Effects of inertia on the slow motion of aerosol particles

The translational motion of a spherical particle and a circular cylindrical particle (in the direction normal to its axis) in a quiescent unbounded fluid at small but finite Reynolds number is examined theoretically. The fluid, which may be a slightly rarefied gas, is allowed to slip at the surfaces of the particles. The axisymmetric Navier-Stokes equation for the fluid flow around the sphere and the two-dimensional equation of motion for the flow surrounding the cylinder are solved by using a method of matched asymptotic expansions. The approximate expressions for the drag force exerted by the fluid on the sphere and the cylinder are obtained analytically. For both cases of a sphere and a circular cylinder, the normalized drag force is found to increase monotonically with the Reynolds number and to decrease monotonically with the dimensionless slip coefficient (or the Knudsen number). The resulting formulas presented here include the previous results for a no-slip rigid sphere, a perfect-slip fluid sphere, and a no-slip circular cylinder as special cases. (C) 2000 Elsevier Science Ltd. All rights reserved.