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We consider the evolution of a reactive soluble substance introduced into the Poiseuille flow in a slit channel. The reactive transport happens in presence of dominant Péclet and Damköhler numbers. We suppose Péclet numbers corresponding to Taylor's dispersion regime. The two main results of the paper are the following. First, using the anisotropic(More)
Usually the Stokes equations that govern a flow in a smooth thin domain (with thickness of order ε) are related to the Reynolds equation for the pressure p smooth. In this paper, we show that for a rough thin domain (with rugosities of order ε 2) the flow is governed by a modified Reynolds equation for a pressure p rough. Moreover we find the relation p(More)
Existence of weak solutions to a degenerate pseudo-parabolic equation modeling two-phase flow in porous media Abstract In this paper, we consider a degenerate pseudo-parabolic equation modeling two-phase flow in porous media, where dynamic effects in the difference of the phase pressures are included. Because of the special form of the capillary induced(More)
We derive rigorously homogenized models for the displacement of one compressible miscible fluid by another in fractured porous media. We denote by the characteristic size of the heterogeneity in the medium. A parameter α ∈ [0, 1] characterizes the cracking degree of the rock. We carefully define an adapted microscopic model which is scaled by appropriate(More)
We prove that the lubrication approximation is perturbed by a non-regular roughness of the boundary. We show how the flow may be accelerated using adequate rugosity profiles on the bottom. We explicit the possible effects of some abrupt changes in the profile. The limit system is mathematically justified through a variant of the notion of two-scale(More)
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