Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers
@article{Mikeli2006RigorousUO, title={Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers}, author={Andro Mikeli{\'c} and Vincent M. Devigne and C. J. van Duijn}, journal={SIAM J. Math. Anal.}, year={2006}, volume={38}, pages={1262-1287} }
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…
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References
SHOWING 1-10 OF 19 REFERENCES
A centre manifold description of containment dispersion in channels with varying flow properties
- Physics
- 1990
High-order asymptotic approximations to the equation governing the longitudinal dispersion of a passive contaminant in Poiseuille channel flow are derived, and their validity discussed. The…
On the dispersion of a solute in a fluid flowing through a tube
- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1956
Sir Geoffrey Taylor has recently discussed the dispersion of a solute under the simultaneous action of molecular diffusion and variation of the velocity of the solvent. A new basis for his analysis…
SIMPLIFIED MODELS FOR TURBULENT DIFFUSION : THEORY, NUMERICAL MODELLING, AND PHYSICAL PHENOMENA
- Physics
- 1999
Dispersion and convection in periodic porous media
- Physics
- 1986
The problem of transport of a passive solute in a porous medium by convection and dispersion is analysed by the method of homogenization. Assuming that the geometry is periodic, the expressions for…
Dispersion of soluble matter in solvent flowing slowly through a tube
- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1953
When a soluble substance is introduced into a fluid flowing slowly through a small-bore tube it spreads out under the combined action of molecular diffusion and the variation of velocity over the…
Crystal dissolution and precipitation in porous media: Pore scale analysis
- Mathematics
- 2003
Abstract In this paper we discuss a pore scale model for crystal dissolution and precipitation in porous media. We consider first general domains, for which existence of weak solutions is proven. For…
Stability of one‐dimensional boundary layers by using Green's functions
- Mathematics
- 2001
The aim of this paper is to investigate the stability of one‐dimensional boundary layers of parabolic systems as the viscosity goes to 0 in the noncharacteristic case and, more precisely, to prove…
Averaging a transport equation with small diffusion and oscillating velocity
- Mathematics, Environmental Science
- 2001
A complete asymptotic expansion is constructed for the transport equation with diffusion term small with respect to the convection. Error estimates are obtained by using matched asymptotic expansion…
Dispersion in pulsed systems—I: Heterogenous reaction and reversible adsorption in capillary tubes
- Physics
- 1983
Boundary Layers for Viscous Perturbations of Noncharacteristic Quasilinear Hyperbolic Problems
- Mathematics
- 1998
Abstract In this paper, we study viscous perturbations of quasilinear hyperbolic systems in several dimensions as the viscosity goes to zero. The boundary is noncharacteristic for the hyperbolic…