SHEAR STABILIZATION OF MISCIBLE DISPLACEMENT PROCESSES IN POROUS-MEDIA

The interface region between two fluids of different densities and vis cosities in a porous medium in which gravity is directed at various an gles to the interface is analyzed. Under these conditions, base states exist that involve both tangential and normal velocity components. Th ese base states support traveling waves. In the presence of a normal d isplacement velocity, the amplitude of these waves grows according to the viscous fingering instability. For the immiscible case, it can eas ily be shown that the growth rate is not affected by the tangential ve locities, while surface tension results in the usual stabilization. Fo r the case of two miscible fluids, the stability of the base states us ing the quasi-steady-state approximation is investigated. The resultin g equations are solved analytically for time t=0 and a criterion for i nstability is formulated. The stability of the flow for times t>0 is i nvestigated numerically using a spectral collocation method. It is fou nd that the interaction of pressure forces and viscous forces is modif ied by tangential shear as compared to the classical problem, resultin g in a stabilizing effect of the tangential shear. The key to understa nding the physical mechanism behind this stabilization lies in the vor ticity equation. While the classical problem gives rise to a dipole st ructure of the vorticity field, tangential shear leads to a quadrupole structure of the perturbation vorticity field, which is less unstable . This quadrupole structure is due to the finite thickness of the tang ential base state velocity profile, i.e., the finite thickness of the dispersively spreading front, and hence cannot emerge on the sharp fro nt maintained in immiscible displacements.