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# The Faraday-Instability: Pattern formation in vibrating thin liquid films

- If a horizontal vibration is combined with a normal one, the motion of a droplet on a horizontal plane can be controled.
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- © MB

Abstract:

Since the first experimental observations of Michael Faraday in
1831 it is known that a vertically vibrating liquid may show an
instability of its flat free surface with respect to oscillating
regular surface patterns, normally squares. These squares oscillate
with half of the driverâ€™s frequency and are in resonance with
gravity waves of the unforced liquid.

In this lecture, thin liquid
films on a horizontal substrate are studied in the longwave
approximation. The films are parametrically excited by mechanical
vertical and/or horizontal oscillations. Inertia effects are taken
into account and the standard thin film formulation is extended by a
second equation for the horizontal mass flow rate. Linear results
based on a damped Mathieu equation as well as fully nonlinear results
found numerically will be presented. We obtain standard Faraday
patterns such as oscillating squares or hexagons. For lateral
vibrations, long wave instabilities in form of coarsening drops are
detected. These drops can move in a certain direction if an additional
vertical excitation is switched on (see figure).

Fotos/SFB910_Bestehorn.png