Microstructure and velocity fluctuations in sheared suspensions

TL;DR

This study investigates velocity fluctuations in sheared suspensions, revealing how microstructure influences these fluctuations and providing theoretical and simulation insights into their statistical properties at low concentrations.

Contribution

It offers a detailed analysis of velocity fluctuations and microstructure effects in sheared suspensions, including a theoretical prediction validated by simulations and a correction for velocimetry measurements.

Findings

Velocity fluctuations are proportional to volume fraction in dilute suspensions.

Theoretical predictions agree with simulations at low concentrations.

Velocity PDFs transition from Gaussian to Stretched Exponential as concentration decreases.

Abstract

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant, non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only for the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an Exponential and finally to a Stretched Exponential functional form as the volume fraction is decreased. We also show that, although the pair distribution function recovers its fore-aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately described by assuming the complete absence of any permanent doublets of spheres. We finally present a simple correction to the analysis of laser-Doppler velocimetry measurements.