Shaping liquid drops by vibration

We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragmentat into smaller drops

Morphology changes in the evolution of liquid two-layer films

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions or the Marangoni effect. Using a long wave approximation we derive coupled evolution equations for the interafce profiles for a general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses are performed for isothermal ultrathin layers below 100 nm thickness under the influence of destabilizing long-range and stabilizing short-range interactions. Flat films may be unstable to varicose, zigzag or mixed modes. During the long-time evolution the nonlinear mode type can change via switching between two different branches of stable stationary solutions or via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil

Worm Structure in Modified Swift-Hohenberg Equation for Electroconvection

A theoretical model for studying pattern formation in electroconvection is proposed in the form of a modified Swift-Hohenberg equation. A localized state is found in two dimension, in agreement with the experimentally observed ``worm" state. The corresponding one dimensional model is also studied, and a novel stationary localized state due to nonadiabatic effect is found. The existence of the 1D localized state is shown to be responsible for the formation of the two dimensional ``worm" state in our model

Mean flow in hexagonal convection: stability and nonlinear dynamics

Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-B\'enard convection at low Prandtl numbers. The mean flow is found to (1) affect only one of the two long-wave phase modes of the hexagons and (2) suppress the mixing between the two phase modes. As a consequence, for small Prandtl numbers the transverse and the longitudinal phase instability occur in sufficiently distinct parameter regimes that they can be studied separately. Through the formation of penta-hepta defects, they lead to different types of transient disordered states. The results for the dynamics of the penta-hepta defects shed light on the persistence of grain boundaries in such disordered states.Comment: 33 pages, 20 figures. For better figures:http://astro.uchicago.edu/~young/hexmeandi