Pattern forming instabilities in mechanically vibrating thin films (INVITED)

Abstract eng:
Thin liquid films with a free surface on a planar horizontal substrate are examined. The substrate is subjected to oscillatory accelerations in normal direction. The description is based on the longwave approximation including inertia effects which are important due to the large velocities imparted by external vibrations. The linearized system is studied using Floquet analysis. Pattern formation in the nonlinear regime is computed numerically from an integrated model of two (three) coupled PDEs for the thickness and the flow rate of the fluid in two (three) spatial dimensions. The treatment can be systematically extended to multi-layer systems of stratified inmiscible liquids.

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