Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 1, 2008, Pages

  Hill, Reghan J ^a   Ostoja Starzewski, M ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC DEFORMATION; ELECTRIC FIELD EFFECTS; POLYELECTROLYTES; SATURATION (MATERIALS COMPOSITION);

CHARGED COLLOIDAL PARTICLES; ELASTIC BRINKMAN MEDIUM; ELECTROLYTE-SATURATED POLYMER GEL;

CHARGED PARTICLES;

EID: 38749096636     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.011404     Document Type: Article

References (33)

1. A. M. Lowman, T. D. Dziubla, P. Bures, and N. A. Peppas, Advances in Chemical Engineering, 1st ed. (Elsevier, San Diego, 2004), Vol. 29, pp. 75-130.
2. Reflexive Polymers and Hydrogels, edited by, N. Yui, R. J. Mrsny, and, K. Park, (CRC Press, Boca Raton, FL, 2004).
3. M. J. Bassetti, A. N. Chatterjee, N. R. Aluru, and D. J. Beebe, J. Microelectromech. Syst. JMIYET 1057-7157 10.1109/JMEMS.2005.845407 14, 1198 (2005).
4. M. A. Matos, L. R. White, and R. D. Tilton, J. Colloid Interface Sci. 300, 429 (2006). 0021-9797
5. R. J. Hill, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112005008517 551, 405 (2006).
6. F. C. MacKintosh and C. F. Schmidt, Curr. Opin. Colloid Interface Sci. COCSFL 1359-0294 10.1016/S1359-0294(99)90010-9 4, 300 (1999).
7. E. M. Furst, Curr. Opin. Colloid Interface Sci. COCSFL 1359-0294 10.1016/j.cocis.2005.04.001 10, 79 (2005).
8. M. R. Solomon and Q. Lu, Curr. Opin. Colloid Interface Sci. COCSFL 1359-0294 10.1016/S1359-0294(01)00111-X 6, 430 (2001).
9. N. Willenbacher and C. Oelschlaeger, Curr. Opin. Colloid Interface Sci. 12, 43 (2007). 1359-0294
10. W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989).
11. J. L. Anderson, Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.21.1.61 21, 61 (1989).
12. Here, the elastic restoring force is the value when a rigid sphere with radius a is embedded in an elastic continuum with Young's modulus E and Poisson's ratio ν=0.5.
13. H. C. Brinkman, Appl. Sci. Res., Sect. A ASRAA9 0365-7132 10.1063/1.1312272 1, 27 (1949).
14. F. Booth, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 203, 514 (1950).
15. R. J. Hill, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2140285 124, 014901 (2006).
16. R. W. O'Brien and L. R. White, J. Chem. Soc., Faraday Trans. 2 JCFTBS 0300-9238 10.1039/f29787401607 74, 1607 (1978).
17. R. J. Hill, D. A. Saville, and W. B. Russel, J. Colloid Interface Sci. JCISA5 0021-9797 10.1016/S0021-9797(02)00043-7 258, 56 (2003).
18. R. J. Hill, Phys. Fluids 18, 043103 (2006). 1070-6631
19. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd ed. (Pergamon, New York, 1986).
20. M. Ostoja-Starzewski and C. Wang, Acta Mech. AMHCAP 0001-5970 10.1007/BF01178180 80, 61 (1989).
21. X. Du and M. Ostoja-Starzewski, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 462, 2949 (2006).
22. M. Ostoja-Starzewski, Microstructural Randomness and Scaling in Mechanics of Materials (Chapman and Hall/CRC/Taylor and Francis, New York, 2007).
23. K. Urayama, T. Takigawa, and T. Masuda, Macromolecules MAMOBX 0024-9297 10.1021/ma00064a016 26, 3092 (1993).
24. T. Takigawa, Y. Morino, K. Urayama, and T. Masuda, Polym. Gels Networks PGNEEI 0966-7822 10.1016/0966-7822(95)00013-5 4, 1 (1996).
25. B. Schnurr, F. Gittes, F. C. MacKintosh, and C. F. Schmidt, Macromolecules MAMOBX 0024-9297 10.1021/ma970555n 30, 7781 (1997).
26. Assuming a constant shear modulus E/ [2 (1+ν)].
27. T. Mura, I. Jasiuk, and B. Tsuchida, Int. J. Solids Struct. IJSOAD 0020-7683 10.1016/0020-7683(85)90002-2 21, 1165 (1985).
28. With a slipping boundary condition (i.e., zero radial displacement and zero tangential stress at r=a), the force is -12πEaZ (1-ν) / [(7-8ν) (1+ν)].
29. A finite-difference scheme based on the methodology of Hill, Saville, and Russel is adopted. This features an adaptive, nonuniform grid to handle the disparate length scales.
30. The electrophoretic mobilities reported here were calculated using software (called MPEK, available from the corresponding author) based on the methodology of Hill, Saville, and Russel for the electrophoretic mobility and other single-particle properties of spherical polymer-coated colloids. Here, the influence of a polymer coating is removed by specifying an infinite (large) Darcy permeability for the coating. The mobilities in Figs. 5 6 are in excellent agreement with the O'Brien and White calculations; small differences can be attributed to the opposite sign of the ζ potential.
31. T. M. Squires and J. F. Brady, Phys. Fluids 17, 073101 (2005). 1070-6631
32. Squires and Brady present a compelling case to associate Sutherland with this famous relationship.
33. P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, New York, 1979).