Phoretic motion of arbitrary clusters of N spheres

Phoretic motion of particle clusters suspended in a liquid or a gas is obse rved when an external gradient of some physical property (temperature, spec ies concentration, electrostatic potential, etc.) is applied to the system. In this study, a theory of phoretic motion of clusters of arbitrary number of spherical particles is built for example of thermophoresis in the near- continuum regime. Using a multipole expansion of the temperature and flow v elocity in a series of spherical harmonics and formulating the Lamb's bound ary conditions for velocity on the cluster surface, the problem is reduced to solution of the infinite system of linear equations for the expansion co efficients. For practical applications, the system is truncated and the tru ncation level is the only parameter, determining the accuracy of obtained n umerical solution. The method is characterized by good convergence, as show n by comparing predictions of the described theory with available theoretic al results. Based on the developed theory, influence of shape and size of v arious particle clusters on their thermophoretic velocity is established. I n another application, the electrophoretic behavior of binary clusters, con sisting of spherical colloidal particles with different signs of zeta-poten tials, is investigated. It is found that ensemble-averaged electrophoretic velocity in general case can be adequately described using the Smoluchowski model with average value of zeta potential in the cluster. (C) 2001 Academ ic Press.