Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Pattern Formation

DY 15.4: Vortrag

Dienstag, 2. April 2019, 10:45–11:00, H3

DNS of liquid films under lateral and normal excitations — •Sebastian Richter and Michael Bestehorn — Department of Theoretical Physics, BTU, 03044, Cottbus, Germany

We investigate the dynamics of a two-dimensional liquid film on a horizontal substrate with free and deformable surface. The system is subjected to a time-periodic gravitation field in normal or lateral direction. We present a finite-difference method on staggered-grids for the full incompressible Navier-Stokes equations. To avoid surface tracking and to reduce the necessary interpolations to a minimum, the time-dependent free surface is mapped to a constant rectangular region using the non-linear transformation z=h(x,t)·z of the vertical coordinate. Taking the continuity equation into account, a sparse linear system for the pressure, whose solution fulfills momentum and mass conservation, can be computed directly from the discretized Navier-Stokes equations allowing us to refrain from applying pressure corrections. We compare our findings to those of a simplified model studied in [1] and [2]. Vertical excitations generate the classic Faraday waves and lateral forces engender the formation of coarsening droplets. A preferred direction of motion of the drops and a non-vanishing mean flow rate is observed for lateral excitations that break the horizontal mirror symmetry x → −x. Our results show good agreement with the model.

[1] M. Bestehorn, "Laterally extended thin liquid films with inertia under external vibrations", Phys. Fluids 25, 114106 (2013)

[2] S. Richter and M. Bestehorn, "Thin-Film Faraday patterns in three dimensions", Eur. Phys. J. Special Topics 226, 1253 (2017)