On the velocity of steady fall of spherical particles through fluid medium

Abstract

1. Recent investigations have called attention to the question as to how closely the rate of fall of particles through a fluid when very small approximates to that given by the law obtained by Stokes from hydrodynamical reasoning. This paper deals theoretically with two of the main sources of divergence from that law. Firstly, taking the particles to be smooth spheres moving through a gas, it is shown that the deviation to be expected on account of the diameter of the particle being small, compared with the molecular free path, is extremely small for such particles as have been experimented with; and a modified formula is given which may be taken to hold approximately for lower pressures or particles of smaller dimensions. Secondly, an approximate treatment is made of the effect of the simultaneous presence of a large number of particles moving with the same velocity through the fluid, and it is found that the force required to maintain the motion of one of them depends not only on the diameter, but on the ratio of the diameter to the distance between the particles, and in such a way as to increase rapidly as this ratio increases beyond the value 0·1.