Critical Condition for Collision of Suspended Small Particles with a Body in a Viscous Fluid

Abstract

Critical condition for a small particle to collide with the wall is studied theoretically in an axially symmetrical stagnation point flow of an incompressible viscous fluid. In the phase plane the equation governing a particle trajectory has a singularity at the origin and the behavior of a particle motion near the wall is complex. The critical condition, under which a particle velocity is proportinal to the distance from the wall, is found by using the solution of particle trajectory expanded near the wall. It is governed by three parameters, that is, the Stokes number, the initial position and the initial velocity. On the contrary, in case of an ideal fluid, it is governed by two parameters, that is, the Stokes number and the initial velocity. The particle trajectory is obtained by matching a numerical solution far from the wall with an asymptotic solution near the wall in the phase plane. The results obtained here are also valid in case of the oblique stagnation point flow.