Mark F. Hurwitz

Drag in a Porous Medium: An Example of the Use of Ensemble Averaged Hydrodynamic Potentials

The drag in a porous medium, composed of randomly positioned identical rigid spheres, is calculated as an example of a general framework for the analysis of multiphase flows. The field variables are treated as sums of known fluid fields, independent of the presence of the solid phase, and disturbance fields which account for the effect of the solid phase on the fluid phase. The problem of calculating the ensemble average interaction force is transformed to one related to singular solutions of Stokes equations by representing the disturbance fields in terms of hydrodynamic potentials. Approximate solutions of the problem of a point force outside of two spheres are used to directly calculate the flow resistance in a porous medium. The result is very accurate for solid volume fractions less than 0.5. Because of the inaccuracy of the approximation of the far field interactions among the rigid spheres, the solution is less accurate for more densely packed porous media.