Control of liquid film instability

The thesis consists of two parts. In the first part, the energy budget in a liquid film flow down a vertical plane subject to three-dimensional disturbances is calculated. The equation relating the average time rate of change of disturbance kinetic energy to the rates of work done by the surface tension, the shear stress, the Reynolds stress, and the rate of mechanical energy dissipation is obtained. Each term in the equation is evaluated in various regions of parameter space to elucidate the physical mechanism of stabilizing an inherently unstable vertical film flow by use of plate oscillation. The Squire theorem which states that two-dimensional disturbances are more dangerous than three-dimensional ones is violated in certain parameter ranges. In these parameter ranges the Reynolds stress enhanced by plate oscillation may cause a falling liquid film, which is stable with respect to two-dimensional short waves, to become unstable with respect to three-dimensional disturbances. In the second part, the control of the onset instability of two-layered flow with free surface down a vertical plate is studied. Numerical results are used to demonstrate that the onset of instability of interface mode and the surface mode can be suppressed simultaneously by oscillating the plate with appropriate amplitudes and frequencies which depend on seven other dimensionless flow parameters. The regions of possible suppression of instability are delineated in the parameter space spanned by the Reynolds number, Strouhal number, the amplitude of oscillation, the Weber numbers (at free surface and interface), the ratios of density, viscosity, and thickness of the two fluids. The effects of all the parameters are discussed. The numerical method used to extract the information from the Floquet linear stability analysis is a Chebeshev collocation point method.