Numerical Simulation of the Dynamics of a Periodically Forced Spherical Particle in a Quiescent Newtonian Fluid at Low Reynolds Numbers

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In this paper we present the results of a numerical simulation of the dynamics of a periodically forced spherical particle in a quiescent Newtonian fluid at low Reynolds number. We describe the simulation and tests performed to validate our simulation. We have obtained results which are physically reasonable and hence we have confidence in our results. We include the effects of both convective and unsteady inertia on the dynamics at low Reynolds numbers. The inclusion of inertia results in additional linear and nonlinear terms in the equations representing a fading memory of the entire history of the motion. The nonlinearity though small in the parametric regime of interest, gives rise to some interesting features in the solution of the problem.