A correction tensor for approximating drag on slow-moving particles of arbitrary shape and Knudsen number

Abstract

In 1910, Cunningham developed a heuristic expression to predict the drag on a slow-moving spherical particle in a gas; a drag that deviates from Stokes' law when the particle's size is comparable to the gas's mean free path. More than a decade later, Millikan proposed a physical argument for correcting Cunningham's work: the resulting expression is known today as the 'Cunningham correction factor'. Despite his contribution, Millikan missed a simpler way to correct Cunningham's expression, one that would have preserved its generality. In this article, this new, simpler form of the Cunningham correction factor is expanded to provide a predictive heuristic for non-spherical particles through the definition of a 'correction tensor'. Its accuracy is tested against experiments and kinetic theory for the sphere, and solutions to the Boltzmann equation for a range of spheroids and an infinitesimally thin circular disc.