Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

Abstract

Abstract. We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Bénard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a multimode Galerkin expansion. The oscillatory competition of squares and rolls in the form of crossroll oscillations is reviewed. They undergo a subharmonic bifurcation cascade where the oscillation period grows in integer steps as a consequence of an entrainment process.

Oscillatory Longwave Marangoni Convection in a Binary Liquid. Part 2: Square Patterns

“…They are always unstable near the stability threshold; at finite supercriticality, similarly to AP, stable SCRs may emerge as a result of a secondary bifurcation. For instance, SCRs referred to as "oscillatory cross rolls" were found in [5,6] in the case of buoyancy convection in binary mixtures and ferrofluids, respectively.…”

“…Analysis of pattern formation for wavy patterns is known to be a difficult task which usually leads to massive three-dimensional computations [5,6]. This is the reason that most studies in this field deal with a selection of small-amplitude patterns near the stability threshold of a simple base state where perturbation techniques can be applied [26].…”

Oscillatory convection in binary mixtures: Thermodiffusion, solutal buoyancy, and advection

“…The Poisson equation for the pressure field that results from taking the divergence of (2.2) was solved iteratively using the artificial viscosity method [26]. In addition we used multi-mode Galerkin expansion methods [27].…”

Roll convection of binary fluid mixtures in porous media

“…Especially, if the binary mixture shows a non-vanishing Soret effect, i.e., if concentration currents are driven by temperature gradients, the dynamics of the system are expected to change due to a coupling of the temperature field into the concentration field. For the classical Rayleigh-Bénard system without porous medium, there has been a large body of work dealing with binary mixtures under the influence of the Soret effect (Eaton et al (1991); Barten et al (1995); Huke. & Lücke (2002); Le Gal et al (1985); Dominguez-Lerma et al (1995); Barten et al (1989); Schöpf & Zimmermann (1993); Knobloch & Moore (1988); Cross & Kim (1988); Kolodner et al (1986); Fütterer & Lücke (2002); Touiri et al (1996); Ahlers & Rehberg (1986); Walden et al (1985)).…”

“…if concentration currents are driven by temperature gradients, the dynamics of the system are expected to change due to a coupling of the temperature field into the concentration field. For the classical Rayleigh-Bénard system without porous medium, there has been a large body of work dealing with binary mixtures under the influence of the Soret effect (Le Gal, Pocheau & Croquette 1985;Walden et al 1985;Ahlers & Rehberg 1986;Kolodner et al 1986;Cross & Kim 1988;Knobloch & Moore 1988;Barten et al 1989;Eaton et al 1991;Schöpf & Zimmermann 1993;Barten et al 1995;Dominguez-Lerma, Ahlers & Cannell 1995;Touiri, Platten & Chavepeyer 1996;Fütterer & Lücke 2002;Huke. & Lücke 2002).…”