Inertialess instability of a two-layer liquid film flow

The physical mechanism of instability in a superposed two-layer liquid film flow down an incline plane is analyzed. If the layer adjacent to the wall is sufficiently thin and less viscous in certain two-layer parallel Newtonian liquid flows of the same density with an interface but without a free surface, the flows are stable with respect to long waves. This is the so-called "thin lubrication layer effect." However, when a free surface exists in the two-layered flow, the flow becomes unstable even when the Reynolds number approaches zero. Thus the thin-layer lubrication effect is lost due to the presence of the free surface, and inertialess instability occurs. The reason for the loss of the lubrication effect and the mechanism of inertialess instability are explained by use of the energy budget in the mechanical energy equation. Contrary to the case of two-layer flows without a free surface, the flow with a free surface is stable if the layer adjacent to the solid wall is more viscous. The stabilization is achieved even without help from surface or interfacial tension. The mechanism of stabilization is also elucidated from an energy consideration. Navier-Stokes simulations are then performed to determine the effect of the layer viscosity ratio when nonlinear effects are included. (C) 2004 American Institute of Physics.