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

Abstract

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 ($\hbox{\it Sl}$) and the particle Reynolds numbers ($\hbox{\it Re}_p$), as well as the fluid-to-particle density ratio $\alpha$. The experiments were designed to cover a range of $\hbox{\it Sl} \hbox{\it Re}_p$ from 0.015 to 5 while keeping $\hbox{\it Re}_p < 0.5$ and $\hbox{\it Sl} > 1$. 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 $a^2/\nu$ is of the same order of the flow time scale $9/\Omega$, where $9$ is a geometrical factor for the sphere, $\nu$ 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.