Streaming-potential phenomena in the thin-Debye-layer limit. Part 1. General theory

Journal of Fluid Mechanics

Volumn 685, Issue , 2011, Pages 306-334

  Yariv, Ehud ^a   Schnitzer, Ory ^a   Frankel, Itzchak ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

colloids; low Reynolds number flows; micro nano fluid dynamics

Indexed keywords

COLLOIDS; ELECTRIC FIELDS; ELECTRODYNAMICS; REYNOLDS NUMBER; SOLS; VISCOUS FLOW;

ASYMPTOTIC STRUCTURES; ELECTRO-VISCOUS EFFECTS; ELECTROKINETIC PHENOMENA; ELECTROKINETIC STREAMING POTENTIAL; LOW REYNOLDS NUMBER FLOW; MICRO-/NANO-FLUID DYNAMICS; SINGULAR PERTURBATION ANALYSIS; VELOCITY PERTURBATION;

DRAG;

ELECTRIC FIELD; ELECTROKINESIS; FLUID DYNAMICS; REYNOLDS NUMBER;

EID: 80053998923     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2011.316     Document Type: Article

References (34)

1. ALEXANDER, B. M. & PRIEVE, D. C. 1987 A hydrodynamic technique for measurement of colloidal forces. Langmuir 3 (5), 788-795.
2. ANDERSON, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 30, 139-165.
3. BIKE, S. G., LAZARRO, L. & PRIEVE, D. C. 1995 Electrokinetic lift of a sphere moving in slow shear flow parallel to a wall I. Experiment. J. Colloid Interface Sci. 175 (2), 411-421.
4. BIKE, S. G. & PRIEVE, D. C. 1990 Electrohydrodynamic lubrication with thin double layers. J. Colloid Interface Sci. 136 (1), 95-112.
5. BIKE, S. G. & PRIEVE, D. C. 1992 Electrohydrodynamics of thin double layers: a model for the streaming potential profile. J. Colloid Interface Sci. 154, 87-96.
6. BIKE, S. G. & PRIEVE, D. C. 1995 Electrokinetic lift of a sphere moving in slow shear flow parallel to a wall II. Theory. J. Colloid Interface Sci. 175 (2), 422-434.
7. BOLÉVE, A., CRESPY, A., REVIL, A., JANOD, F. & MATTIUZZO, J. L. 2007 Streaming potentials of granular media: influence of the Dukhin and Reynolds numbers. J. Geophys. Res. 112, B08204.
8. BOOTH, F. 1950 The electroviscous effect for suspensions of solid spherical particles. Proc. R. Soc. Lond. A 203 (1075), 533-551.
9. BOOTH, F. 1954 Sedimentation potential and velocity of solid spherical particles. J. Chem. Phys. 22, 1956-1968.
10. BRENNER, H. 1964 The Stokes resistance of an arbitrary particle-IV. Arbitrary fields of flow. Chem. Engng Sci. 19, 703-727.
11. COX, R. G. 1997 Electroviscous forces on a charged particle suspended in a flowing liquid. J. Fluid Mech. 338, 1-34.
12. DOI, M. & MAKINO, M. 2008 Electrokinetic boundary condition compatible with the Onsager reciprocal relation in the thin double layer approximation. J. Chem. Phys. 128, 044715.
13. HAPPEL, J. & BRENNER, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
14. HINCH, E. J. & SHERWOOD, J. D. 1983 Primary electroviscous effect in a suspension of spheres with thin double layers. J. Fluid Mech. 132, 337-347. (Pubitemid 13603785)
15. LAC, E. & SHERWOOD, J. D. 2009 Streaming potential generated by a drop moving along the centreline of a capillary. J. Fluid Mech. 640, 55-77.
16. LEAL, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.
17. LYKLEMA, J. 1995 Fundamentals of Interface and Colloid Science, vol. II. Academic.
18. OHSHIMA, H., HEALY, T. W., WHITE, L. R. & O'BRIEN, R. W. 1984 Sedimentation velocity and potential in a dilute suspension of charged spherical colloidal particles. J. Chem. Soc. Faraday Trans. 80 (10), 1299-1317.
19. PRIEVE, D. C., EBEL, J. P., ANDERSON, J. L. & LOWELL, M. E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247-269.
20. RUBINSTEIN, I. & ZALTZMAN, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Meth. Appl. Sci. 11, 263-300.
21. RUSSEL, W. B. 1978 The rheology of suspensions of charged rigid spheres. J. Fluid Mech. 85 (2), 209-232.
22. SAVILLE, D. A. 1977 Electrokinetic effects with small particles. Annu. Rev. Fluid Mech. 9, 321-337.
23. SHERWOOD, J. D. 1980 The primary electroviscous effect in a suspension of spheres. J. Fluid Mech. 101 (3), 609-629.
24. SHERWOOD, J. D. 2007 Streaming potential generated by two-phase flow in a capillary. Phys. Fluids 19, 053101.
25. SHERWOOD, J. D. 2008 Streaming potential generated by a long viscous drop in a capillary. Langmuir 24 (18), 10011-10018.
26. SHERWOOD, J. D. 2009 Streaming potential generated by a small charged drop in Poiseuille flow. Phys. Fluids 21, 013101.
27. SMOLUCHOWSKI, M. 1921 Elektrische Endosmose und Strömungsströ me. In Handbuch der Elektrizität und des Magnetismus, Band II, Stationaire Ströme (ed. L. Graetz). Barth.
28. TABATABAEI, S. M. & VAN DE VEN, T. G. M. 2010 Tangential electroviscous drag on a sphere surrounded by a thin double layer near a wall for arbitrary particle-wall separations. J. Fluid Mech. 656, 360-406.
29. TABATABAEI, S. M., VAN DE VEN, T. G. M. & REY, A. D. 2006 Electroviscous sphere-wall interactions. J. Colloid Interface Sci. 301 (1), 291-301. (Pubitemid 44092755)
30. VAN DYKE, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
31. VAN DE VEN, T. G. M., WARSZYNSKI, P. & DUKHIN, S. S. 1993a Attractive electroviscous forces. Colloids Surf. A 79 (1), 33-41.
32. VAN DE VEN, T. G. M., WARSZYNSKI, P. & DUKHIN, S. S. 1993b Electrokinetic lift of small particles. J. Colloid Interface Sci. 157 (2), 328-331.
33. WARSZYNSKI, P. & VAN DE VEN, T. G. M. 2000 Electroviscous forces on a charged cylinder moving near a charged wall. J. Colloid Interface Sci. 223, 1-15. (Pubitemid 30131713)
34. YARIV, E. 2010 An asymptotic derivation of the thin-Debye-layer limit for electrokinetic phenomena. Chem. Engng Commun. 197, 3-17.