Publication Date:
2013-08-07
Description:
The hydrodynamic diffusion of sedimenting point particles in a vertically sheared periodic system is investigated numerically and theoretically. In both the velocity-gradient direction and the vorticity direction, the rate of hydrodynamic diffusion is reduced as the shear rate is increased. In the velocity-gradient direction, two-particle interactions cause no net displacement, and three-particle interactions are necessary for diffusive behaviour. In contrast to an unsheared system, the resulting diffusion coefficient is only weakly dependent upon the size of the system and Dxx ∼ 4.2× 10-4 n2 f μ 4 ̇ γ-3 ln (0.42 Lμ γ/f1/2, where n is the particle number density, f the force per particle, μ the fluid viscosity, ̇ γ the imposed shear rate, and L the system size. In the vorticity direction, although individual two-particle interactions cause no net displacement, a superposition of interactions is sufficient to cause diffusion-like linear growth of the ensemble-averaged square particle displacements. The associated diffusion coefficient is given by Dyy ∼ 9.47× 10- 4 n2f/μ 2 L γ 1. At sufficiently long times, the effect of multi-particle interactions cannot be neglected and there is a transition to another regime in which the diffusion coefficient is similar in form, but slightly reduced from this value. The dependence of Dxx and Dyy on the number density and dimensionless shear rate is explained using theoretical scaling arguments and analyses. © 2013 Cambridge University Press.
Print ISSN:
0022-1120
Electronic ISSN:
1469-7645
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
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