Classification of homogenized limits of diffusion problems with spatially dependent reaction over critical-size particles

ABSTRACT

The main goal of this paper is to characterize the change of structural behavior (i.e. the appearance of the so-called ‘strange terms’) arising in the homogenization process when applied to distributed microscopic chemical reactions taking place on fixed-bed nanoreactors, at the microscopic level, on the boundary of the particles of critical size. The presence of non-homogeneous distributed functions $b_{\epsilon }^j(x)$ of the reaction kinetics may be originated by many different reasons. The case of quick oscillation is often due to own structure of the fixed bed reactor since the flux of the fluid acts on each particle in a non-homogeneous way. In some other cases, the non-homogeneous distributed functions $b_{\epsilon }^j(x)$ of the reaction kinetics is artificially provoked in order to control a certain desired global effect. Our main result gives a complete classification of the strange terms according the assumed periodicity on the distributed functions $b_{\epsilon }^j(x)$ of the reaction kinetic.

KEYWORDS:

• Homogenization
• diffusion processes
• periodic asymmetric particles
• microscopic distributed boundary reaction
• critical sizes

AMS SUBJECT CLASSIFICATIONS:

• 35B25
• 35B40
• 35J05
• 35J20

Notes

No potential conflict of interest was reported by the authors.

Dedicated to the memory of V.V. Zhikov.

Additional information

Funding

The research of D. Gómez-Castro is supported by a FPU fellowship from the Spanish government.The research of J.I. Díaz and D. Gómez-Castro was partially supported by the project ref. Ministerio de Economía y Competitividad [MTM 2014-57113-P] of the DGISPI (Spain).