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Jump Condition At The Boundary Between A Porous Catalyst And A Homogeneous Fluid, Francisco J. Valdes-Parada, J. Alberto Ochoa-Tapia
Jump Condition At The Boundary Between A Porous Catalyst And A Homogeneous Fluid, Francisco J. Valdes-Parada, J. Alberto Ochoa-Tapia
Francisco J. Valdes-Parada
The method of volume averaging (Whitaker, 1999) is used to derive the jump conditions between a porous catalyst and a homogeneous fluid. To simplify the analysis a first order kinetics is used and the convective transport is neglected. The statement for the derivation is in terms of the spatially smoothed equations obtained by Wood et al. (2000). We have followed a similar procedure to the one used by those authors to derive, besides a jump boundary condition that couples the two media transport, a closure problem to predict the effective reaction rate coefficient at the interregion dividing surface as a …
Darcy's Law For Immiscible Two-Phase Flow: A Theoretical Development, Francisco J. Valdes-Parada, Gilberto Espinoza-Paredes
Darcy's Law For Immiscible Two-Phase Flow: A Theoretical Development, Francisco J. Valdes-Parada, Gilberto Espinoza-Paredes
Francisco J. Valdes-Parada
The aim of this paper is to show how the method of volume averaging can be used to obtain a closed set of averaged equations for bubbling flow. The Navier–Stokes equations are considered as the starting point for the volume-averaging method. The closure was formulated as an associated problem with the deviations around averaged values of the local variables. When the traditional length-scale restrictions are imposed, the volume-averaged momentum equation can be given by &#;vk k – &#;vm m = Kk⋅ (–∇ &#;pk k + ρkgk), which is equivalent to Darcy’s law. The tensor Kk is determined by closure problems …