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

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The motion of a small particle in viscous flow through a narrow and sinusoidally wavy channel is studied. Assuming that the ratio of the amplitude to the period, the aspect ratio, is small in the walls of the channel, we find an approximate solution of the equations of motion on the fluid and the particle, maintaining 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 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 channel. This condition is shown concretely in the aspect ratio-amplitude space by choosing the Stokes number and the Reynolds number as the parameters.

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