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In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Numer. Math. and Advanced Appl. Springer Verlag (2010)] and in the present paper, we provide a self-contained...
We study pressure-driven, two-layer flow in inclined channels with high density and
viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the
Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics.
Two distinguished limits are considered: where the viscosity ratio is small with density
ratios of order unity, and where both density and viscosity ratios are small. The evolution equations
account for the presence of...
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