Simulation of Deformation and Break-up of Droplets in the Presense of Electric Field in Porous Media Using Lattice Boltzmann Method
Authors
Abstract
In order to simulate multiphase flow in the presence of dielectric current using the Lattice Boltzmann Method (LBM), three distribution functions are used, two of which for using the He-Chen-Zhang phase field model and one for solving the potential field. Initially, the ability of the code to apply surface tension was tested using the Laplace law and the drop release test. The results show that the present numerical program is capable of modeling well the regulated surface tension force. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability in applying volume forces. The results by the developed numerical program are in good agreement with the numerical results in the references. In this study, for the first time, the effect of electric field on a droplet immersed in another fluid and the presence of droplet in a porous medium is investigated by LBM. For this purpose, first the droplet motion due to the potential difference in the porous and non-porous media is investigated. After modeling the droplet motion due to the potential difference, two electric fields areapplied to the droplet to reverse the droplet deformation. Through various tests, it is shown that at a given potential difference, the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique in the production of monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer science experts.
Keywords
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9. Lee, S. M., Im, D. J., and Kang, I. S., “Circulating Flows Inside a Drop under Time-Periodic Nonuniform Electric Fields”, Physics of Fluids, Vol. 12, No. 8, pp. 1899-1910, 2000.
10. Trau, M., Sankaran, S., Saville, D. A., and Aksay, I. A., “Pattern Formation in Nonaqueous Colloidal Dispersions Via Electrohydrodynamic Flow”, Langmuir, Vol. 11, No. 12, pp. 4665-4672, 1995.
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12. Succi, S., The lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Oxford University Press, 2001.
13. Chen, S., and Doolen, G. D., “Lattice Boltzmann Method for Fluid Flows”, Annual Review of Fluid Mechanics, Vol. 30, No. 1, pp. 329-364, 1998.
14. Hou, S., Shan, X., Zou, Q., Doolen, G. D., and Soll, W.E., “Evaluation of Two Lattice Boltzmann Models for Multiphase Flows”, Journal of Computational Physics, Vol. 138, No. 2, pp. 695-713, 1997.
15. Huang, H., Wang, L. and Lu, X. Y., “Evaluation of Three Lattice Boltzmann Models for Multiphase Flows in Porous Media”, Computers & Mathematics with Applications, Vol. 61, No. 12, pp. 3606-3617, 2011.
16. Zhang, J. and Kwok, D. Y., “A 2D Lattice Boltzmann Study on Electrohydrodynamic Drop Deformation with the Leaky Dielectric Theory”, Journal of Computational Physics, Vol. 206, No. 1, pp. 150-161, 2005.
17. Shan, X. and Chen, H., “Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components”, Physical Review E, Vol. 47, No. 3, p. 1815, 1993.
18. Kupershtokh, A.L. and Medvedev, D. A., “Lattice Boltzmann Equation Method in Electrohydrodynamic Problems”, Journal of Electrostatics, Vol. 64, No. 7-9, pp.581-585, 2006.
19. Singh, R., Bahga, S. S. and Gupta, A., “Electrohydrodynamics in Leaky Dielectric Fluids Using Lattice Boltzmann Method”, European Journal of Mechanics-B/Fluids, Vol. 74, pp. 167-179, 2019.
20. He, X., Chen, S. and Zhang, R., “A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and its Application in Simulation of Rayleigh–Taylor Instability”, Journal of Computational Physics, Vol. 152, No. 2, pp. 642-663, 1999.
21. Chao, J., Mei, R., Singh, R., and Shyy, W., “A Filter‐Based, Mass‐Conserving Lattice Boltzmann Method for Immiscible Multiphase Flows”, International Journal For Numerical Methods in Fluids, Vol. 66, No. 5, pp. 622-647, 2011.
22. He, X. and Li, N., “Lattice Boltzmann Simulation of Electrochemical Systems”, Computer Physics Communications, Vol. 129, No. 1-3, pp. 158-166, 2000.
23. Mohamad, A. A., Lattice Boltzmann Method, Vol. 70, London, Springer, 2011.
24. Singh, R., Bahga, S. S., and Gupta, A., “Electrohydrodynamics in Leaky Dielectric Fluids Using Lattice Boltzmann Method”, European Journal of Mechanics-B/Fluids, Vol. 74, pp. 167-179, 2019.
25. Komrakova A. E., Orest Sh., Eskinb, D., Derksen J. J., “A Lattice Boltzmann Simulations of Drop Deformation and Breakup in Shear Flow”, International Journal of Multiphase Flow, Vol. 59, pp. 24-43, 2014.
26. Rallison, J. M., “The deformation of Small Viscous Drops and Bubbles in Shear Flows”, Annual Review of Fluid Mechanics, Vol. 16, No. 1, pp. 45-66, 1984.
27. Cristini, V. and Renardy, Y., “Scalings for Droplet Sizes in Shear-Driven Breakup: Non-Microfluidic Ways to Monodisperse Emulsions”, Fluid Dynamics and Materials Processing, Vol. 2, No. 2, pp.77-94, 2006.
2. Melcher, J. R., and Taylor, G.,I., “Electrohydrodynamics: a Review of the Role of Interfacial Shear Stresses”, Annual Review of Fluid Mechanics, Vol. 1, No. 1, pp. 111-146, 1969.
3. Taylor, G. I., “Electrically Driven Jets”, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 313, No. 1515, pp. 453-475, 1969.
4. Castellanos, A. and Gonzalez, A., “Nonlinear Electrohydrodynamics of Free Surfaces”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 5, No. 3, pp. 334-343m 1998.
5. Ha, J. W., and Yang, S. M., “Electrohydrodynamics and Electrorotation of a Drop with Fluid Less Conductive than that of the Ambient Fluid”, Physics of Fluids, Vol. 12, No. 4, pp. 764-772, 2000.
6. Allan, R. S., and Mason, S. G., “Particle Behaviour in Shear and Electric Fields. I. Deformation and Burst of Fluid Drops”, Proceedings of the Royal Society of London, Series A. Mathematical and Physical Sciences, Vol. 267, No. 1328, pp. 45-61, 1962.
7. Taylor, G.I., “Studies in Electrohydrodynamics. I. The Circulation Produced in a Drop by an Electric Field”, Proceedings of the Royal Society of London, Series A. Mathematical and Physical Sciences, Vol. 291, No. 1425, pp. 159-166, 1966.
8. Torza, S., Cox, R. G., and Mason, S. G., “Electrohydrodynamic Deformation and Bursts of Liquid Drops”, Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, Vol. 269, No. 1198, pp. 295-319, 1971.
9. Lee, S. M., Im, D. J., and Kang, I. S., “Circulating Flows Inside a Drop under Time-Periodic Nonuniform Electric Fields”, Physics of Fluids, Vol. 12, No. 8, pp. 1899-1910, 2000.
10. Trau, M., Sankaran, S., Saville, D. A., and Aksay, I. A., “Pattern Formation in Nonaqueous Colloidal Dispersions Via Electrohydrodynamic Flow”, Langmuir, Vol. 11, No. 12, pp. 4665-4672, 1995.
11. Feng, J.Q., “Electrohydrodynamic Behaviour of a Drop Subjected to a Steady Uniform Electric Field at Finite Electric Reynolds Number”, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, No. 1986, pp. 2245-2269, 1999.
12. Succi, S., The lattice Boltzmann Equation: For Fluid Dynamics and Beyond, Oxford University Press, 2001.
13. Chen, S., and Doolen, G. D., “Lattice Boltzmann Method for Fluid Flows”, Annual Review of Fluid Mechanics, Vol. 30, No. 1, pp. 329-364, 1998.
14. Hou, S., Shan, X., Zou, Q., Doolen, G. D., and Soll, W.E., “Evaluation of Two Lattice Boltzmann Models for Multiphase Flows”, Journal of Computational Physics, Vol. 138, No. 2, pp. 695-713, 1997.
15. Huang, H., Wang, L. and Lu, X. Y., “Evaluation of Three Lattice Boltzmann Models for Multiphase Flows in Porous Media”, Computers & Mathematics with Applications, Vol. 61, No. 12, pp. 3606-3617, 2011.
16. Zhang, J. and Kwok, D. Y., “A 2D Lattice Boltzmann Study on Electrohydrodynamic Drop Deformation with the Leaky Dielectric Theory”, Journal of Computational Physics, Vol. 206, No. 1, pp. 150-161, 2005.
17. Shan, X. and Chen, H., “Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components”, Physical Review E, Vol. 47, No. 3, p. 1815, 1993.
18. Kupershtokh, A.L. and Medvedev, D. A., “Lattice Boltzmann Equation Method in Electrohydrodynamic Problems”, Journal of Electrostatics, Vol. 64, No. 7-9, pp.581-585, 2006.
19. Singh, R., Bahga, S. S. and Gupta, A., “Electrohydrodynamics in Leaky Dielectric Fluids Using Lattice Boltzmann Method”, European Journal of Mechanics-B/Fluids, Vol. 74, pp. 167-179, 2019.
20. He, X., Chen, S. and Zhang, R., “A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and its Application in Simulation of Rayleigh–Taylor Instability”, Journal of Computational Physics, Vol. 152, No. 2, pp. 642-663, 1999.
21. Chao, J., Mei, R., Singh, R., and Shyy, W., “A Filter‐Based, Mass‐Conserving Lattice Boltzmann Method for Immiscible Multiphase Flows”, International Journal For Numerical Methods in Fluids, Vol. 66, No. 5, pp. 622-647, 2011.
22. He, X. and Li, N., “Lattice Boltzmann Simulation of Electrochemical Systems”, Computer Physics Communications, Vol. 129, No. 1-3, pp. 158-166, 2000.
23. Mohamad, A. A., Lattice Boltzmann Method, Vol. 70, London, Springer, 2011.
24. Singh, R., Bahga, S. S., and Gupta, A., “Electrohydrodynamics in Leaky Dielectric Fluids Using Lattice Boltzmann Method”, European Journal of Mechanics-B/Fluids, Vol. 74, pp. 167-179, 2019.
25. Komrakova A. E., Orest Sh., Eskinb, D., Derksen J. J., “A Lattice Boltzmann Simulations of Drop Deformation and Breakup in Shear Flow”, International Journal of Multiphase Flow, Vol. 59, pp. 24-43, 2014.
26. Rallison, J. M., “The deformation of Small Viscous Drops and Bubbles in Shear Flows”, Annual Review of Fluid Mechanics, Vol. 16, No. 1, pp. 45-66, 1984.
27. Cristini, V. and Renardy, Y., “Scalings for Droplet Sizes in Shear-Driven Breakup: Non-Microfluidic Ways to Monodisperse Emulsions”, Fluid Dynamics and Materials Processing, Vol. 2, No. 2, pp.77-94, 2006.
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