EFFECT OF WAVEFORM AND DURATION OF IMPULSE ON THE SOLUTION TO THE BASSET-LANGEVIN EQUATION

New analytic solutions to the continuum hydrodynamic equations for the transient response of a spherical particle at low Reynolds number to several simple excitation forces f(t) of varying duration and different waveforms are presented. The new solutions permit the exploration of the effect of the waveform and the duration of impulse on the relative magnitude of the inertia, quasi-steady Stokes' drag and unsteady boundary layer (Basset) force components throughout the time history of the motion. It is shown that for an impulse of constant magnitude the net displacement of the particle is independent of both the duration and waveform of the excitation force. This simple result is used to explain why one obtains the correct Stokes-Einstein expression for the infinite time diffusion coefficient from a traditional Langevin analysis in which, historically, an incorrect quasi-steady linear Stokes resistance law has been used. © 1979 American Institute of Physics.