The motion of small particles in a vicous flow toward a plane wall.

The motion of a small particle in a viscous flow which is driven toward a plane wall by a steady uniform injection at a given distance from the wall is investigated. The particle is assumed to start with the same velocity as the injection velocity of the fluid and to be driven by the interaction force due to Stokes' drag law. The governing equations of the fluid and the particle are found to be simultaneously solvable in the form of similar solutions. That is, they can be reduced to the ordinary differential system. The following results are obtained: the collision between the particle and the wall depends only on the fluid velocity in the direction perpendicular to the wall; the critical Stokes number, above which a particle can collide with the wall, decreases as the Reynolds number increases; the collision can occur more easily in the case of a three-dimensional flow compared with the case of a two-dimensional flow; the critical Stokes number is asymptotically close to that in the case of an ideal fluid with increasing the Reynolds number when the value of the Reynolds number is several thousands, but the critical Stokes number in the case of viscous flow is rather different from that in the case of an ideal fluid, that is, the effect of viscosity is important; the collision in the case of this flow can occur more easily compared with the case of the stagnation-point flow; in the case where the particle collides with the wall, the collision must always occur on the wall at a finite distance from the origin, the frequency of collision increases as the Stokes number increases, and the frequency of collision increases as the Reynolds number increases.