TY - BOOK

T1 - Effective dispersion equations for reactive flows involving free boundaries at the micro-scale

AU - Kumar, K.

AU - Noorden, van, T.L.

AU - Pop, I.S.

PY - 2010

Y1 - 2010

N2 - We consider a pore-scale model for reactive flow in a thin 2-D strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a non-negligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two dimensional solution.

AB - We consider a pore-scale model for reactive flow in a thin 2-D strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a non-negligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two dimensional solution.

M3 - Report

T3 - CASA-report

BT - Effective dispersion equations for reactive flows involving free boundaries at the micro-scale

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -