Rotation of non-spherical axi-symmetric particles in the slip regime

Abstract

Aerosol particles are often non-spherical, and the shape has an important influence on the frictional drag and torque, and hence the Brownian motion, the deposition, the sampling and the coagulation of the particles. Since the particle sizes of interest span a wide range, it is important to have experimental as well as theoretical understanding of the frictional drag and torque for particles of arbitrary shapes and sizes. It is also desirable to know the extent to which some useful shape factors can be defined. In recent years there has been considerable progress in the study of non-spherical particles in the continuum regime (low Reynolds number hydrodynamics), and the problem of frictional torque has been solved numerically. This paper addresses the problem of frictional torque of non-spherical axi-symmetric particles at low Reynolds number but with slip boundary conditions. The use of slip boundary conditions is pertinent in aerosol dynamics as it permits consideration of particles in an important size range, where use of a zero slip condition cannot be justified, especially locally, because of the large curvatures of some non-spherical particles. The slip condition does introduce a few complications, both conceptual and numerical. This paper shows that the problem of the rotation of non-spherical axi-symmetric particles with slip conditions can be converted to an integral equation, which can be solved quite effectively by subtraction of singularity and use of quadrature techniques. As an example, numerical results for spheroids (oblate/prolate) are reported, and are shown to be in excellent agreement with analytical results obtained through series expansions. First order approximations to the solution of the underlying equations are given and dependence of the torque on the aspect ratio and Knudsen number is also explored.