Dresden 2017 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 48: Pattern Formation / Reaction-Diffusion II (joint session DY/BP)
DY 48.3: Talk
Thursday, March 23, 2017, 15:30–15:45, ZEU 118
Surface instabilities in vibrating thin fluid films — •Sebastian Richter1 and Michael Bestehorn2 — 1Department of Theoretical Physics, BTU, 03044, Cottbus, Germany — 2Department of Theoretical Physics, BTU, 03044, Cottbus, Germany
We investigate the spatio-temporal evolution of a thin fluid layer, which is located on a horizontal, solid substrate and is either subjected to a constant or to a time-periodic gravitational force field in normal direction. Starting with an appropriate initial state, the behavior of the liquid is simulated numerically considering both the exact problem and a long wave lubrication approximation based model obtained from the incompressible Navier-Stokes equations. The model includes inertia and viscous friction. For the case of a periodic external force, we observe the formation of time-periodic surface waves (Faraday instabilities) if the frequency and amplitude of excitation meet certain critical values. A Floquet analysis is made to determine the exact stability criteria of the linearized system. Both approaches show good agreement in the limit of a thin fluid geometry: Harmonic excitations generate patterns oscillating harmonically with the driver's frequency (ω) for low frequency ranges and subharmonically (ω/2) at higher frequencies.