On the Trajectories of a Small Particle Passing Through a Narrow Curved Channel

Abstract

The motion of a small particle is studied in a viscous flow through a narrow and sinusoidally wavy channel. Assuming that the ratio of the amplitude to the period, the aspect ratio, is small in the walls of the channel, an approximate solution of the equations of motion on the fluid and the particle is found maintainig the precision of the third order of the ratio. It is found that there is only one kind of trajectory along which it is possible for a small particle to pass through the wavy channel. The condition under which a particle passes through the channel is found as a relation of the aspect ratio, the Stokes number, the Reynolds number and the amplitude of the wavy channel. This condition is shown concretly in the aspect ratio-amplitude space by choosing the Stokes number and the Reynolds number as the parameter.