Hydrodynamic and hydromagnetic stability

The long-wave instability of a vertical multicomponent fluid layer is investigated. The basic state is a plane parallel flow with linear profiles of temperature and composition in the cross section. The compositional stratification is induced by the Soret effect. The problem is reduced to that without cross-diffusion effect by a linear change of composition and separation ratios that characterize the Soret separation. This is the first report where such transformation is derived for the equations of multicomponent convection with thermal diffusion. It simplifies the system reducing the number of control parameters and can be applied to a variety of multidiffusive convection problems (e.g., Rayleigh–Benard configuration). It is shown that the long-wave instability is caused by the interplay between the basic flow and concentration waves with long scale in the vertical direction. In the general case of n-component mixture, several stable regions in the parameter space are identified. A complete parametric s...

Long-wave instability of a multicomponent fluid layer with the Soret effect

Thermal convection is investigated experimentally in a microgel suspension that consists of core-shell colloids, which change their size with temperature. The swelling and shrinking of the particles strongly modify their volume fraction in the carrier fluid and therefore the viscosity of the suspension. In this experiment, thermal convection in a Hele–Shaw-like apparatus is monitored using the shadowgraph technique. When compared to a normal fluid, the threshold temperature difference is reduced dramatically, which is interpreted as a manifestation of the Soret effect, i.e. the temperature gradient applied to the suspension induces an unstable gradient of the colloid concentration. The wavelength in the nonlinear regime is very different from the one observed in water. Furthermore, transient oscillations of the patterns are detected in the nonlinear regime and are investigated as a function of the applied temperature difference.

https://iopscience.iop.org/article/10.1088/1367-2630/12/5/053003/pdf

Thermal convection in a thermosensitive colloidal suspension

Thermosolutal and binary fluid convection as a 2×2 matrix problem

The convective stability thresholds and nonlinear evolution of convective rolls are numerically investigated in a plane horizontal layer of a colloidal suspension with positive separation ratio in the case of no-slip, impermeable horizontal boundaries. The characteristics of the steady and oscillatory patterns are analyzed under heating and gravity stratification. The standing and traveling waves are found as stable solutions within certain domains of parameters (on the plane of the Rayleigh and the Boltzmann numbers). Complex bifurcation and spatiotemporal properties are caused by the interaction of gravity sedimentation, Soret-induced gradients, and convective mixing of the fluid.

Convection of colloidal suspensions stratified by thermodiffusion and gravity.

Linear, weakly nonlinear, and strongly nonlinear pattern forming properties of binary fluid convection and of systems with throughflow are elucidated with a broad spectrum of numerical and analytical methods and reviewed in comparison with experimental and other theoretical work. Growth dynamics, spatiotemporal behavior, stability, scaling properties, and bifurcation behavior of spatially extended stationary, traveling wave, and standing wave convective roll structures are presented. Also pulselike spatially localized traveling wave convection is investigated. The Dufour effect in gas mixtures is reviewed. 3D square and crossroll patterns and oscillations between them which occur in liquid mixtures are analyzed. In the second part the influence of an externally imposed shear flow on structure formation is investigated. The unique selection of a self sustained forwards bifurcating pattern in the absolutely unstable parameter regime is shown to be a nonlinear eigenvalue problem. Noise sustained pattern growth in the convectively unstable regime is analyzed as a result of bulk thermal fluctuations and of perturbations that are swept by the throughflow into the system via the inlet. Finally, the influence of a lateral flow on linear and nonlinear properties of binary mixture convection is studied with special emphasis on the symmetry breaking of Hopf degenerate traveling waves and their sub critical bifurcation topology.

Pattern Formation in Binary Fluid Convection and in Systems with Throughflow

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Pattern Formation in Binary Fluid Convection and in Systems with Throughflow