DOI: 10.1021/la902113s 47 Langmuir 2010, 26(1), 47–55 Published on Web 08/27/2009 pubs.acs.org/Langmuir © 2009 American Chemical Society Diffusiophoresis of Concentrated Suspensions of Spherical Particles with Charge-regulated Surface: Polarization Effect with Nonlinear Poisson-Boltzmann Equation James Lou, Chun-Yu Shih, and Eric Lee* Department of Chemical Engineering, Institute of Polymer Science and Engineering, National Taiwan University, Taipei, Taiwan 10617 Received June 12, 2009. Revised Manuscript Received July 23, 2009 Diffusiophoresis in concentrated suspensions of spherical colloids with charge-regulated surface is investigated theoretically. The charge-regulated surface considered here is the generalization of conventional constant surface potential and constant surface charge density situations. Kuwabara’s unit cell model is adopted to describe the system and a pseudospectral method based on Chebyshev polynomial is employed to solve the governing general electrokinetic equations. Excellent agreements with experimental data available in literature were obtained for the limiting case of constant surface potential and very dilute suspension. It is found, among other things, that in general the larger the number of dissociated functional groups on particle surface is, the higher the particle surface potential, hence the larger the magnitude of the particle mobility. The electric potential on particle surface depends on both the concentration of dissociated hydrogen ions and the concentration of electrolyte in the solution. The electric potential on particle surface turns out to be the dominant factor in the determination of the eventual particle diffusiophoretic mobility. Local maximum of diffusiophoretic mobility as a function of double layer thickness is observed. Its reason and influence is discussed. Corresponding behavior for the constant potential situation, however, may yield a monotonously increasing profile. Introduction Diffusiophoresis, the motion of a charged particle in an electrolyte solution due to the concentration gradient of the electrolytes, is an important and interesting fundamental electro- kinetic phenomenon with potential in practical industrial applica- tions, such as the deposition of colloidal paints in the traditional car industry. 1,2 Moreover, in recent years, diffusiophoresis has found abundant novel applications in various fields involving manipulation of colloidal particles, which has been triggered in particular by the huge development of lab-on-a-chip technolo- gies in the context of biological and chemical analysis. 3 On the other hand, in the fundamental study of biological transport, the diffusiophoretic phenomenon shares similarities with chemotaxis, the ability of organisms such as bacteria or cells to move toward higher or lower concentrations of chemicals, nutrients, or poisons. 4-7 Although chemotaxis motion is known to be turned actively by chemosensors detecting chemical gradi- ent, diffusiophoresis appears to be the subsequent physiological driving force, at least in consistent with it. As these salts or chemicals are everywhere within a living biological system, corresponding diffusiophoresis of a suspending colloid is univer- sal as well, although it may be coupled with other phoretic transport phenomena simultaneously. The term “Diffusiophoresis” was first introduced by Deryagin and co-workers. 8,9 They indicated that diffusiophoresis was caused by the polarization of the double layer under the influence of a bulk concentration gradient. The results of their theoretical analysis were verified both theoretically 9 and experimentally 10 later. Meanwhile, Anderson et al. 11,12 conducted a theoretical investigation of the diffusiophoresis of a spherical particle im- mersed in both the electrolyte and nonelectrolyte solutions. Prieve and his co-workers 1,13 studied a very dilute latex system, used in the car industry, both experimentally and theoretically. As for the concentrated colloidal dispersions, Lee and his co- workers 14,15 considered recently the diffusiophoresis of concen- trated spherical particles with arbitrary double layer thickness and zeta potential suspended in electrolyte solutions. The effect of double layer overlapping was considered. They showed, among other things, that the diffusiophoretic velocity exhibits a local maximum as well as a local minimum with varying zeta potential or double layer thickness due to the double layer polarization effect. In the study of suspensions of liquid drops, 16 they observed that invicid liquid drops have a magnitude about three times greater in magnitude as compared with the corresponding rigid particles, while about two times as compared with liquid drops with similar viscosity of the suspending medium. Moreover, Lee *To whom correspondence should be addressed. Telephone: 886-2- 23622530. Fax: 886-2-23622530. E-mail: ericlee@ntu.edu.tw. (1) Smith, R. E.; Prieve, D. C. Chem. Eng. Sci. 1982, 37, 1213–1223. (2) Dukhin, S. S.; Ulberg, Z. R.; Dvornichenko, G. L.; Deryagin, B. V. Bull. Russ. Acad. Sci., Div. Chem. Sci. 1982, 31, 1535–1544. (3) Abecassis, B.; Cottin-Bizonne, C.; Ybert, C.; Ajdari, A.; Bocquet, L. Nat. Mater. 2008, 7, 785–789. (4) Parent, C. A.; Devreotes, P. N. Science 1999, 284, 765–770. (5) Dekker, L. V.; Segal, A. W. Science 2000, 287, 982. (6) Paxton, W. F.; Sundararajan, S.; Mallouk, T. E.; Sen, A. Angew. Chem., Int. Edit. 2006, 45, 5420–5429. (7) Prieve, D. C. Nat. Mater. 2008, 7, 769–770. (8) Deryagin, B. V.; Dukhin, S. S.; Korotkova, A. A. Colloid J. USSR 1978, 40, 531–536. (9) Dukhin, S. S.; Deryagin, B. V. Surface and Colloid Science; Wiley: New York, 1974; Vol. 7. (10) Ulberg, Z. R.; Dukhin, A. S. Prog. Org. Coat. 1990, 18,1–41. (11) Anderson, J. L.; Lowell, M. E.; Prieve, D. C. J. Fluid Mech. 1982, 117, 107–121. (12) Prieve, D. C.; Anderson, J. L.; Ebel, J. P.; Lowell, M. E. J. Fluid Mech. 1984, 148, 247–269. (13) Prieve, D. C.; Roman, R. J. Chem. Soc., Faraday Trans. 2 1987, 83, 1287–1306. (14) Lou, J.; He, Y. Y.; Lee, E. J. Colloid Interface Sci. 2006, 299, 443–451. (15) Hsu, J. P.; Lou, J.; He, Y. Y.; Lee, E. J. Phys. Chem. B. 2007, 111, 2533– 2539. (16) Lou, J.; Lee, E. J. Phys. Chem. C 2008, 112, 12455–12462.