A. Podolny

Long-wave Marangoni instability in a binary-liquid layer with deformable interface in the presence of Soret effect: Linear theory

We investigate the long-wave Marangoni instability in a binary-liquid layer in the limit of a small Biot number B. The surface deformation and the Soret effect are both taken into account. It is shown that the problem is characterized by two distinct asymptotic limits for the disturbance wave number k, k∼B1∕4 and k∼B1∕2, which are caused by the action of two instability mechanisms, namely, the thermocapillary and solutocapillary effects. The asymptotic limit of k∼B1∕2 is novel and is not known for pure liquids. A diversity of instability modes is revealed. Specifically, a new long-wave oscillatory mode is found for sufficiently small values of the Galileo number.

Periodic Stationary Patterns Governed by a Convective Cahn--Hilliard Equation

We investigate bifurcations of stationary periodic solutions of a convective Cahn--Hilliard equation,

Linear and nonlinear theory of long-wave Marangoni instability with the Soret effect at finite Biot numbers

u_t + Duu_x + (u - u^3 + u_{xx})_{xx} = 0

Long-Wave Marangoni Instability in a Binary-Liquid Layer with a Deformable Interface in the Presence of the Soret Effect: The Case of Finite Biot Numbers

, describing phase separation in driven systems, and study the stability of the main family of these solutions. For the driving parameter

Stability of Stationary Periodic Solutions of the Convective Cahn-Hilliard Equation

D D_0

Dynamics of domain walls governed by the convective Cahn-Hilliard equation

, the periodic stationary solutions are stable if their wavelength belongs to a certain stability interval. It is therefore shown that in a driven phase-separating system that undergoes spinodal decomposition the coarsening can be stopped by the driving force, and formation of stable periodic structures is possible. The modes that destroy the stability at the boundaries of the stability interval are also found.

Long-wave Marangoni instability in a binary liquid layer on a thick solid substrate.

We investigate the long-wave Marangoni instability in binary-liquid layers in the presence of the Soret effect in the case of finite Biot numbers. Linear stability theory reveals both long-wave monotonic and oscillatory modes of instability in various parameter domains. A set of nonlinear evolution equations governing the spatiotemporal dynamics of a thin binary-liquid film is derived. Based on this set of equations, weakly nonlinear analysis is carried out. Selection of stable supercritical patterns is investigated in the limit of low gravity. Various parameter domains are examined in which supercritical standing and traveling waves are found. Stability of superposed two-wave traveling solutions is also investigated.

Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

Abstract We consider a system that consists of a layer of an incompressible binary liquid with a deformable free surface, and a solid substrate layer heated or cooled from below. The surface tension is assumed to depend linearly on both the temperature and the solute concentration. The Soret effect is taken into account. We investigate the long-wave Marangoni instability in the case of asymptotically small Lewis and Galileo numbers for finite surface tension and Biot numbers. We find both long-wave monotonic and oscillatory modes of instability in various parameter domains of the Biot and the Soret number. The weakly nonlinear analysis is carried out in the case of a specified heat flux at the rigid substrate.

Rayleigh-Marangoni Instability of Binary Fluids with Small Lewis Number and Nano-Fluids in the Presence of the Soret Effect

The stability of the main family of odd stationary periodic solutions of the convective Cahn-Hilliard equation is studied. The boundaries of the stability intervals are obtained numerically for selected values of driving force.