Suppression of instability in a liquid film flow

The stability of a viscous liquid film flow down an inclined plane that oscillates in the direction parallel to the flow is analyzed by use of a Chebyshev series solution with the Floquet theory. When the inclined plane is stationary, it is known that the onset of the film instability manifests itself as long surface waves [J. Fluid Mech. 554, 505 (1957); Phys. Fluids 6, 321 (1963)] or relatively short shear waves [''Critical angle of shear wave instability in a film,'' to appear in J. Appl. Mech.; J. Eng. Math. 8, 259 (1974); Phys. Fluids 30, 983 (1987)], depending on the angle of inclination: It is demonstrated that the unstable film can be stabilized by use of appropriate amplitudes and frequencies of the plate oscillation to suppress the shear waves as well as the long waves. The ranges of amplitude and frequency in which the film can be stabilized depend on the flow parameter. (C) 1996 American Institute of Physics.