A viscoelastic fluid flow through mixing grids


We study the asymtotic behaviour of a viscoelastic fluid in a porous medium ω_\varepsilon (\varepsilon>0) obtained by removing from an open set ω small obstacles (T<sup>\varepsilon</sup><sub>v</sub>)_{1≤{v}≤{n(\varepsilon)}} of size a_\varepsilon periodically distributed on a hyperplane H which intersects ω. We establish that the fluid behave differently depending on whether the size a_\varepsilon is greater than or smaller than a critical size c_\varepsilon. If a_\varepsilon = c_\varepsilon , a convolution term appears in the limit problem. This corresponds to a long memory effect. If a_\varepsilon is smaller than c_\varepsilon, the fluid behaves as if there where no obstacles. If a_\varepsilon is greater than c_\varepsilon or is of the order of the period, the fluid adheres on the hyperplane H which plays a thin solid plate role and the fluid behaves separately on each side of this plate.

DOI Code: 10.1285/i15900932v19n2p153

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