Cho, S. K., Moon, H., and Kim, C. J., 2003, “Creating, Transporting, Cutting, and Merging Liquid Droplets by Electrowetting-Based Actuation for Digital Microfluidic Circuits,” J. Microelectromech. Syst.
[CrossRef], 12 (1), pp. 70–80.
Cooney, C. G., Chen, C.-Y., Nadim, A., and Sterling, J. D., 2006, “Electrowetting Droplet Microfluidics on a Single Planar Surface,” Microfluid. Nanofluid.
[CrossRef], 2 (5), pp. 435–446.
Lee, J., Moon, H., Fowler, J., Kim, C. J., and Schoellhammer, T., 2001, “Addressable Micro Liquid Handling by Electric Control Of Surface Tension,” "Proceedings of the IEEE International Conference MEMS", Interlaken, Switzerland, Jan., pp. 499–502.
Pollack, M. G., Fair, R. B., and Shenderov, A. D., 2000, “Electrowetting-Based Actuation of Liquid Droplets for Microfluidic Applications,” Appl. Phys. Lett.
[CrossRef], 77 (11), pp. 1725–1726.
Pollack, M. G., Shenderov, A. D., and Fair, R. B., 2002, “Electrowetting-Based Actuation of Droplets for Integrated Microfluidics,” Lab Chip
[CrossRef], 2 (2), pp. 96–101.
Shapiro, B., Moon, H., Garrell, R. L., and Kim, C. J., 2003, “Equilibrium Behavior of Sessile Drops Under Surface Tension, Applied External Fields, and Material Variations,” J. Appl. Phys.
[CrossRef], 93 (9), pp. 5794–5811.
Wang, K. L., and Jones, T. B., 2005, “Electrowetting Dynamics of Microfluidic Actuation,” Langmuir
[CrossRef], 21 , pp. 4211–4217.
Charkrabarty, K., and Zeng, J., 2006, "Design Automation Methods and Tools for Microfluidics-Based Biochips", Springer, New York.
Baird, E., and Mohseni, K., 2008, “Digitized Heat Transfer: A New Paradigm for Thermal Management of Compact Micro-Systems,” IEEE Trans. Compon. Packag. Technol., 31 (1), pp. 143–151.
Mohseni, K., 2005, “Effective Cooling of Integrated Circuits Using Liquid Alloy Electrowetting,” "Proceedings of the Semiconductor Thermal Measurement, Modeling, and Management Symposium (SEMI-Therm)", San Jose, CA, Mar. 15–17. IEEE.
Mohseni, K., and Baird, E., 2007, “Digitized Heat Transfer Using Electrowetting on Dielectric,” Nanoscale Microscale Thermophys. Eng., 11 (1&2), pp. 99–108.
Mohseni, K., and Dolatabadi, A., 2006, “An Electrowetting Microvalve: Numerical Simulation,” Ann. N.Y. Acad. Sci.
[CrossRef], 1077 (1), pp. 415–425.
Dolatabadi, A., Mohseni, K., and Arzpeyma, A., 2006, “Behaviour of a Moving Droplet Under Electrowetting Actuation, Numerical Simulation,” Can. J. Chem. Eng., 84 (1), pp. 17–21.
Chang, Y.-J., Mohseni, K., and Bright, V., 2007, “Fabrication of Tapered SU-8 Structure and Effect of Sidewall Angle for a Variable Focus Microlens Using EWOD,” Sens. Actuators, A, 136 (2), pp. 546–553.
Cho, S. K., Fan, S. K., Moon, H., and Kim, C. J., 2002, “Towards Digital Microfluidic Circuits: Creating, Transporting, Cutting, and Merging Liquid Droplets by Electrowetting-Based Actuation,” in "Technical Digest. MEMS, Proceedings 15th IEEE International Conference MEMS", pp. 32–35.
Fair, R. B., Srinivasan, V., Ren, H., Paik, P., and Pollack, M. G., 2003, “Electrowetting-Based On-Chip Sample Processing for Integrated Microfluidics,” Tech. Dig. - Int. Electron Devices Meet., 2003 , pp. 32.5.1–32.5.4.
Moon, H., Cho, S. K., Garrell, R., and Kim, C. J., 2002, “Low Voltage Electrowetting-On-Dielectric,” J. Appl. Phys.
[CrossRef], 92 (7), pp. 4080–4087.
Deval, J., Tabeling, P., and Ho, C. M., 2002, “A Dielectrophoretic Chaotic Mixer,” "15th IEEE International Conference on MEMS (MEMS 2002)", Las Vegas, NV, pp. 36–39.
Gascoyne, P. R. C., Vykoukal, J. V., Schwartz, J. A., Anderson, T. J., Vykoukal, D. M., Current, K. W., McConaghy, C., Becker, F. F., and Andrews, C., 2004, “Dielectrophoresis-Based Programmable Fluidic Processors,” Lab Chip
[CrossRef], 4 (4), pp. 299–309.
Jones, T. B., 2002, “On the Relationship of Dielectrophoresis and Electrowetting,” Langmuir
[CrossRef], 18 , pp. 4437–4443.
Jones, T. B., Fowler, J. D., Chang, Y. S., and Kim, C. J., 2003, “Frequency-Based Relationship of Electrowetting and Dielectrophoretic Liquid Microactuation,” Langmuir
[CrossRef], 19 , pp. 7646–7651.
Jones, T. B., and Wang, K. L., 2004, “Frequency-Dependent Electromechanics of Aqueous Liquids, Electrowetting and Dielectrophoresis,” Langmuir
[CrossRef], 20 , pp. 2813–2818.
Walker, S. W., and Shapiro, B., 2006, “Modeling the Fluid Dynamics of Electrowetting on Dielectric (EWOD),” J. Microelectromech. Syst.
[CrossRef], 15 (4), pp. 986–1000.
Singh, P., and Aubry, N., 2007, “Transport and Deformation of Droplets in a Microdevice Using Dielectrophoresis,” Electrophoresis
[CrossRef], 28 , pp. 644–657.
Bahadur, V., and Garimella, S. V., 2006, “An Energy-Based Model for Electrowetting-Induced Droplet Actuation,” J. Micromech. Microeng., 11 (8), pp. 1994–1503.
Baird, E., Young, P., and Mohseni, K., 2007, “Electrostatic Force Calculation for an Ewod-Actuated Droplet,” Microfluid. Nanofluid.
[CrossRef], 3 (6), pp. 635–644.
Buehrle, J., Herminghaus, S., and Mugele, F., 2003, “Interface Profiles Near Three-Phase Contract Lines in Electric Fields,” Phys. Rev. Lett.
[CrossRef], 91 (4), p. 208301.
Kang, K. H., 2002, “How Electrostatic Fields Change Contact Angle in Electrowetting,” Langmuir
[CrossRef], 18 (26), pp. 10318–10322.
Vallet, M., Vallade, M., and Berge, B., 1999, “Limiting Phenomena for the Spreading of Water on Polymer Films by Electrowetting,” Eur. Phys. J. B
[CrossRef], 11 (4), pp. 583–591.
Jackson, J. D., 1998, "Classical Electrodynamics", Wiley, New York.
Landau, L. D., Lifshitz, E. M., and Pitaevskii, L. P., 1984, "Electrodynamics of Continuous Media", 2nd ed., Pergamon, New York, Vol. 8 .
Saville, D. A., 1984, “Electrohydrodynamics: The Taylor–Melcher Leaky-Dielectric Model,” Annu. Rev. Fluid Mech.
[CrossRef], 29 , pp. 27–64.
For the electrostatic approximation to apply, the characteristic time scale for electric phenomena, τ=ϵ=σ must be small. Note that τ is the ratio of dielectric permeability to conductivity of the medium. For the microfluidic applications considered here, this condition will usually be valid. For example, pure water has a electrical relaxation time of ≈10−4 and a hydrodynamic time scale of ≈0.045. See (
45) for more details.
Penfield, P. A., and Haus, H. A., 1967, "Electrodynamics of Moving Media", MIT, Cambridge.
Stratton, J. A., 1941, "Electromagnetic Theory", McGraw-Hill, New York.
Woodson, H. H., and Melcher, J. R., 1968, "Electromechanical Dynamics, Part I: Discrete Systems", Wiley, New York.
Bobbio, S., 2000, "Electrodynamics of Materials: Forces, Stresses, and Energies in Solids and Fluids", Academic, New York.
Melcher, J. R., 1981, "Continuum Mechanics", MIT, Cambridge.
Woodson, H. H., and Melcher, J. R., 1968, "Electromechanical Dynamics, Part II: Fields, Forces, and Motion", Wiley, New York.
Woodson, H. H., and Melcher, J. R., 1968, "Electromechanical Dynamics, Part III: Elastic and Fluid Media", John, New York.
Mohseni, K., and Baird, E., 2007, “A Unified Velocity Model for Digital Microfluidics,” Nanoscale Microscale Thermophys. Eng., 11 (1&2), pp. 109–120.
If the droplet is initially charged or if it is short cut to the electrodes on one side of the channel while isolated from the electrodes on the other side, there will be another source of force on the droplet represented locally by ρfE. Our approach here can be easily extended to this case as well.
Unless the droplet is isolated only from the electrodes on one side of the channel. In this case the droplet stays at the voltage of the electrodes on the other side of the channel.
Holst, T. L., 1977, “Numerical Solution of Axisymmetric Boattail Flow Fields With Plume Simulators,” "15th Aerospace Sciences Meeting and Exhibit", Los Angeles, CA, Jan. 24–26, Paper No. AIAA 77-224.
Melcher, J. R., and Taylor, G. I., 1969, “Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses,” Annu. Rev. Fluid Mech.
[CrossRef], 1 , pp. 111–146.