Microstructure and velocity fluctuations in sheared suspensions
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 (the so-called suspension temperature) is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only 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.
- Publication:
-
Journal of Fluid Mechanics
- Pub Date:
- July 2004
- DOI:
- 10.1017/S0022112004009577
- arXiv:
- arXiv:cond-mat/0307478
- Bibcode:
- 2004JFM...511..237D
- Keywords:
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- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Statistical Mechanics;
- Nonlinear Sciences - Chaotic Dynamics;
- Physics - Fluid Dynamics
- E-Print:
- Submitted to Journal of Fluid Mechanics