Analytical Collection Efficiency of Fine Particles on a Sphere Due to Image Forces

Abstract

The analytic collection efficiencies were obtained for a system in which particles moving in an external flow field impinge upon a spherical collector, where the particles or the collector was electrically charged. The charge on the particles or the collector induces image forces, that is, attractive forces between an electrically charged object and another object in which it induces a polarization. Two types of image force are considered: the charged collector-induced image force (CCIF) and charged particle-induced image force (CPIF). Due to difficulties in determining the exact particle trajectory, the solenoidal assumption, asymptotic stream function, and velocity node were employed. The flow around a spherical collector was modeled for three flow conditions— potential flow, Stokes flow, and Kuwabara flow—and analytic solutions were developed for both the CCIF and CPIF. The collection efficiencies derived for CPIF were in good agreement with numerical data and previous experimental results. For CCIF, the analytic collection efficiencies were a little lower than the numerical results. Analytical solutions for image forces have not been considered before. The present work represents the first time image forces have been accounted for in a theoretical model of particle collection.