Janus droplet as a catalytic micromotor

Self-propulsion of a Janus droplet in a solution of surfactant, which reacts on a half of a drop surface, is studied theoretically. The droplet acts as a catalytic motor creating a concentration gradient, which generates its surface-tension-driven motion; the self-propulsion speed is rather high, $60\; {\rm \mu m/s}$ and more. This catalytic motor has several advantages over other micromotors: simple manufacturing, easily attained neutral buoyancy. In contrast to a single-fluid droplet, which demonstrates a self-propulsion as a result of symmetry breaking instability, for Janus one no stability threshold exists; hence, the droplet radius can be scaled down to micrometers. The paper was finalized and submitted by Denis S. Goldobin after Sergey Sklyaev had sadly passed away on June 2, 2014.Comment: 5 pages, 4 figures, submitted to Europhys. Let

Marangoni instability of a heated liquid layer in the presence of a soluble surfactant

We consider the influence of adsorption kinetics on a longwave oscillatory instability in a layer of a binary liquid heated from below. It is shown that an advection of the adsorbed surfactant leads to a strong stabilization of the mode. Qualitative explanation of the numerical results is provided

Superexponential droplet fractalization as a hierarchical formation of dissipative compactons

We study the dynamics of a thin film over a substrate heated from below in a framework of a strongly nonlinear one-dimensional Cahn-Hilliard equation. The evolution leads to a fractalization into smaller and smaller scales. We demonstrate that a primitive element in the appearing hierarchical structure is a dissipative compacton. Both direct simulations and the analysis of a self-similar solution show that the compactons appear at superexponentially decreasing scales, which means vanishing dimension of the fractal

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

Oscillatory long-wave Marangoni convection in a layer of a binary liquid: Hexagonal patterns

We consider a long-wave oscillatory Marangoni convection in a layer of a binary liquid in the presence of the Soret effect. A weakly nonlinear analysis is carried out on a hexagonal lattice. It is shown that the derived set of cubic amplitude equations is degenerate. A three-parameter family of asynchronous hexagons (AH), representing a superposition of three standing waves with the amplitudes depending on their phase shifts, is found to be stable in the framework of this set of equations. To determine a dominant stable pattern within this family of patterns, we proceed to the inclusion of the fifth-order terms. It is shown that depending on the Soret number, either wavy rolls 2 (WR2), which represents a pattern descendant of wavy rolls (WR) family, are selected or no stable limit cycles exist. A heteroclinic cycle emerges in the latter case: the system is alternately attracted to and repelled from each of three unstable solutions

Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis

We consider a sessile hemispherical bubble sitting on the transversally oscillating bottom of a deep liquid layer and focus on the interplay of the compressibility of the bubble and the contact angle hysteresis. In the presence of contact angle hysteresis, the compressible bubble exhibits two kinds of terminal oscillations: either with the stick-slip motion of the contact line or with the completely immobile contact line. For the stick-slip oscillations, we detect a double resonance, when the external frequency is close to eigenfrequencies of both the breathing mode and shape oscillations. For the regimes evolving to terminal oscillations with the fixed contact line, we find an unusual transient resembling modulated oscillations

Influence of a low frequency vibration on a long-wave Marangoni instability in a binary mixture with the Soret effect

We study the influence of a low frequency vibration on a long-wave Marangoni convection in a layer of a binary mixture with the Soret effect. A linear stability analysis is performed numerically by means of the Floquet theory; several limiting cases are treated analytically. Competition of subharmonic, synchronous, and quasiperiodic modes is considered. The vibration is found to destabilize the layer, decreasing the stability threshold. Also, a vibration-induced mode is detected, which takes place even for zero Marangoni number

Enhanced stability of a dewetting thin liquid film in a single-frequency vibration field

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