The steady motion of a sphere in a dusty gas

Abstract

The paper considers the effect on the steady flow past a sphere of a uniform upstream distribution of dust particles having a small relaxation time. Using a potential solution as an upstream model of the gas flow at large Reynolds numbers R , an equation for the concentration of dust near the sphere is derived and solved numerically. It is shown that in this inviscid model there exists a dustfree layer adjacent to the sphere. A drag force is computed, and it is also shown that particles do not collide with the sphere until the Stokes number σ is greater than $\frac{1}{12}$ if we assume the gas flow unchanged by the presence of dust particles, which is in agreement with previous work of Langmuir & Blodgett (1946). The paper concludes with a discussion of the effect of a viscous boundary layer in which it is suggested that the dust-free layer is preserved when σ R ½ [Gt ] 1, but is prevented from forming by the viscous boundary layer when σ R ½ [Lt ] 1.