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An analytic form for the pair distribution function and rheology of a dilute suspension of rough spheres in plane strain flow. (English) Zbl 1074.76051
Summary: The effect of particle-particle contact on the stress of a suspension of small spheres in plane strain flow is investigated. We provide an analytic form for the particle pair distribution function in the case of no Brownian motion, and calculate the viscosity and normal stress difference based on this. We show that the viscosity is reduced by contact, and a normal stress difference is induced, both at order $$c^2$$ for small particle volume concentration $$c$$. In addition, we investigate the effect of a small amount of diffusion on the structure of the distribution function, giving a self-consistent form for the density in the $$O(aPe^{-1})$$ boundary layer and demonstrating that diffusion reduces the magnitude of the contact effect but does not qualitatively alter it (here $$Pe$$ is Péclet number, and $$a$$ characterizes the inter-particle surface-surface separation).

##### MSC:
 76T20 Suspensions 76M35 Stochastic analysis applied to problems in fluid mechanics
##### Keywords:
normal stress difference; diffusion; boundary layer
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