LAUSR

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.