Stability of thin liquid films

Two topics are discussed in the present progress report. The first is a study of the stability of the interface between two thin immiscible fluid layers in a two-dimensional channel. The flowrates may be specified, or alternatively the total pressure drop and the flowrate of one fluid. The channel may be horizontal or inclined. A long-wave 3D nonlinear evolution equation is derived for the local layer thickness, whose coefficients are high-order polynomials of the viscosity ratio and the initial volume fraction. With a further restriction to small wave amplitude, as well as many slopes, a Kuramoto-Sivashinsky-type (KS) is derived. In countercurrent flow the {open_quotes}group velocity{close_quotes} of the interface can become very small, possibly signaling the onset of flooding. In this case a cubic nonlinearity becomes significant. The properties of this modified KS equation are explored in considerable detail. The classical Yih-Benjamin linear stability theory for long waves on an unforced thin liquid film down a vertical wall has never been experimentally verified, owing to the sensitivity to small random disturbances. However, by careful balancing and by operating under very quiet conditions, the theoretical predictions were verified for the first time. For pointwise measurements, 25-{mu}m resistivity probes were employed, and formore » global measurements fluorescent imaging.« less