed for droplet positions at 100 µm increments in either direction from the midpoint between the coplanar electrodes. Figure 2.14 shows the values of coplanar capacitance obtained from simulation as well as from Equation 2.9 as a function of the fraction of overlap area on the right-side electrode. Results verify that coplanar capacitance is indeed a quadratic function of the overlap-area fraction. In addition, the capacitances are significantly lower for a droplet of 80 µm height than those for a droplet of 40 µm height. The capacitances calculated using the analytical model follows closely the trend of those from a finite element analysis, yet the analytical model fails to capture a small portion of the total capacitance corresponding to the contributions of fringe fields in the droplet and in the dielectric layer between the coplanar electrodes. The value of capacitance, unexplained by the analytical model, ranges from ~400 fF to ~650 fF. The effect of inter-electrode gap was also investigated and the results are shown in Figure 2.15 for three inter-electrode gaps while the droplet height was kept constant at 80 µm. The coplanar capacitance is increased when a narrower gap between the electrodes is used. This is evident more in the results obtained from the numerical analysis than those from the analytical model. A 14% increase in the total capacitance is achieved by reducing the gap from 145 µm to 20 µm. The major contribution in this change is from the capacitances corresponding to the fringing electric field lines. Since these capacitances are not accounted for in Equation 2.9, the change in capacitance due to change in inter-electrode gap is significant only when the droplet is near the midpoint between the electrodes. This change in capacitance Figure 2.14: Capacitance between coplanar electrodes for two droplet heights 0 1 2 3 4 5 6 7 0 0.2 0.4 0.6 0.8 1 C ap ac it an ce , p F Area fraction (fAR) Model (D: 40 µm) Numerical (D: 40 µm) Model (D: 80 µm) Numerical (D: 80 µm) 41 Figure 2.15: Capacitance between coplanar electrodes for three inter-electrode gaps Figure 2.16: Maximum capacitance between coplanar electrodes in a DMFS with inter-electrode gap of 60 µm and droplet height of 80 µm. originates from the increase in the total overlap area as a result of a smaller gap. The dependence of coplanar capacitance on the total area of droplet overlap on the adjacent electrodes is illustrated in Figure 2.16. Coplanar capacitances were computed for droplets of different volumes by positioning them at the midpoint between the electrodes. Simulations were performed 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.2 0.4 0.6 0.8 1 C ap ac it an ce , p F Area fraction (fAR) Model (G: 20 µm) Numerical (G: 20 µm) Model (G: 60 µm) Numerical (G: 60 µm) Model (G: 145 µm) Numerical (G: 145 µm) 0 50 100 150 200 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 Droplet volume, nl C ap ac it an ce , p F Droplet area, mm2 Model Numerical 42 considering an inter-electrode gap of 60 µm and a droplet height of 80 µm. Results verify that the maximum capacitance between two coplanar electrodes increases with droplet size. However, the change in maximum capacitance occurs at a high rate for droplets with diameters smaller than the electrode size. 2.2.3 Experimental 2.2.3.1 Sensing electronics Capacitance measurement was performed by counting the resonant frequency of an oscillator. The stable and sensitive oscillator circuit was formed by three Schmitt trigger inverters out of the six in a MM74HC14N IC, two 2 KΩ resistors and the capacitance formed between the coplanar electrodes. The frequency of oscillation with 50% duty cycle is given by (Fairchild Semiconductor Corporation) (2.13) Thus, the capacitance of the system can be calculated based on the knowledge of the resonant frequency and the resistor. The IC was connected to a 5 Vdc output from a PXI 4110 power supply and the frequency was measured through the PXI 6224 data acquisition (DAQ) system, shown in Figure 2.17. The sampling time and the number of samples for the counters in the DAQ Figure 2.17: Schematic diagram showing the capacitance measurement circuitry 5 V VCC 2 KΩ 2 KΩ DAQ (Frequency counter) PXI 6224 MM74HC14N LabVIEW program 43 were configured through a LabVIEW program. Figure 2.18 shows the experimental setup used to verify the efficacy of the proposed sensing method. Droplets of the desired volume were dispensed at appropriate positions using the PipeJet P9 Nanoliter Dispenser. Images of droplets were acquired using HiSpec 5 monochromatic camera with a resolution of 1696 × 1710 and each pixel is 8 µm × 8 µm. The areas of overlap on the side electrodes were calculated through image analysis in MATLAB. In each top-view image of the, the meniscus was identified first and then the total number of pixels were calculated. The accuracy of meniscus detection in MATLAB was 1~2 pixels, determined by enlarging the region of the image containing the meniscus, corresponding to a lateral accuracy of 4~8 µm considering the magnification by the lens. This results in an error less than 2% in the calculation of overlap area. Figure 2.18: Photograph of the experimental setup for capacitance measurement 2.2.3.2 Results Investigation of the capacitance between coplanar electrodes was performed on DMFS fabricated following the procedure as outlined in chapter 5. Droplets of approximately equal volume were deposited using the droplet dispenser at various positions between two adjacent electrodes, shown in Figure 2.19. Figure 2.20 shows the capacitance measured in a DMFS with a gap of 40 µm between the upper and lower plates. The values of capacitance shown are obtained by subtracting the parasitic capacitance from the capacitances measured in presence of droplets. The parasitic capacitance results from the capacitances between the connecting wires, the electrodes and the neighboring substances and the capacitance due to the dielectric layer in the inter-electrode gap. Results verify Equation 2.9 that the coplanar capacitance is a quadratic function of the fraction of overlap of the droplet. A maximum value of ~ 18 pF results when the droplet is at the midpoint between the adjacent electrodes. Although the variability in experimental data is quite high, the dominant characteristic of data can be explained by the Sensing electronics NI PXI Controller Digital microfluidic device DAQ connector LabVIEW Interface High-speed camera 44 Figure 2.19: Images of droplet at five different positions between the two adjacent coplanar electrodes connected to measure capacitance. Electrode size: 1.4 mm × 1.4 mm, Inter-electrode gap: 60 µm, Droplet height: 80 µm. 100 µm 100 µm 100 µm 100 µm 100 µm 45 Figure 2.20: Measured capacitance in a DMFS with 40 µm gap between the upper and lower plates. analytical model given by Equation 2.9. The capacitances obtained from the analytical model were calculated based on the overlap areas in the images corresponding to the experimental data points. As expected, the variability of data obtained from the analytical model is low compared to that of the experimental data. The capacitance measurement is highly sensitive to the tolerance of circuit elements, imperfections in material property as well as geometry of the device and noise from the environment external to the active area of measurement. In a microdevice involving a droplet of volume less than a microliter, the capacitance measurement is especially sensitive to the condition of the instrumentation as well as of the device, and the measurement is more susceptible to noise. As such, variations were unavoidable even though the setup was prepared according to guidelines for minimizing measurement error. The measured frequency often varied within a few seconds even though the position of the droplet was not changed. This variation was not always unidirectional disproving the reasoning that only the reduction of volume due to evaporation results in the change in system capacitance. Although evaporation could affect the measurements, a significant change in the resonant frequency due to evaporation in our device required a much longer period than a few seconds. Moreover, the variations in experimental data originated from those of dispensed volumes of droplets. Investigation of the effect of increasing 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1 C ap ac it an ce , p F Area fraction (fAR) Experiment Model 46 the droplet height was conducted by measuring the capacitances at different droplet positions between the coplanar electrodes. It is worth mentioning that the scatter in data points for the model originates from the fact that measured capacitance depends on the volume of the droplet. This means that droplets of different sizes will result in different capacitances even though the overlap area-fractions are equal. Figure 2.21 shows the capacitances measured for a droplet height of 80 µm along with those obtained from analytical model. The measured values of capacitance are significantly lower than those for a device with a plate gap of 40 µm. The analytical model results in overestimated values of capacitance which indicates the possibility of a limit of droplet height within which the analytical equation is applicable. The experimental data shows skewness with maximum capacitance corresponding to droplet position at an offset from the midpoint. The most probable source of this skewness is the gradual decrease in the thickness of the dielectric layer over the right-side electrode. Since the dielectric layer was deposited by spin coating, the thickness of the layer was not uniform all over the device surface. However, the variability of data points is lower than that for 40 µm plate spacing. Figure 2.21: Measured capacitance in a DMFS with 80 µm gap between the upper and lower plates. The relation between coplanar capacitance and the size of the droplet was studied by depositing droplets of different volume at the midpoint between the electrodes, shown in Figure 2.22. The measured capacitances of droplets of different volume are shown in Figure 2.23 to verify the dependence of capacitance on the total area of overlap on the electrodes. Droplets were positioned at the midpoint between the coplanar electrodes having an inter-electrode gap of 60 µm while the gap between the upper and lower plates was fixed at 80 µm. Results validate the 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 C ap ac it an ce , p F Area fraction (fAR) Experiment Model 47 theory, as discussed in previous sections, that the capacitance between the coplanar electrode for a given position of the droplet is linearly dependent on the total area of overlap. In other words, the value of maximum capacitance corresponding to the droplet at midpoint is higher for larger droplets. It is worth noting that obtaining the accurate value of the maximum capacitance is quite difficult by placing the droplet manually at the midpoint. Any misalignment of the droplet with respect to the midpoint results in a capacitance lower than the maximum value. The maximum value of capacitance increases with the total droplet area at a high rate until up to ~1.5 mm 2 . For droplets having diameters greater than the size of an electrode, the droplet overlap area increases at a lower rate owing to larger radii of curvature. Figure 2.22: Droplets of different volumes placed at the center of two coplanar. Electrode size: 1.4 mm × 1.4 mm, Inter-electrode gap: 60 µm, Droplet height: 80 µm. 100 µm 100 µm 100 µm 48 Figure 2.23: Maximum capacitance measured when the droplet is at the midpoint between electrodes (1.4 mm 1.4 mm); Inter-electrode gap: 60 µm, Droplet height: 80 µm. This section presented a novel method of droplet position sensing by measuring the capacitance between two coplanar electrodes. The total capacitance consists of a network of capacitances due to the presence of the droplet and the overlapped portions of the dielectric and hydrophobic layers. The capacitance is a nonlinear function of the position of the droplet and a maximum capacitance is developed when the droplet is at the midpoint between the two adjacent electrodes. Results of simulation performed in a finite element-based software package, COMSOL ® , verify that the analytical model predicts the capacitance very well. Experiments were conducted to test the new method of capacitance measurement as well as to verify the analytical model. Experimental results verify that the total capacitance is a nonlinear function of the droplet position and is maximal when the droplet is at the midpoint. Moreover, both numerical and experimental results show that the total capacitance depends on the diameter and height of the droplet, and the gap between the electrodes. This new method of droplet position sensing through capacitance measurement between electrodes on the lower plate significantly enhances the functionality of a DMFS by setting the upper plate free to accommodate other features, e.g. a photodetector. Since the proposed method relies on the droplet overlap on the adjacent electrodes, a feedback control system for splitting a droplet can be developed by measuring two coplanar capacitances from the three electrodes involved in the splitting process. In the traditional method of droplet sensing through capacitance measurement, both the upper and lower plates are electrically connected and hence, adding any desirable feature to the upper plate is impossible. Moreover, the capacitance measurement for one operation might affect the measurement for 56 57 58 59 60 61 62 63 0 0.5 1 1.5 2 2.5 C ap ac it an ce , p F Droplet area, mm2 49 another operation at a nearby location due to the common connection to the upper plate. This is especially important in sensing liquid accumulation over the electrodes during splitting. Therefore, the measurement of capacitance between coplanar electrodes is particularly advantageous for feedback control of splitting, which is the main motivation for the development of new capacitance measurement method. The applicability and effectiveness of this method in the control of splitting will be verified through experiments in future research. 50 2.3 EWOD droplet actuation As discussed in chapter 1, EWOD is the most suitable actuation method for manipulating droplets on a planar surface and capable of performing all the basic fluidic operations efficiently. Low power consumption, ease of fabrication and programmable generation of control signals are the main advantages of EWOD-based DMFS. Moreover, splitting a droplet, which is the focus of this thesis, is not feasible with other actuation methods. Therefore, EWOD is chosen as the most appropriate method of actuation for splitting droplets. However, the investigation of the underlying physics of and the parameters affecting the EWOD is fundamental to the implementation and proper use in a DMFS to control the complex process of droplet splitting accurately. 2.3.1 EWOD force Figure 2.24 shows the side view of a conductive droplet in an EWOD driven DMFS. It is assumed that the curvature of the spherical surface of the droplet is small and hence the droplet between the two hydrophobic surfaces can be approximated by a cylinder with a height equal to the gap between two plates. Furthermore, the deviation of the footprint of the droplet from circular shape during transition is also assumed to be negligible. The two assumptions are justified by the fact that most practical systems have small gap between two plates and the contact angles of droplets on commonly used hydrophobic surfaces are around 90 0 . The droplet of aqueous solution is considered as a perfect conductor. When the electrode on the bottom plate, over which the droplet is residing, and that on the top plate are electrically grounded and an adjacent electrode is energized by applying a voltage, a capacitor is formed between the droplet and the energized electrode. The materials of both hydrophobic and dielectric layers act as the dielectric layer of the capacitor. Although the hydrophobic layer between the droplet and the top ground electrode forms another capacitor, the capacitance is very high compared to the bottom one as the thickness of the hydrophobic layer is usually very small compared to that of the dielectric layer on the bottom plate. As a result, the potential drop across the top hydrophobic layer is negligible and almost all of the applied voltage is dropped at the bottom capacitor. In other words, the droplet can be considered as the virtual ground of the bottom capacitor. As the droplet is usually quite flat in typical designs, the fringe-field effects of the parallel-plate capacitor are ignored in this paper. 51 Figure 2.24: Capacitance formed between the conductive droplet and the energized electrode. The effective area of the capacitor shown in Figure 2.24 is identified in the top view. The energy stored in the system is not minimal since the surface area of the capacitor is not maximal. Thus, the system will try to reach the minimum energy state by inducing a force on the movable conductor and thereby, maximize the area on the activated electrode on which the droplet resides. According to the above discussion, the EWOD force on the droplet is given by ( ) (2.14) where V is the applied voltage, x is the droplet position, td is the thickness of the dielectric layer, th is the thickness of the hydrophobic layer, εrd is the dielectric constant of dielectric layer, εrh is the dielectric constant of hydrophobic layer, εo is the permittivity of vacuum and Ap is the area of the droplet over the activated electrode. According to this model, a certain amount of overlap of the droplet towards the activated electrode is necessary for the generation of a nonzero driving force. The relative size of the droplet with respect to the electrode can vary depending on the requirements of the assay operation, accuracy and precision of the droplet generation and any other intermediate manipulation of the droplet, such as division and merging. On the other hand, the overlapped area, Ap, is a function of the droplet position as well as the size of the droplet relative to that of the electrode. More precisely, for a given size of the droplet, Ap changes at different rates at different positions of the droplet. Different rate of change of Ap results in V Droplet droplet Variable area capacitor Capacitor area 52 different magnitude and direction of the actuating force. In general, the droplet size with respect to that of the square electrode can form a total of five distinct configurations. Three primary configurations can be identified as a droplet with a diameter (i) greater than the length of the electrode but less than the diagonal length of the electrode, (ii) equal to the diagonal length and (iii) greater than the diagonal length. A closer investigation of configuration (i), as depicted in Figure 2.25 (i) reveals that this configuration can appear in three different configurations. The relative magnitude of the dimensions p and q determines the sequence of different magnitudes and directions of the actuating force as the droplet moves from its current electrode to the adjacent electrode. If the droplet diameter is closer to the diagonal length of the electrode, p is greater than q; if the diameter is closer to the length of the electrode, p is less than q; and finally, for r = 5L/8, where r is the radius of the droplet and L is the length of the electrode, p and q are equal. Hence, the droplet size can be classified into five groups: (1) L/2L/√2. Figure 2.25 (i) shows a droplet (L/2L/sqrt(2) 0 5 10 15 20 25 30 35 40 45 50 -2 0 2 4 6 8 10 12 Time (milliseconds) V e lo c it y ( c m /s e c .) L/2L/sqrt(2) 0.4 20 L/2L/√2 0.8 1.2 1.6 0 0 40 P o si ti o n ( m m ) Time (milliseconds) 0 4 8 12 -2 0 20 40 Time (milliseconds) V el o ci ty ( cm /s ) L/2L/√2 59 also shows successful continued motion of droplets provided that the period in each cycle allowed sufficient time for the droplet to have certain amount of overlap on the next adjacent electrode. Figure 2.30: Electrowetting driving force for droplets of different sizes. Figure 2.31: Resistive forces against droplet motion. Figure 2.32: Dynamic response (position) of droplets of different sizes due to successive actuation of electrodes. Figure 2.33: Droplet transition times for different actuation voltages. 0 5 10 15 20 25 30 35 40 45 50 -10 0 10 20 30 40 50 60 D ri v in g f o rc e ( m ic ro n e w to n ) Time (milliseconds) L/2L/sqrt(2) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -5 Time (sec.) R e s is ti v e F o rc e s ( N ) F c F d F f 0 50 100 150 200 250 0 1 2 3 4 5 6 7 8 P o s it io n ( m il li m e te r) Time (milliseconds) L/2L/sqrt(2) 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 140 150 Voltage (volts) T ra n s it io n t im e ( m il li s e c o n d s ) L/2L/sqrt(2) D ri v in g f o rc e (µ N ) 60 50 40 30 20 10 0 -10 L/2L/√2 Time (milliseconds) 0 10 20 30 40 50 R es is ti v e fo rc e (µ N ) 1 2 3 4 0 -0.5 0 10 20 30 Time (milliseconds) Fc Fd Ff P o si ti o n ( m m ) 8 7 5 4 3 2 1 6 0 0 50 100 Time (milliseconds) 150 200 250 T ra n si ti o n t im e (m il li se co n d s) 140 120 100 80 60 40 20 0 30 50 70 90 Voltage (V) L/2L/√2 L/2L/√2 60 The actuation voltage, geometric parameters and material properties are related to the driving as well as the resistive forces which in turn affects the dynamic response of an individual droplet and the overall throughput of the chemical/biological analysis. Experimental investigation of all the effects and interactions will be expensive and time consuming. In this study, several simulations are performed to identify how the droplet response is influenced by actuation voltage, spacing between the top and bottom plates, electrode size, dielectric thickness and dielectric constant and the results are shown in Figures 2.33, 2.34, 2.35, 2.36 and 2.37. The transition time decreases with higher voltage, shown in Figure 2.33, since the driving force is quadratically related to the actuation voltage. For weaker driving force, corresponding to lower voltages, the variations in transition times among droplets of different sizes are significant. The variations in transition times among droplets of different sizes are not significant for actuation voltages greater than 70 volts. Figure 2.34 shows the transition times of droplets of different sizes as a function of the spacing between two plates. Viscous friction inside the droplet is inversely related to the plate spacing resulting in higher transition times for smaller spacing. Although the drag force due to the filler-fluid increases with plate spacing, the transition times are not affected as the drag force is the weakest resistive force. However, the droplet mass also increases with plate spacing and for larger spacing the transition times increase. One of the crucial geometrical parameters in a DMFS which should be determined for optimal performance of the device is electrode size. Figure 2.35 shows the variations of droplet transition times with the size of the electrode. Droplet sizes are changed so that the percentages of overlap on the adjacent electrodes are the same for all the electrode sizes considered in the simulation. The plate spacing is also changed proportionately in order to simulate practical systems. The results show that the response is faster with smaller electrodes because of smaller droplets and resulting lower resistive forces. As the variations in droplet size relative to a given electrode size is greater for larger electrodes, the variations in transition times increases with electrode size. The thickness of the dielectric layer is another design parameter that should be carefully selected. Equation 2.14 suggests that the driving force increases with thinner dielectric layer. Figure 2.36 shows that the transition times are less for smaller thicknesses of the dielectric layer than those for thicker dielectric layers. The variations of transition times among different droplet sizes are higher for thicker dielectric layers. Although higher driving force can be generated with thinner dielectric layer, the dielectric breakdown strength should also be considered so that there is no electric short between the electrode and the droplet during operation. The electrowetting driving force increases with dielectric constant of the material in the dielectric layer. 61 Consequently, the droplet transition time is shorter for higher dielectric constant, shown in Figure 2.37. For low dielectric constant, corresponding to weak driving force, the variations in the transition times of droplets of different sizes are significant compared to that with high dielectric constant. However, the reduction in transition time becomes insignificant with higher dielectric constants. Figure 2.34: Droplet transition times for different plate spacing. Figure 2.35: Droplet transition times for different electrode sizes. Figure 2.36: Droplet transition times for different dielectric thicknesses. Figure 2.37: Droplet transition times for different dielectric constants. Equation 2.14 can be used only when the applied voltage is DC. Application of AC voltage results in a lower actuation force due to the voltage drop across the droplet. The intensity of electric field generated inside the droplet depends on the conductivity of the liquid as well as the frequency of applied voltage and can be explained with the help of complex permittivity, defined as (Chatterjee et al. 2006) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 20 30 40 50 60 70 80 90 Plate spacing (mm) T ra n s it io n t im e ( m ill is e c o n d s ) L/2L/sqrt(2) 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Electrode size (mm) T ra n s it io n t im e ( s e c o n d s ) L/2L/sqrt(2) 0.5 1 1.5 2 2.5 3 0 20 40 60 80 100 120 140 160 180 Dielectric thickness (micrometer) T ra n s it io n t im e ( m il li s e c o n d s ) L/2L/sqrt(2) 0 5 10 15 0 20 40 60 80 100 120 140 153 Dielectric constant T ra n s it io n t im e ( m ill is e c o n d s ) L/2L/sqrt(2) T ra n si ti o n t im e (m il li se co n d s) 20 L/2L/√2 80 100 120 140 40 60 0 0 5 10 15 Dielectric constant 80 120 40 T ra n si ti o n t im e (m il li se co n d s) 160 0 0.5 1 1.5 2 2.5 3 Dielectric thickness (µm) L/2L/√2 30 10 L/2L/√2 50 70 90 T ra n si ti o n t im e (m il li se co n d s) 0.1 0.3 0.5 0.7 0.9 Plate spacing (mm) 40 80 120 0 0.4 0.8 1.2 1.6 2 r=5L/8 Electrode size (mm) r=L/√2 r>L/√2 L/2