Homogenization in perforated domains: a Stokes grill and an adsorption process

ABSTRACT

We address the homogenization of a model for the diffusion of a substance through an incompressible fluid in a perforated domain , . The perforations (obstacles for the fluid) are periodically placed along a surface . Their size is much smaller than the period . An adsorption phenomenon can occur on the boundaries of the perforations, where we assume a nonlinear law with a large adsorption parameter. The unknowns of the problem are the velocity of the fluid and the concentration of the substance. Using matched asymptotic expansions, we obtain the homogenized models which depend on the relations between the parameters , sizes and adsorption. In particular, we extend the results in the literature for non-homogeneous data on the velocity and general shapes of perforations for the adsorption problem.

Keywords:

• Boundary homogenization
• Stokes problem
• nonlinear problems
• extended capacity
• asymptotic expansions

AMS Subject Classifications:

• 35B27
• 35C20
• 76D30
• 35J65
• 35B40
• 35Q35
• 35J05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the Ministerio de Economía, Industria y Competitividad (MINECO) [grant number MTM2013-44883-P].