Porous media instability

When one phase is displaced by another in a porous medium, instabilities may develop that allow the displacing phase to finger through the displaced phase, bypassing major portions of it. For this reason, sweep control measures are very important to the success of commercial displacement operations. 

Jang, Jiin Yuh and Chen, Jiing Lin. Thermal Dispersion and Inertia Effects on Vortex Instability of a Horizontal Mixed Convection Flow in a Saturated Porous Medium . Int. J. Heat and Mass Transfer. Vol. 36. No. 2, pp. 383-389. 1993. 

A model of filtration combustion in a thin porous layer, immersed in a bath of gaseous reactant, has also been investigated (Shkadinskii et al, 1992a). In this case, only filtration of gas from the surroundings to the sample, normal to the direction of combustion propagation (cross-flow filtration), should be considered. New pulsating instabilities associated with the gas-solid chemical reaction and mass transfer of gas to the porous medium were identified. 

The third problem is known as the Saffinan-Taylor instability of a fluid interface for motion of a pair of fluids with different viscosities in a porous medium. It is this instability that leads to the well-known and important phenomenon of viscous fingering. In this case, we first discuss Darcy s law for motion of a single-phase fluid in a porous medium, and then we discuss the instability that occurs because of the displacement of one fluid by another when there is a discontinuity in the viscosity and permeability across an interface. The analysis presented ignores surface-tension effects and is thus valid strictly for miscible displacement. ... 

A problem that is somewhat analogous to the instability of an accelerating interface occurs when two superposed viscous fluids are forced by gravity and an imposed pressure gradient through a porous medium. This problem was analyzed in a classic paper by Saffman and Taylor.16 If the steady state is one of uniform motion with velocity V vertically upwards and the interface is horizontal, then it can be shown that the interface is stable to infinitesimal perturbations if... 

Problem 12-17. Buoyancy-Driven Instability of a Fluid Layer in a Porous Medium Based on Darcy s Law. We consider the classical Rayleigh-Benard problem of a fluid layer that is heated from below, except in this case, the fluid is within a porous medium so that the equations of motion are replaced with the Darcy equations, which were discussed in Subsection Cl of this chapter. Hence the averaged velocity within the porous medium is given by Darcy s law... 

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... 

The mosl important early work on interfacial instabilities is that of Saffman and Taylor (1958) who considered the stability of an interface between two immiscible fluids moving vertically through a porous medium. Wooding (1959,... 

In the case of porous solids, powders and fabrics, the measurement of contact angles is not an easy task. Any method is limited to the packing instability of the powders in the test medium, and all data should be viewed with caution, and whenever possible, the contact angles measured in compressed powder cakes should be confirmed by other independent measurements such as measurements on films of this substance prepared by solvent casting or dip coating. There are mainly two methods to measure the contact angle of solid powders ... 

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