37 research outputs found
Long-wave Marangoni convection in a thin film heated from below
We consider long-wave Marangoni convection in a liquid layer atop a substrate of low thermal conductivity,
heated from below.We demonstrate that the critical perturbations are materialized at the wave number K ∼
√Bi, where Bi is the Biot number which characterizes the weak heat flux from the free surface. In addition to the
conventional monotonic mode, a novel oscillatory mode is found. Applying the K ∼ √Bi scaling, we derivea new set of amplitude equations. Pattern selection on square and hexagonal lattices shows that supercritical branching is possible. A large variety of stable patterns is found for both modes of instability. Finite-amplitude
one-dimensional solutions of the set, corresponding to either steady or traveling rolls, are studied numerically;
a complicated sequence of bifurcations is found in the former case. The emergence of an oscillatory mode in the case of heating from below and stable patterns with finite-amplitude surface deformation are shown in this system for the first time
Analysis of vibration impact on stability of dewetting thin liquid film
Dynamics of a thin dewetting liquid film on a vertically oscillating
substrate is considered. We assume moderate vibration frequency and large
(compared to the mean film thickness) vibration amplitude. Using the
lubrication approximation and the averaging method, we formulate the coupled
sets of equations governing the pulsatile and the averaged fluid flows in the
film, and then derive the nonlinear amplitude equation for the averaged film
thickness. We show that there exists a window in the frequency-amplitude domain
where the parametric and shear-flow instabilities of the pulsatile flow do not
emerge. As a consequence, in this window the averaged description is reasonable
and the amplitude equation holds. The linear and nonlinear analyses of the
amplitude equation and the numerical computations show that such vibration
stabilizes the film against dewetting and rupture.Comment: 19 pages, 11 figure