Porous media Brinkman model

Problem 9-22. Flow in a Brinkman Medium. Fluid flow in a packed bed or porous medium can be modeled as flow in a Brinkman medium, which we may envision as a bed of spherical particles. Each particle in the bed (there are n particles per unit volume) exerts a drag force on the fluid proportional to fluid velocity relative to the particle given by Stokes law, i.e., ( —Gtt/hiu, where a is the characteristic size of a bed particle). Thus the equations describing the fluid motion on an averaged scale (averaged over many bed particles, for example) are... 

Problem 12-18. Buoyancy-Driven Instability of a Fluid Layer in a Porous Medium Based on the Darcy-Brinkman Equations. A more complete model for the motion of a fluid in a porous medium is provided by the so-called Darcy Brinkman equations. In the following, we reexamine the conditions for buoyancy-driven instability when the fluid layer is heated from below. We assume that inertia effects can be neglected (this has no effect on the stability analysis as one can see by reexamining the analysis in Section H) and that the Boussinesq approximation is valid so that fluid and solid properties are assumed to be constant except for the density of the fluid. The Darcy Brinkman equations can be written in the form... 

Rigid random arrays have generally been simulated by cell models that have not been limited to dilute suspensions. An early example of a cell model is that of Brinkman (1947), who eonsidered flow past a single sphere in a porous medium of permeability k. The flow is deseribed by an equation that collapses to Darcy s (1856) law (in its post-Darcy form, which includes viscosity) for low values of and to the creeping flow version of the Navier Stokes equation for high values of K. His solution is... 

In order to investigate the influence of shear stresses on the flow property in a yam assembly, the Brinkman equations are used to model flow in a porous medium, as shown in Eqs 4.36 and 4.37. 

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