Dynamics of pressure propulsion of a sphere in a viscous compressible fluid

A mechanical model of pressure propulsion of a sphere in a viscous compressible fluid is studied on the basis of the linearized Navier-Stokes equations. It is assumed that chemical reactions in the neighborhood of the sphere cause pressure waves which push the sphere. A simple expression is derived for the displacement after a single pulse on the basis of a generalized Faxén theorem. The cooperation of many pulses leads to stochastic behavior of the sphere displacement due to randomness in position of the pulses relative to the sphere surface and due to randomness in time of expansion events.