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Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions

Leonid Berlyand·Yuliya Gorb·Alexei Novikov
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Abstract

We present a two-dimensional (2D) mathematical model of a highly concentrated suspension or a thin film of the rigid inclusions in an incompressible Newtonian fluid. Our objectives are two-fold: (i) to obtain all singular terms in the asymptotics of the overall viscous dissipation rate as the interparticle distance parameter $δ$ tends to zero, (ii) to obtain a qualitative description of a microflow between neighboring inclusions in the suspension.

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Leonid Berlyand, Yuliya Gorb, Alexei Novikov. 2006-08-28. Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions. https://arxiv.org/abs/math/0608671

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