Introduction

When a viscous flow has a deformable interface, small inertial effects can give rise to an instability which is manifested as interfacial waves. The principal types of such flows are illustrated in Figure 6.1: liquid films falling down an inclined plane, flows induced by a pressure gradient, and shear flows.

Falling films composed of a single layer (Figure 6.1a) or of several layers (Figure 6.1b) are often encountered in coating processes. Examples are coating of paints and varnishes, printing inks, magnetic tape and disks, photographic film, and so on. Flows set in motion by a pressure gradient (Figure 6.1c) are encountered in extrusion of polymers in planar or annular geometries. The third type of flow, shear flow, typically corresponds to a liquid film sheared by a gas (Figure 6.1d), a situation encountered in chemical reactors or heat exchangers, or by Marangoni stresses. In these applications it is often required that the films have uniform thickness, and so it is essential to avoid instabilities. On the other hand, instabilities may actually be desirable because they typically augment rates of heat and mass transfer.

Figure 6.2 illustrates an instability observed in the oil industry in the transport of oil of very high viscosity on the order of a million times that of water. Water, which is injected into the pipe in order to reduce the viscous friction, migrates to the wall where it forms a lubricating film (Joseph et al., 1997).