The dynamic mobility of particles in a non-dilute suspension

Abstract

When an alternating electric field is applied to a colloid the particles oscillate at a velocity proportional to the applied field strength. The complex constant of proportionality is termed the dynamic mobility (O'Brien 1988). Although this quantity can now be determined from electroacoustic measurements in suspensions of arbitrary concentration (O'Brien 1990), the theory for interpreting these measurements in terms of the size and charge of the particles is limited to dilute suspensions.In this paper we derive an expression for the O(ϕ) correction to the dynamic mobility in a random suspension of uniform spheres with volume fraction ϕ. It is assumed that the particle radius is much greater than the double layer thickness but much smaller than the sound wavelength. The mobility is calculated using O'Brien's 1979 macroscopic boundary integral technique. This method ensures a correct mathematical formulation of the problem, and yields an absolutely convergent expression for the average particle velocity. The evaluation of this expression to O(ϕ) involves the determination of the velocities of an isolated pair of particles at various separations and frequencies of oscillation. These velocities are computed using the collocation technique and the O(ϕ) correction to the dynamic mobility is then obtained by numerically integrating over all particle separations.