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Iterative dipole moment method for calculating dielectrophoretic forces of particle-particle electric field interactions

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Abstract

Dielectrophoresis (DEP) is one of the most popular techniques for bio-particle manipulation in microfluidic systems. Traditional calculation of dielectrophoretic forces of single particle based on the approximation of equivalent dipole moment (EDM) cannot be directly applied on the dense particle interactions in an electrical field. The Maxwell stress tensor (MST) method is strictly accurate in the theory for dielectrophoretic forces of particle interaction, but the cumbersome and complicated numerical computation greatly limits its practical applications. A novel iterative dipole moment (IDM) method is presented in this work for calculating the dielectrophoretic forces of particle-particle interactions. The accuracy, convergence, and simplicity of the IDM are confirmed by a series of examples of two-particle interaction in a DC/AC electrical field. The results indicate that the IDM is able to calculate the DEP particle interaction forces in good agreement with the MST method. The IDM is a purely analytical operation and does not require complicated numerical computation for solving the differential equations of an electrical field while the particle is moving.

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References

  1. Jones, T. B. Electromechanics of Particles, Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  2. Morgan, H. and Green, N. G. AC Electrokinetics: Colloids and Nanoparticles, Research Studies Press, Hertfordshire (2003)

    Google Scholar 

  3. Kang, Y. and Li, D. Electrokinetic motion of particles and cells in microchannels. Microfluidics and Nanofluidics, 6(4), 431–460 (2009)

    Article  Google Scholar 

  4. Pohl, H. A. Dielectrophoresis: the Behavior of Neutral Matter in Nonuniform Electric Fields, Cambridge University Press, Cambridge (1978)

    Google Scholar 

  5. Aubry, N. and Singh, P. Control of electrostatic particle-particle interactions in dielectrophoresis. Europhysics Letters, 74(4), 623–629 (2006)

    Article  Google Scholar 

  6. Kumar, S. and Hesketh, P. J. Interpretation of ac dielectrophoretic behavior of tin oxide nanobelts using Maxwell stress tensor approach modeling. Sensors and Actuators B: Chemical, 161(1), 1198–1208 (2012)

    Article  Google Scholar 

  7. Kang, K. H. and Li, D. Dielectric force and relative motion between two spherical particles in electrophoresis. Langmuir, 22(4), 1602–1608 (2006)

    Article  MathSciNet  Google Scholar 

  8. House, D. L., Luo, H., and Chang, S. Numerical study on dielectrophoretic chaining of two ellipsoidal particles. Journal of Colloid and Interface Science, 374(1), 141–149 (2012)

    Article  Google Scholar 

  9. Ai, Y., Beskok, A., Gauthier, D. T., Joo, S. W., and Qian, S. DC electrokinetic transport of cylindrical cells in straight microchannels. Biomicrofluidics, 3(4), 044110 (2009)

    Article  Google Scholar 

  10. Ai, Y., Joo, S.W., Jiang, Y., Xuan, X., and Qian, S. Transient electrophoretic motion of a charged particle through a converging-diverging microchannel: effect of direct current-dielectrophoretic force. Electrophoresis, 30(14), 2499–2506 (2009)

    Article  Google Scholar 

  11. Ai, Y., Park, S., Zhu, J., Xuan, X., Beskok, A., and Qian, S. DC electrokinetic particle transport in an L-shaped microchannel. Langmuir, 26(4), 2937–2944 (2009)

    Article  Google Scholar 

  12. Ai, Y. and Qian, S. DC dielectrophoretic particle-particle interactions and their relative motions. Journal of Colloid and Interface Science, 346(2), 448–454 (2010)

    Article  Google Scholar 

  13. Xie, C., Chen, B., Ng, C. O., Zhou, X., and Wu, J. Numerical study of interactive motion of dielectrophoretic particles. European Journal of Mechanics, B: Fluids, 49, 208–216 (2015)

    Article  MathSciNet  Google Scholar 

  14. Kang, S. and Maniyeri, R. Dielectrophoretic motions of multiple particles and their analogy with the magnetophoretic counterparts. Journal of Mechanical Science and Technology, 26(11), 3503–3513 (2012)

    Article  Google Scholar 

  15. Hossan, M. R., Dillon, R., Roy, A. K., and Dutta, P. Modeling and simulation of dielectrophoretic particle-particle interactions and assembly. Journal of Colloid and Interface Science, 394, 619–629 (2013)

    Article  Google Scholar 

  16. Kang, S. Two-dimensional dipolophoretic motion of a pair of ideally polarizable particles under a uniform electric field. European Journal of Mechanics, B: Fluids, 41, 66–80 (2013)

    Article  MathSciNet  Google Scholar 

  17. Kurgan, E. Stress calculation in two-dimensional DC dielectrophoresis. Przeglad Elektrotechniczny, 87, 107–110 (2011)

    Google Scholar 

  18. Kurgan, E. Comparison of different force calculation methods in DC dielectrophoresis. Przeglad Elektrotechniczny, 88, 11–14 (2012)

    Google Scholar 

  19. Washizu, M. and Jones, T. Multipolar dielectrophoretic force calculation. Journal of Electrostatics, 33(2), 187–198 (1994)

    Article  Google Scholar 

  20. Washizu, M. and Jones, T. B. Dielectrophoretic interaction of two spherical particles calculated by equivalent multipole-moment method. IEEE Transactions on Industry Applications, 32(2), 233–242 (1996)

    Article  Google Scholar 

  21. La Magna, A., Camarda, M., Deretzis, I., Fisicaro, G., and Coffa, S. Coupled Monte Carlo-Poisson method for the simulation of particle-particle effects in dielectrophoretic devices. Applied Physics Letters, 100(13), 134104 (2012)

    Article  Google Scholar 

  22. Lee, D. H., Yu, C., Papazoglou, E., Farouk, B., and Noh, H. M. Dielectrophoretic particle-particle interaction under AC electrohydrodynamic flow conditions. Electrophoresis, 32(17), 2298–2306 (2011)

    Google Scholar 

  23. Ai, Y., Zeng, Z., and Qian, S. Direct numerical simulation of AC dielectrophoretic particle-particle interactive motions. Journal of Colloid and Interface Science, 417, 72–79 (2014)

    Article  Google Scholar 

  24. Moncada-Hernandez, H., Nagler, E., and Minerick, A. R. Theoretical and experimental examination of particle-particle interaction effects on induced dipole moments and dielectrophoretic responses of multiple particle chains. Electrophoresis, 35, 1803–1813 (2014)

    Article  Google Scholar 

  25. Wang, X., Wang, X. B., and Gascoyne, P. R. General expressions for dielectrophoretic force and electrorotational torque derived using the Maxwell stress tensor method. Journal of Electrostatics, 39(4), 277–295 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Le Liu, Chuanchuan Xie & Bo Chen

  2. Wenhua Institute, Wuhan, 430074, China

    Jiankang Wu

Authors
  1. Le Liu
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  2. Chuanchuan Xie
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  3. Bo Chen
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  4. Jiankang Wu
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Corresponding author

Correspondence to Jiankang Wu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11172111)

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Liu, L., Xie, C., Chen, B. et al. Iterative dipole moment method for calculating dielectrophoretic forces of particle-particle electric field interactions. Appl. Math. Mech.-Engl. Ed. 36, 1499–1512 (2015). https://doi.org/10.1007/s10483-015-1998-7

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  • DOI: https://doi.org/10.1007/s10483-015-1998-7

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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