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

Theory of electrostatically induced shape transitions in carbon nanotubes

A mechanically bistable single-walled carbon nanotube can act as a variable-shaped capacitor with a voltage-controlled transition between collapsed and inflated states. This external control parameter provides a means to tune the system so that collapsed and inflated states are degenerate, at which point the tube's susceptibility to diverse external stimuli-- temperature, voltage, trapped atoms -- diverges following a universal curve, yielding an exceptionally sensitive sensor or actuator that is characterized by a vanishing energy scale. For example, the boundary between collapsed and inflated states can shift hundreds of Angstroms in response to the presence or absence of a single gas atom in the core of the tube. Several potential nano-electromechanical devices can be based on this electrically tuned crossover between near-degenerate collapsed and inflated configurations

Osmotic propulsion of colloidal particles via constant surface flux

We propose a model for the self-propulsion of a small motor particle that generates a nonuniform concentration distribution of solute in the surrounding fluid via a constant solute flux asymmetrically from the motor surface. The net osmotic driving force and motor speed are investigated in the limits of slow and fast product particle flux (relative to the diffusive flux of the product species). When the only solute species in solution is that produced by the motor, the motor's speed is shown to be proportional to the solute flux for slow flux rates and to the square root of the solute flux for large flux rates. When solute species are already present in solution at concentration high compared to that generated by the motor, the motor speed at high flux rates saturates and scales as the diffusivity of the solute divided by the motor size. The analytical results compare well with Brownian dynamics simulations. Full hydrodynamic interactions are taken into account in the theoretical analysis

About causes of slow relaxation of melted intermetallic alloys

Ascertainment of the nature of the slow relaxation processes observed after melting in glass-forming eutectic melts is the subject of this work. We claim that the diffusion processes nonlinearity in heterogeneous melt with inclusions of refractory stoichiometry is the origin of this phenomenon. The cause for this nonlinearity is the thermodynamic instability similar to one taking place at spinodal decomposition, and indispensable condition is the initially non-homogenous. For confirmation of our devotes, we consider the model of liquid solution of a binary system, which evolution described by the Cahn-Hilliard equation with combined Gibbs potential assuming the presence of remains after melting stoichiometric phase. Exemplified by the Al-Y and Al-Yb alloys, using Gibbs potentials from a standard database we show that subject to initial heterogeneity in these systems the instability can develop leading to the slow relaxation processes, and determine the regions of this instability in the phase diagrams

Particle entrapment as a feedback effect

We consider a suspension of polarizable particles under the action of traveling wave dielectrophoresis (DEP) and focus on particle induced effects. In a situation where the particles are driven by the DEP force, but no external forces are exerted on the fluid, the joint motion of the particles can induce a steady fluid flow, which leads to particle entrapment. This feedback effect is proven to be non-negligible even for small volume concentration of particles.Comment: 4 pages, 4 figures, submitte