Boundary homogenization in perforated domains for adsorption problems with an advection term

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.

Keywords:

• Boundary homogenization
• porous media
• adsorption
• Stokes problem

AMS Subject Classifications:

• 35B27
• 35B40
• 35J65
• 35J05
• 36D07

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the Spanish project MTM2013-44883-P.