On the stochastic nature of the motion of nonspherical aerosol particles: IV. Gradient convective rotational velocities in a simple shear flow

Abstract

The rotational diffusion coefficient and the gradient rotational velocities of Brownian cylindrical and discoidal aerosol particles in a pure shear flow were calculated for free molecular regime conditions. The calculations were carried out via the evaluation of the torque operating on the rotating particles due to the momentum exchange with the gas molecules. To that purpose, Chapman's truncated velocity distribution function was adopted and Maxwell's boundary conditions for the reflected molecules used. Under justifiable approximations, it was obtained that the torque along particles' axis i can be given by an equation of the type T M, i = − A ωi + F i , where A i is exactly the inverse of the mobility of the particle in a still medium, ω i is its rotational velocity component, and F i is a function of the particles' orientation and flow gradient. By employing this expression in the Euler equations of rotation and solving the latter numerically as well as analytically for a specific case, it was found that after a negligible transient time the particles acquire an asymptotic gradient rotational velocity identical with the value achieved by neglecting their acceleration. This asymptotic (gradient) rotational velocity was observed to be essentially identical with the classical fluid dynamic values of Jeffery for prolate ellipsoids of the same axes as our particles and which are immersed in a similar flow. An explanation of this equality is offered.