Axisymmetric thermophoresis of multiple aerosol spheres

A semianalytic study of the thermophoretic motion of a finite chain of aerosol spheres along the line through their centers is presented. The spheres may differ in radius, in thermal conductivity, and in surface properties, and they are allowed to be unequally spaced. Also, the spheres can be either freely suspended in the gaseous medium or connected by infinitesimally thin rods. The Knudsen numbers are assumed to be small so that the fluid flow is described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surfaces. Through the use of a boundary-collocation method, a set of energy and momentum equations governing this problem is solved in the quasisteady limit and the interaction effects are computed for various cases. For the thermophoretic motion of two-sphere systems, our numerical results for the particle velocities agree very well with the exact calculations using spherical bipolar coordinates. For the cases of two or three spheres touching one another, the numerical solutions for the particle interaction parameters compare quite favorably with the formulas derived analytically. Generally speaking, the particle interaction effects can be significant under appropriate conditions. The influence of the interaction is stronger on the smaller particles than on the larger ones.