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Time-dependent electrophoresis of a dielectric spherical particle embedded in Brinkman medium

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Abstract

An expression for electrophoretic apparent velocity slip in the time-dependent flow of an electrolyte solution saturated in a charged porous medium within an electric double layer adjacent to a dielectric plate under the influence of a tangential uniform electric field is derived. The velocity slip is used as a boundary condition to solve the electrophoretic motion of an impermeable dielectric spherical particle embedded in an electrolyte solution saturated in porous medium under the unsteady Darcy–Brinkman model. Throughout the system, a uniform electric field is applied and maintains with constant strength. Two cases are considered, when the electric double layer enclosing the particle is thin, but finite and when of a particle with a thick double layer. Expressions for the electrophoretic mobility of the particle as functions of the relevant parameters are found. Our results indicate that the time scale for the growth of mobility is significant and small for high permeability. Generally, the effect of the relaxation time for starting electrophoresis is negligible, irrespective of the thickness of the double layer and permeability of the medium. The effects of the elapsed time, permeability, mass density and Debye length parameters on the fluid velocity, the electrophoretic mobility and the acceleration are shown graphically.

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References

  1. Reuss, F.F.: Sur un nouvel effet de l’électricité galvanique. Mem. Soc. Imp. Nat. Moscou 2, 326–337 (1809)

    Google Scholar 

  2. Russel, W.B., Saville, D.A., Schowalter, W.R.: Colloidal Dispersions. Cambridge Univ. Press, New York (1989)

    Book  MATH  Google Scholar 

  3. Dukhin, A.S., Goetz, P.J.: Ultrasound for Characterizing Colloids: Particle Sizing. Zeta Potential Rheology. Elsevier, Amsterdam (2002)

    Google Scholar 

  4. Smoluchowski, M.: Contribution à la théorie de l’endosmose électrique et de quelques phénomènes corrélatifs. Bull. Int. Acad. Sci. Cracovie 8, 182–200 (1903)

    MATH  Google Scholar 

  5. Burgreen, D., Nakache, F.R.: Electrokinetic flow in ultrafine capillary slits. J. Phys. Chem. 68, 1084–1091 (1964)

    Article  Google Scholar 

  6. Berli, C.L.A., Olivares, M.L.: Electrokinetic flow of non-Newtonian fluids in microchannels. J. Colloid Interface Sci. 320, 582–589 (2008)

    Article  Google Scholar 

  7. Chang, C.C., Wang, C.Y.: Electro-osmotic flow in a sector microchannel. Phys. Fluids 21, 042002 (2009)

    Article  MATH  Google Scholar 

  8. Zhao, C., Yang, C.: Advances in electrokinetics and their applications in micro/nano fluidics. Microfluid. Nanofluid. 13, 179–203 (2012)

    Article  Google Scholar 

  9. Morrison, F.A.: Transient electrophoresis of an arbitrarily oriented cylinder. J. Colloid Interface Sci. 36, 139–145 (1971)

    Article  Google Scholar 

  10. Ivory, C.F.: Transient electroosmosis: the momentum transfer coefficient. J. Colloid Interface Sci. 96, 296–298 (1983)

    Article  Google Scholar 

  11. Keh, H.J., Tseng, H.C.: Transient electrokinetic flow in fine capillaries. J. Colloid Interface Sci. 242, 450–459 (2001)

    Article  Google Scholar 

  12. Jian, Y., Yang, L., Liu, Q.: Time periodic electro-osmotic flows through a microannulus. Phys. Fluids 22, 042001 (2010)

    Article  MATH  Google Scholar 

  13. Morrison, F.A.: Transient electrophoresis of a dielectric sphere. J. Colloid Interface Sci. 29, 687–691 (1969)

    Article  Google Scholar 

  14. Keh, H.J., Huang, Y.C.: Transient electrophoresis of dielectric spheres. J. Colloid Interface Sci. 291, 282–291 (2005)

    Article  Google Scholar 

  15. Chen, G.Y., Keh, H.J.: Start-up of electrokinetic flow in a fibrous porous medium. J. Phys. Chem. C 118, 2826–2833 (2014)

    Article  Google Scholar 

  16. Chiang, C.C., Keh, H.J.: Transient electroosmosis in the transverse direction of a fibrous porous medium. Colloids Surf. A 481, 577–582 (2015)

    Article  Google Scholar 

  17. Chiang, C.C., Keh, H.J.: Startup of electrophoresis in a suspension of colloidal spheres. Electrophoresis 36, 3002–3008 (2015)

    Article  Google Scholar 

  18. Jones, E.H., Reynolds, D.A., Wood, A.L., Thomas, D.G.: Use of electrophoresis for transporting nano-iron in porous media. Ground Water 49, 172–183 (2010)

    Article  Google Scholar 

  19. Pomès, V., Fernández, A., Houi, D.: Characteristic time determination for transport phenomena during the electrokinetic treatment of a porous medium. Chem. Eng. J. 87, 251–260 (2002)

    Article  Google Scholar 

  20. Oyanader, M.A., Arce, P., Dzurik, A.: Design criteria for soil cleaning operations in electrokinetic remediation: hydrodynamic aspects in a cylindrical geometry. Electrophoresis 26, 2878–2887 (2005)

    Article  Google Scholar 

  21. Riviere, J.E., Heit, M.C.: Electrically-assisted transdermal delivery. Pharm. Res. 14, 687–697 (1997)

    Article  Google Scholar 

  22. Pyell, U.: Characterization of nanoparticles by capillary electromigration separation techniques. Electrophoresis 31, 814–831 (2010)

    Article  Google Scholar 

  23. Calladine, C.R., Collis, C.M., Drew, H.R., Mott, M.R.: A study of electrophoretic mobility of DNA in agarose and polyacrylamide gels. J. Mol. Biol. 221, 981–1005 (1991)

    Article  Google Scholar 

  24. Shi, Q., Jackowski, G.: One-dimensional polyacrylamide gel electrophoresis. In: Hames, B.D. (ed.) Gel Electrophoresis of Proteins: A Practical Approach, pp. 1–52. Oxford University Press, Oxford (1998)

    Google Scholar 

  25. Magdeldin, S.: Gel Electrophoresis Principles and Basics. InTech, Rijeka (2012)

    Book  Google Scholar 

  26. Paillat, T., Moreau, E., Grimaud, P.O., Touchard, G.: Electrokinetic phenomena in porous media applied to soil decontamination. IEEE Trans. Dielectr. Electr. Insul. 7, 693–704 (2000)

    Article  Google Scholar 

  27. Wu, Y.F., Chou, W.L., Yen, S.C.: Removal of mercury and methylmercury from contaminated soils by applying an electric field. J. Environ. Sci. Health A 35, 1153–1170 (2000)

    Article  Google Scholar 

  28. Feng, J., Ganatos, P., Weinbaum, S.: Motion of a sphere near planar confining boundaries in a Brinkman medium. J. Fluid Mech. 375, 265–296 (1998)

    Article  MATH  Google Scholar 

  29. Tsai, P., Huang, C.H., Lee, E.: Electrophoresis of a charged colloidal particle in porous media: boundary effect of a solid plane. Langmuir 27, 13481–13488 (2011)

    Article  Google Scholar 

  30. Ingham, D.B., Pop, I.: Transport Phenomena in Porous Media II. Elsevier, Oxford (2002)

    MATH  Google Scholar 

  31. Kaviany, M.: Principles of Heat Transfer in Porous Media, 2nd edn. Springer, New York (1995)

    Book  MATH  Google Scholar 

  32. Nabovati, A., Llewellin, E.W., Sousa, A.C.M.: A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method. Compos. A 40, 860–869 (2009)

    Article  Google Scholar 

  33. Vafai, K.: Handbook of Porous Media, 3rd edn. CRC Press, New York (2015)

    MATH  Google Scholar 

  34. Neale, G., Epstein, M., Nader, W.: Creeping flow relative to permeable spheres. Chem. Eng. Sci. 28, 1865–1874 (1973)

    Article  Google Scholar 

  35. Durlofsky, L., Brady, J.F.: Analysis of the Brinkman equation as a model for flow in porous media. Phys. Fluids 30, 3329–3341 (1987)

    Article  MATH  Google Scholar 

  36. Sherief, H.H., Faltas, M.S., Saad, E.I.: Stokes resistance of a porous spherical particle in a spherical cavity. Acta Mech. 227, 1075–1093 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  37. El-Sapa, S., Saad, E.I., Faltas, M.S.: Axisymmetric motion of two spherical particles in a Brinkman medium with slip surfaces, fluid. Eur. J. Mech. B Fluids 67, 306–313 (2018)

    Article  MathSciNet  Google Scholar 

  38. He, Y.Y., Lee, E.: Electrophoresis in concentrated dispersions of charged porous spheres. Chem. Eng. Sci. 63, 5719–5727 (2008)

    Article  Google Scholar 

  39. Keh, H.J., Anderson, J.L.: Boundary effects on electrophoretic motion of colloidal spheres. J. Fluid Mech. 153, 417–439 (1985)

    Article  MATH  Google Scholar 

  40. Tsay, R., Weinbaum, S.: Viscous flow in a channel with periodic cross-bridging fibres: exact solutions and Brinkman approximation. J. Fluid Mech. 226, 125–148 (1991)

    Article  MATH  Google Scholar 

  41. Uematsu, Y.: Electrophoresis of electrically neutral porous spheres induced by selective affinity of ions. Phys. Rev. E 91, 022303 (2015)

    Article  Google Scholar 

  42. Happel, J., Brenner, H.: Low Reynolds Number Hydrodynamics. Martinus Nijoff, The Hague (1983)

    MATH  Google Scholar 

  43. Maribo-Mogensen, B., Kontogeorgis, G.M., Thomsen, K.: Comparison of the Debye-Hückel and the mean spherical approximation theories for electrolyte solutions. Ind. Eng. Chem. Res. 51, 5353–5363 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Damanhour University, Damanhûr, Egypt

    E. I. Saad

  2. Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

    M. S. Faltas

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  1. E. I. Saad
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  2. M. S. Faltas
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Correspondence to E. I. Saad.

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Saad, E.I., Faltas, M.S. Time-dependent electrophoresis of a dielectric spherical particle embedded in Brinkman medium. Z. Angew. Math. Phys. 69, 43 (2018). https://doi.org/10.1007/s00033-018-0939-4

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  • DOI: https://doi.org/10.1007/s00033-018-0939-4

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