Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.65: Poster
Thursday, March 27, 2003, 15:30–18:00, P1
Front and back instability of a liquid film on a slightly inclined plate — •Uwe Thiele1 and Edgar Knobloch2 — 1MPI Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden — 2Dep. Physics, UC Berkeley, CA 94720, USA
We study the transversal instability of a liquid ridge on horizontal and inclined substrates using a film evolution equation based on a long wave approximation. The equation incorporates an additional pressure term – the disjoining pressure – accounting for the effective interaction of the film with the substrate. On a horizontal substrate the dominant instability mode is varicose, but may turn into a zigzag mode on a slightly inclined substrate depending on the inclination angle and the ridge volume. For larger angles or volumes the instabilities at the front and back decouple. The linear stability properties of a one-dimensional ridge-like state are studied in detail, and an energy analysis is used to demonstrate that the disjoining pressure provides the dominant instability mechanism at both the front and the back, while the body force is responsible for the main differences between these two instabilities. An amplitude equation for the time evolution of perturbations with small transverse wavenumbers is derived that predicts correctly the linear crossing of the most dangerous eigenvalues at zero wavenumber in the inclined case, in contrast to the situation on a horizontal substrate.