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 σR½ [Gt ] 1, but is prevented from forming by the viscous boundary layer when σR½ [Lt ] 1.