Scaling properties of interfacial flows in tubes of rectangular cross-section.

This proposal concerns the propagation of air fingers in liquid-filled tubes of rectangular cross-section. This fundamental interfacial flow is encountered in a wide range of applications from thin-film coating to enhanced oil recovery. The aim of the proposed research is to gain an understanding of the dependence of such flows on the aspect-ratio of the tube, alpha (the ratio of the width to the height of the cross-section). Promising experimental results, obtained in Manchester, suggest that certain global features of finger propagation in tubes of different aspect ratios can be obtained by rescaling master curves , obtained for a square tube, by functions of the aspect ratio. This result is of fundamental significance because it suggests a connection between the interfacial dynamics in square or nearly square tubes (alpha =1- 2) and those in Hele-Shaw cells (alpha >> 1). The evolution of the flow between these two limiting geometries will be characterised in detail using the powerful combination of experiments and three-dimensional numerical simulations.