Weakly nonlinear electrophoresis of a highly charged colloidal particle

Physics of Fluids

Volumn 25, Issue 5, 2013, Pages

  Schnitzer, Ory ^a   Zeyde, Roman ^a   Yavneh, Irad ^a   Yariv, Ehud ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; ELECTROPHORETIC MOBILITY; NONLINEAR ANALYSIS; OSMOSIS; SPHERES; ZETA POTENTIAL;

ASYMPTOTIC CORRECTION; CHARGED COLLOIDAL PARTICLES; CONCENTRATION POLARIZATION; ELECTROKINETIC TRANSPORT; ELECTROPHORETIC VELOCITY; FAR-FIELD CONDITIONS; FIELD APPROXIMATIONS; HEAT AND MASS TRANSFER;

ELECTRODYNAMICS;

EID: 84878603168     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4804672     Document Type: Article

References (57)

1. Lyklema J. Fundamentals of Interface and Colloid Science 1995, II. Vol. (Academic, New York).
2. Hunter R.J. Foundations of Colloidal Science 2000, (Oxford University Press, Oxford, UK).
3. Chang H.-C. Yeo L.Y. Electrokinetically Driven Microfluidics and Nanofluidics 2010, and (Cambridge University Press, New York, NY).
4. Kostal V. Katzenmeyer J. Arriaga E.A. Capillary electrophoresis in bioanalysis. Anal. Chem. 2008, 80:4533. 10.1021/ac8007384, and .
5. Smoluchowski M. Contribution to the theory of electro-osmosis and related phenomena. Bull. Int. Acad. Sci. Cracovie 1903, 184:199. .
6. Yariv E. An asymptotic derivation of the thin-Debye-layer limit for electrokinetic phenomena. Chem. Eng. Commun. 2009, 197:3-17. 10.1080/00986440903076590, .
7. Wiersema P.H. Loeb A.L. Overbeek J.T. G. Calculation of the electrophoretic mobility of a spherical colloid particle. J. Colloid Interface Sci. 1966, 22:78-99. 10.1016/0021-9797(66)90069-5, and .
8. O'Brien R.W. White L.R. Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc., Faraday Trans. 2 1978, 74:1607-1626. 10.1039/F29787401607, and .
9. Derjaguin B.V. Dukhin S.S. Nonequilibrium double layer and electrokinetic phenomena. Electrokinetic phenomena 1974, 7:273-336. E. Matijevic, and in Surface and Colloid Science Vol. edited by (John Wiley, New York, ), pp.
10. Dukhin S.S. Non-equilibrium electric surface phenomena. Adv. Colloid Interface Sci. 1993, 44:1-134. 10.1016/0001-8686(93)80021-3, .
11. O'Brien R.W. Hunter R.J. The electrophoretic mobility of large colloidal particles. Can. J. Chem. 1981, 59:1878-1887. 10.1139/v81-280, and .
12. O'Brien R.W. The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 1983, 92:204-216. 10.1016/0021-9797(83)90129-7, .
13. Schnitzer O. Frankel I. Yariv E. Electrokinetic flows about conducting drops. J. Fluid Mech. 2013, 722:394-423. 10.1017/jfm.2013.102, and .
14. It turns out in certain problems, such as electrophoresis of a moderately-charged particle and electro-osmotic flow through straight channels, the linear response actually prevails even for β ~ O(1), see Ref. 23.
15. Kumar A. Elele E. Yeksel M. Khusid B. Qiu Z. Acrivos A. Measurements of the fluid and particle mobilities in strong electric fields. Phys. Fluids 2006, 18:123301. 10.1063/1.2397573, and .
16. Barany S. Electrophoresis in strong electric fields. Adv. Colloid Interface Sci. 2009, 147-148:36-43. 10.1016/j.cis.2008.10.006, .
17. Leinweber F.C. Tallarek U. Concentration polarization-based nonlinear electrokinetics in porous media: induced-charge electroosmosis. J. Phys. Chem. B 2005, 109:21481-21485. 10.1021/jp055491u, and .
18. Ben Y. Chang H.-C. Nonlinear Smoluchowski slip velocity and micro-vortex generation. J. Fluid Mech. 2002, 461:229-238. 10.1017/S0022112002008662, and .
19. Ben Y. Demekhin E.A. Chang H.-C. Nonlinear electrokinetics and 'superfast' electrophoresis. J. Colloid Interface Sci. 2004, 276:483-497. 10.1016/j.jcis.2004.04.004, and .
20. Olesen L.H. Bazant M.Z. Bruus H. Strongly nonlinear dynamics of electrolytes in large ac voltages. Phys. Rev. E 2010, 82:011501. 10.1103/PhysRevE.82.011501, and .
21. Chang H.-C. Demekhin E.A. Shelistov V.S. Competition between Dukhin's and Rubinstein's electrokinetic modes. Phys. Rev. E 2012, 86:046319. 10.1103/PhysRevE.86.046319, and .
22. Dukhin A.S. Dukhin S.S. Aperiodic capillary electrophoresis method using an alternating current electric field for separation of macromolecules. Electrophoresis 2005, 26:2149-2153. 10.1002/elps.200410408, and .
23. Schnitzer O. Yariv E. Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction. Phys. Rev. E 2012, 86:021503. 10.1103/PhysRevE.86.021503, and .
24. Hinch E.J. Perturbation Methods 1991, (Cambridge University Press, Cambridge).
25. Acrivos A. Taylor T.D. Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids 1962, 5:387-394. 10.1063/1.1706630, and .
26. Simonova T.S. Dukhin S.S. Nonlinear polarization of the diffusion part of the thin double layer of a spherical particle. Kolloidn. Zh. 1976, 38:79-85. and .
27. Simonova T.S. Dukhin S.S. Nonlinear electrophoresis of a dielectric and conducting ideally polarizable particles. Kolloidn. Zh. 1976, 38:86-93. and .
28. Mishchuk N.A. Dukhin S.S. Electrophoresis of solid particles at large Peclet numbers. Electrophoresis 2002, 23:2012-2022. 10.1002/1522-2683(200207)23:13<2012::AID-ELPS2012>3.0.CO;2-Y
29. Shilov V. Barany S. Grosse C. Shramko O. Field-induced disturbance of the double layer electro-neutrality and non-linear electrophoresis. Adv. Colloid Interface Sci. 2003, 104:159-173. 10.1016/S0001-8686(03)00040-X, and .
30. Happel J. Brenner H. Low Reynolds Number Hydrodynamics 1965, and (Prentice-Hall, Englewood Cliffs, NJ).
31. See supplementary material at E-PHFLE6-25-022305 for these functions.
32. Rivette N.J. Baygents J.C. A note on the electrostatic force and torque acting on an isolated body in an electric field. Chem. Eng. Sci. 1996, 51:5205-5211. 10.1016/S0009-2509(96)00337-5, and .
33. Proudman I. Pearson J.R. A. Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 1957, 2:237-262. 10.1017/S0022112057000105, and .
34. Leal L.G. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes 2007, (Cambridge University Press, New York).
35. Abramowitz M. Stegun I.A. Handbook of Mathematical Functions 1965, and 3rd ed. (Dover, New York, NY).
36. Van Dyke M. Perturbation Methods in Fluid Mechanics 1964, (Academic press, New York).
37. Brenner H. The Stokes resistance of an arbitrary particle - IV. Arbitrary fields of flow. Chem. Eng. Sci. 1964, 19:703-727. 10.1016/0009-2509(64)85084-3, .
38. Mishchuk N.A. Concentration polarization of interface and nonlinear electrokinetic phenomena. Adv. Colloid Interface Sci. 2010, 160:16-39. 10.1016/j.cis.2010.07.001, .
39. Mishchuk N.A. Barinova N.O. Theoretical and experimental study of nonlinear electrophoresis. Colloid J. 2011, 73:88-96. 10.1134/S1061933X11010133, and .
40. Midmore B.R. Pratt G.V. Herrington T.M. Evidence for the validity of electrokinetic theory in the thin double layer region. J. Colloid Interface Sci. 1996, 184:170-174. 10.1006/jcis.1996.0608, and .
41. Hunter R.J. The significance of stagnant layer conduction in electrokinetics. Adv. Colloid Interface Sci. 2003, 100:153-167. 10.1016/S0001-8686(02)00060-X, .
42. Delgado A.V. Gonzalez-Caballero F. Hunter R.J. Koopal L.K. Lyklema J. Measurement and interpretation of electrokinetic phenomena. J. Colloid Interface Sci. 2007, 309:194-224. 10.1016/j.jcis.2006.12.075, and .
43. In contrast, the electrophoretic velocity of moderately charged particles ( Bi ≪1) is linear in the field up to much larger β values: in the absence of strong counter-ion accumulation adjacent to the surface, surface conduction fluxes are only O(βδ) small. Indeed, the moderate-charge macroscale model provided in Ref. 23 yields Smoluchowski's mobility for β ~ O(1). While the above surface-conduction scaling appears to suggest nonlinearities for β ~ O(δ-1), an explicit investigation of that limit shows that surface conduction effects remain subdominant.57 At these conditions, the first violation of linearity may be due to dielectric solid polarization, see Ref. 54.
44. Kalaǐdin E.N. Demekhin E.A. Korovyakovskiǐ A.S. On the theory of electrophoresis of the second kind. Dokl. Phys. 2009, 54:210-214. 10.1134/S1028335809040132, and .
45. Yariv E. Migration of ion-exchange particles driven by a uniform electric field. J. Fluid Mech. 2010, 655:105-121. 10.1017/S0022112010000716, .
46. Baygents J.C. Saville D.A. Electrophoresis of drops and bubbles. J. Chem. Soc., Faraday Trans. 1991, 87:1883-1898. 10.1039/ft9918701883, and .
47. Baygents J.C. Saville D.A. Electrophoresis of small particles and fluid globules in weak electrolytes. J. Colloid Interface Sci. 1991, 146:9-37. 10.1016/0021-9797(91)90003-Q, and .
48. Arroyo F.J. Carrique F. Bellini T. Delgado A.V. Dielectric dispersion of colloidal suspensions in the presence of stern layer conductance: Particle size effects. J. Colloid Interface Sci. 1999, 210:194-199. 10.1006/jcis.1998.5914, and .
49. Booth F. The effect of surface conditions on the electrophoresis of solid particles. J. Colloid Sci. 1951, 6:549-556. 10.1016/0095-8522(51)90053-0, .
50. Dukhin A.S. Biospecific mechanism of double layer formation and peculiarities of cell electrophoresis. Colloids Surf., A 1993, 73:29-48. 10.1016/0927-7757(93)80005-Y, .
51. Squires T.M. Bazant M.Z. Induced-charge electro-osmosis. J. Fluid Mech. 2004, 509:217-252. 10.1017/S0022112004009309, and .
52. Yariv E. Nonlinear electrophoresis of ideally polarizable spherical particles. Europhys. Lett. 2008, 82:54004. 10.1209/0295-5075/82/54004, .
53. Yariv E. Davis A.M. J. Electro-osmotic flows over highly polarizable dielectric surfaces. Phys. Fluids 2010, 22:052006. 10.1063/1.3431695, and .
54. Schnitzer O. Yariv E. Dielectric-solid polarization at strong fields: Breakdown of Smoluchowski's electrophoresis formula. Phys. Fluids 2012, 24:082005. 10.1063/1.4748967, and .
55. Andersen M.B. van Soestbergen M. Mani A. Bruus H. Biesheuvel P.M. Bazant M.Z. Current-induced membrane discharge. Phys. Rev. Lett. 2012, 109:108301. 10.1103/PhysRevLett.109.108301, and .
56. Yariv E. Electrokinetic self-propulsion by inhomogeneous surface kinetics. Proc. R. Soc. London, Ser. A 2011, 467:1645. 10.1098/rspa.2010.0503, .
57. Schnitzer O. Yariv E. Strong-field electrophoresis. J. Fluid Mech. 2012, 701:333-351. 10.1017/jfm.2012.161, and .