The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle

Physics of Fluids

Volumn 21, Issue 4, 2009, Pages

  Khair, Aditya S ^a   Squires, Todd M ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC ANALYSIS; CHARGED PARTICLES; COLLOIDS; ELECTROOSMOSIS; HYDRODYNAMICS; NUMERICAL METHODS; PARTICLE SIZE;

CHARGED SPHERICAL PARTICLES; ELECTROKINETIC EQUATIONS; ELECTROOSMOTIC FLOW; ELECTROPHORETIC MOTION; HYDRODYNAMIC SLIPS; NUMERICAL SOLUTION; SPHERICAL COLLOIDAL PARTICLES; SURFACE CONDUCTION;

ELECTROPHORETIC MOBILITY;

EID: 65549116554     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3116664     Document Type: Article

References (54)

1. R. B. Schoch, J. Han, and P. Renaud, "Transport phenomena in nanofluidics," Rev. Mod. Phys. 80, 839 (2008).
2. H. A. Stone, A. Stroock, and A. Ajdari, "Engineering flows in small devices: Microfluidics toward a lab-on-a-chip," Annu. Rev. Fluid Mech. 36, 381 (2004).
3. T. M. Squires and S. Quake, "Microfluidics: Fluid physics at the nanoliter scale," Rev. Mod. Phys. 77, 977 (2005).
4. J. Lyklema, Fundamentals of Interface and Colloid Science, Solid-Liquid Interfaces Vol. II (Academic, San Diego, CA, 1995).
5. W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, UK, 1989).
6. S. Ghosal, "Electrokinetic flow and dispersion in capillary electrophoresis," Annu. Rev. Fluid Mech. 38, 309 (2006).
7. M. von Smoluchowksi, "Contribution à la théorie de l'endosmose électrique électrique et de quelques phenomènes corrélatifs," Bull. Int. Acad. Sci. Cracovie 8, 182 (1903).
8. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, UK, 2000).
9. H. Lamb, Hydrodynamics (Dover, New York, 1932).
10. E. Lauga, M. P. Brenner, and H. A. Stone, in Handbook of Experimental Fluid Dynamics, edited by C. Tropea, A. Yarin, and J. F. Foss (Springer, New York, 2007), pp. 1219-1240.
11. C. Neto, D. R. Evans, E. Bonaccurso, H.-J. Butt, and V. S. J. Craig, "Boundary slip in Newtonian liquids: A review of experimental studies," Rep. Prog. Phys. 68, 2859 (2005).
12. O. Vinogradova, "Slippage of water over hydrophobic surfaces," Int. J. Min. Process. 56, 31 (1999).
13. L. Bocquet and J. Barrat, "Flow boundary conditions from nano-to microscales," Soft Matter 3, 685 (2007).
14. J. Eijkel, "Liquid slip in micro- and nanofluidics: Recent research and its possible implications," Lab Chip 7, 299 (2007).
15. N. V. Churaev, J. Ralston, I. P. Sergeeva, and V. D. Sobolev, "Electrokinetic properties of methylated quartz capillaries," Adv. Colloid Interface Sci. 96, 265 (2002).
16. C. I. Bouzigues, P. Tabeling, and L. Bocquet, "Nanofluidics in the Debye layer at hydrophilic and hydrophobic surfaces," Phys. Rev. Lett. 101, 114503 (2008).
17. Y. Almeras, J. L. Barrat, and L. Bocquet, "Influence of wetting properties on diffusion in a confined fluid," J. Phys. IV 10, 27 (2000).
18. E. Lauga and T. Squires, "Brownian motion near a partial-slip boundary: A local probe of the no-slip condition," Phys. Fluids 17, 103102 (2005).
19. L. Joly, C. Ybert, E. Trizac, and L. Bocquet, "Hydrodynamics within the electric double layer on slipping surfaces," Phys. Rev. Lett. 93, 257805 (2004).
20. V. M. Muller, I. P. Sergeeva, V. D. Sobolev, and N. V. Churaev, "Boundary effects in the theory of electrokinetic phenomena," Colloid J. USSR 48, 606 (1986).
21. B. A. Grimes and A. I. Liapis, "Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography," J. Colloid Interface Sci. 263, 113 (2003).
22. Y. Ren and D. Stein, "Slip-enhanced electrokinetic energy conversion in nanofluidic channels," Nanotechnology 19, 195707 (2008).
23. T. M. Squires, "Electrokinetic flows over inhomogeneously slipping surfaces," Phys. Fluids 20, 092105 (2008).
24. F. Reuss, "Sur un nouvel effet de le electricite glavanique," Mem. Soc. Imp. Nat. Mosc. 2, 327 (1809).
25. J. Khandurina and A. Guttman, "Microscale separation and analysis," Curr. Opin. Chem. Biol. 7, 595 (2003).
26. J.-L. Viovy, "Electrophoresis of DNA and other polyelectrolytes: Physical mechanisms," Rev. Mod. Phys. 72, 813 (2000).
27. A. Ajdari and L. Bocquet, "Giant amplification of interfacially driven transport by hydrodynamic slip: Diffusio-osmosis and Beyond," Phys. Rev. Lett. 96, 186102 (2006).
28. E. Huckel, "Die Kataphorese der Kugel," Phys. Z. 25, 204 (1924).
29. R. W. O'Brien and L. R. White, "Electrophoretic mobility of a spherical colloidal particle," J. Chem. Soc., Faraday Trans. 2 74, 1607 (1978).
30. H. Ohshima, T. W. Healy, and L. R. White, "Electrokinetic phenomena in a dilute suspension of charged mercury drops," J. Chem. Soc., Faraday Trans. 80, 1643 (1984).
31. C. S. Mangelsdorf and L. R. White, "Effects of Stern-layer conductance on electrokinetic transport properties of colloidal particles," J. Chem. Soc., Faraday Trans. 86, 2859 (1990).
32. Note, our use of the term "surface conduction" refers to the transport - via electromigration, diffusion, and electroconvection - of ions within the diffuse, or mobile, part of the double layer. This should not be confused with the (anomalous) conduction often attributed to an immobile (or Stern) monolayer of ions behind the "plane of shear." Indeed, in the present work we consider the electrical double layer to be comprised of only a diffuse screening cloud and the particle itself; i.e. there is no Stern layer. Hence, the plane of shear coincides with the particle surface.
33. S. S. Dukhin and B. V. Deryaguin, in Surface and Colloid Science, edited by E. Matijevic (Wiley, New York, 1974), Vol. 7.
34. R. W. O'Brien, "The solution of the electrokinetic equations for colloidal particles with thin double layers," J. Colloid Interface Sci. 92, 204 (1983).
35. C. F. Zukoski and D. A. Saville, "An experimental test of electrokinetic theory using measurements of electrophoretic mobility and electrical conductivity," J. Colloid Interface Sci. 107, 322 (1985).
36. R. S. Chow and K. Takamura, "Electrophoretic mobilities of Bitumen and conventional crude-in-water emulsions using the laser Doppler apparatus in the presence of multivalent cations," J. Colloid Interface Sci. 125, 212 (1988).
37. A. B. Basset, A Treatise on Hydrodynamics (Dover, New York, NY, 1961).
38. Properly, for a spherical colloid an analysis of the thin-diffuse-layer limit must account for the variation of the electric field around the particle. In that case, in Eq. (7) the electric body force equals the charge density multiplied by the local tangential field, not the uniform applied field. As such, our expression for the velocity inside the diffuse layer (10) would represent an inner solution (in the matched asymptotic expansion sense), whose limiting value at the diffuse-layer-bulk interface (11) must be matched to the bulk (outerv velocity field. However, in the absence of surface conduction, the simple flat-plate analysis does indeed yield the exact same result for the mobility (14) as a rigorous calculation for a spherical particle (see, e.g., Ref. 5). This is not surprising, of course, and is merely an illustration of the well-known result that for κa→∞ and ζ ≪ 1 (i.e. in the absence of surface conduction) the mobility of a uniformly charged "particle" does not depend on its shape or size.
39. S. S. Dukhin and V. N. Shilov, "Theory of static polarization of diffuse part of thin electric double layer of spherical particles," Colloid J. USSR 31, 564 (1969).
40. A. S. Khair and T. M. Squires, "Fundamental aspects of concentration polarization arising from non-uniform electrokinetic transport," Phys. Fluids 20, 087102 (2008).
41. J. L. Anderson, "Colloid transport by interfacial forces," Annu. Rev. Fluid Mech. 21, 61 (1989).
42. B. V. Deryaguin, S. S. Dukhin, and A. A. Korotkova, "Diffusiophoresis in electrolyte solutions and its role in the mechanism of film formation from rubber latexes by the method of ionic deposition," Kolloidn. Zh. 23, 53 (1961).
43. D. C. Prieve, J. L. Anderson, J. P. Ebel, and M. E. Lowell, "Motion of a particle generated by chemical gradients. Part 2. Electrolytes," J. Fluid Mech. 148, 247 (1984).
44. B. V. Deryaguin and S. S. Dukhin, "Theory of surface conductance," Colloid J. USSR 31, 277 (1969).
45. S. S. Dukhin, "Non-equilibrium electric surface phenomena," Adv. Colloid Interface Sci. 44, 1 (1993).
46. 0/2) (Ref. 5).
47. K. T. Chu and M. Z. Bazant, "Surface conservation laws at microscopically diffuse interfaces," J. Colloid Interface Sci. 315, 319 (2007).
48. J. S. Newman, Electrochemical Systems (Prentice-Hall, Englewood Cliffs, 1973).
49. H. A. Stone and A. D. T. Samuel, "Propulsion of microorganisms by surface distortions," Phys. Rev. Lett. 77, 4102 (1996).
50. e=3.99 occurring at ζ =4.79.
51. C. Cottin-Bizonne, J. L. Barrat, L. Bocquet, and E. Charlaix, "Lowfriction flows of liquid at nanopatterned interfaces," Nature Mater. 2, 237 (2003).
52. J. W. G. Tyrrell and P. Attard, "Images of nanobubbles on hydrophobic surfaces and their interactions," Phys. Rev. Lett. 87, 176104 (2001).
53. A. B. D. Cassie and S. Baxter, "Wettability of porous surfaces," Trans. Faraday Soc. 40, 546 (1944).
54. J. Ou and J. P. Rothstein, "Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces," Phys. Fluids 17, 103606 (2005)