(98y) The Nature of Branching During Hydrodynamic Instability of Miscible Displacement in Porous Media

Miscible displacement in a bounded fluid-saturated porous layer introduces instabilities due to the viscosity variation caused by temperature variation in the layer and due to a viscosity difference across the surfaces separating the layer from the surrounding fluid.  We find that the problem in the layer itself is very similar in many ways to the B´enard problem with the neutral curve exhibiting the characteristic dip leading to the possibility of many flow cells at the critical speed of displacement.

The viscosity difference across the surface modifies the dip, slightly at large surface tensions, completely  at low surface  tensions. The effect  of the surface deflection is present whether or not the surface is stable and can be omitted only if  the viscosity of the driving fluid is very high or the surface tension is very low.

The nature of the branching at the critical speed depends on the cross section of the fluid layer and on how much of the dip in the neutral curve remains.