THE MOTION OF VISCOUS LIQUID FILMS (FREE-SURFACE-FLOW, FINITE-ELEMENT, ROTATING CHANNEL)

Many free surface flows common in the coating industry are intrinsically unsteady. Disturbances in horizontal liquid films decay monotonically if disturbance wavelength is short enough, and initiate standing wave oscillations if liquid inertia is strong enough. Disturbances in inclined liquid films might decay to a steady flat film or grow to a time-periodic wavy film. These flow phenomena are investigated by three approaches. First, flow phenomena are visualized experimentally with the aid of a moire method capable of continuously measuring area-wide surface topography of liquid films. Next, asymptotic methods valid for small amplitude or long wavelength disturbances give insight into flow mechanisms. Finally, unsteady two-dimensional flows are calculated by means of the finite element method. Evolution of disturbances in horizontal and vertical liquid films is reported.;In addition, flow through a square channel which rotates about an axis perpendicular to the channel top is analyzed by applying the finite element method to the penalty formulation of the Navier-Stokes system. Continuation algorithms are designed to efficiently follow solution branches. Solutions clarify effects not fully explained by existing experiments alone, effects important to industry and oceanographic science alike.