title: Long-wave Marangoni convection in a thin film heated from below.
abstract: 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 derive a 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.
authors.affiliation: Department of Chemical Engineering, California Institute of Technology, 1200 California Boulevard, Pasadena, California 91125, USA.
authors.forename: S
authors.initials: S
authors.lastname: Shklyaev
authors.forename: A A
authors.initials: AA
authors.lastname: Alabuzhev
authors.forename: M
authors.initials: M
authors.lastname: Khenner