Influence of shear-induced migration on turbulent resuspension

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In this paper we propose a model which predicts the point at which particles are first ejected from the viscous sublayer of a fluid flowing over a settled layer of particles into the turbulent core. The model, which combines viscous resuspension observations and an understanding of the structure of near-wall turbulence, is expected to be valid only for fine particles where the particle Reynolds number (based on the particle diameter and friction velocity) at resuspension is small. If a settled bed with fluid on top is sheared in a plane Couette device with the bottom plate fixed at low Reynolds nunber (based on the velocity of the top plate and the width of the gap), it has been shown that the shear-induced effective particle diffusivity arising from particle interactions causes the bed to expand. This expansion occurs in a narrow transition region between the settled bed and a region devoid of particles. If this region is thin with respect to the dimensions of the viscous sublayer of the flow, then the turbulent shear stress variations in the near-wall region will be impressed on the resuspending layer. Turbulent resuspension would be expected to occur by this mechanism when the bed has expanded enough that the upward velocity at some point in the resuspending layer caused by the turbulent eddies is greater than the downward settling due to gravity. By formulating the problem in this manner, the contribution of viscous effects to the onset of turbulent resuspension may be predicted from known quantities. The dimensionless steady-state concentration profile caused by the interaction between viscous resuspension and turbulent eddies is found to be characterized by the parameter S = β +[(9/2) ψ] 2(9/2 ψ) 2( Re P +); where β + is the dimensionless magnitude of the vertical velocity of the eddies, measured previously to be β + = 0.005; ψ is the Shields parameter τ/ ΔApga, where τ is the wall shear stress, Δp is the density difference between the particles and the fluid, g is the gravitational acceleration and a is the particle radius; and Re P + is the particle Reynolds number u ∗ d P/v , where u ∗ =(τ/p) 1 2 is the friction velocity, d P is the particle diameter, v is the kinematic viscosity and p is the fluid density. The point at which the model predicts incipient turbulent resuspension to occur is given by S ≈ 5. This point is shown to lie between the Shields criterion for the onset of first motion in a settled layer and the minimum flow condition for the complete resuspension of a settled layerm suggesting that viscous effects do play an important role in incipient turbulent resuspension at low particle Reynolds numbers.