Abstract
We consider a model for the spreading of a substance through an incompressible fluid in a perforated domain , with . The fluid flows in a domain containing a periodical set of perforations () placed along an inner surface . The size of the perforations is much smaller than the size of the characteristic period . An adsorption phenomena can occur on the boundaries of the perforations, where we assume a strongly nonlinear adsorption law with a large adsorption parameter. An advection term appears in the partial differential equation. We obtain the homogenized model which also involves a nonlinear transmission condition for the normal derivative on . The ‘strange term’ arising in this transmission condition is a nonlinear function implicitly defined by a functional equation. We deal with critical relations both for the size of perforations and the adsorption parameter while we use the energy method for variational inequalities to show the convergence.
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