The dynamics of two-layer gravity-driven flows in permeable rock

We examine the motion of a two-layer gravity current, composed of two fluid s of different viscosity and density, as it propagates through a model poro us layer. We focus on two specific situations: first, the case in which eac h layer of fluid has finite volume, and secondly, the case in which each la yer is supplied by a steady maintained flux. In both cases, we find similar ity solutions which describe the evolution of the flow. These solutions ill ustrate how the morphology of the interface between the two layers of fluid depends on the viscosity, density and volume ratios of the two layers. We show that in the special case that the viscosity ratio of the upper to lowe r layers, V, satisfies V = (1 + F)/(1 + RF) where F and R are respectively the ratios of the volume and buoyancy of the lower layer to those of the up per layer, then the ratio of layer depths is the same at all points. Furthe rmore, we show that for V > (<)(1 + F)/(1 + RF), the lower (upper) layer ad vances ahead of the upper (lower) layer. We also present some new laborator y experiments on two-layer gravity currents, using a Hele-Shaw cell, and sh ow that these are in accord with the model predictions. One interesting pre diction of the model, which is confirmed by the experiments, is that for a finite volume release, if the viscosity ratio is sufficiently large, then t he less-viscous layer separates from the source. We extend the model to des cribe the propagation of a layer of fluid which is continuously stratified in either density or viscosity, and we briefly discuss application of the r esults for modelling various two-layer gravity-driven flows in permeable ro ck.