The evolution of a viscous gravity current in a confined geometry

We present a study of a viscous gravity current confined to the space between two horizontal parallel plates. Fluid is released at a constant flux from a source located at the center of the lower plate. Two regions of flow develop: an inner region where the fluid is in contact with both plates and an outer annular region where the fluid has not yet reached the upper plate. We develop a simple theoretical model within the context of lubrication theory with the aim of determining the height profile of the free surface, and the evolution equations for the leading edge of the outer annular region as well as the interface position between the two regions. We then perform a series of experiments for various fluxes and gap spacings and compare the results with the theoretical model. A mismatch between the experimental data and the theoretical model is observed and then reduced by incorporating the effect of surface tension at the interface between the two regions into the theoretical model.