Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers

Andro Mikelić, Vincent Devigne, C. J. van Duijn
2006 SIAM Journal on Mathematical Analysis  
In this paper we present a rigorous derivation of the effective model for enhanced diffusion through a narrow and long 2D pore. The analysis uses a singular perturbation technique. The starting point is a local pore scale model describing the transport by convection and diffusion of a reactive solute. The solute particles undergo a first-order reaction at the pore surface. The transport and reaction parameters are such that we have large, dominant Peclet and Damkohler numbers with respect to
more » ... with respect to the ratio of characteristic transversal and longitudinal lengths (the small parameter ε). We give a rigorous mathematical justification of the effective behavior for small ε. Error estimates are presented in the energy norm as well as in L ∞ and L 1 norms of the space variable. They guarantee the validity of the upscaled model. As a special case, we recover the well-known Taylor dispersion formula.
doi:10.1137/050633573 fatcat:apgffhq5wje5rc3hgpdoydokji