An experimental study on stationary history effects in high-frequency Stokes flows

We report results of a series of detailed experiments designed to unveil the dynamics of a particle of radius a moving in high-frequency, low-Reynolds-number oscillatory flow. The fundamental parameters in the problem are the Strouhal (Sl) and the particle Reynolds numbers (Re-p), as well as the fluid-to-particle density ratio alpha. The experiments were designed to cover a range of SIRep from 0.015 to 5 while keeping Re-p < 0.5 and Sl > 1. The primary objective of the experiments is to investigate stationary history effects associated with the Basset drag, which are maximized when the viscous time scale a(2)/v is of the same order of the flow time scale 9/Omega, where 9 is a geometrical factor for the sphere, v is the kinematic viscosity and Omega is the angular frequency of the background flow. The theoretically determined behaviour of stationary history effects is confirmed unequivocally by the experiments, which also validate the fractional derivative behaviour (of order 1/2) of the history drag for the range of parameters under study.