Model for convection in binary liquids

Abstract

A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and oscillatory convective states seen for negative Soret coupling: backwards stationary and Hopf bifurcations, saddle node bifurcations to stable strongly nonlinear stationary and traveling wave (TW) states, and merging of the TW solution branch with stationary states. Also unstable standing wave solutions are obtained. A systematic analysis of the concentration balance for liquid mixture parameters has lead to a representation of the concentration field in terms of two linear and two nonlinear modes. This truncation captures the important large-scale effects in the laterally averaged concentration field resulting from advective and diffusive mixing. Also the fact that with increasing flow intensity along the TW solution branch the frequency decreases monotonically in the same way as the mixing increases -the variance of the concentration distribution decreases -is ensured and reproduced well. Universal scaling relations between flow intensity, frequency, and variance of the concentration distribution (degree of mixing) in a TW are predicted by the model and have been confirmed by numerical solutions of the full equations. The validity of the model is checked by comparison with numerical solutions of the full field equations. PACS number(s): 47.10.+g, 03.40.Gc

Thermal convection in a ferrofluid supported by thermodiffusion

“…From a comparison between the experimental data and the theory in Ref. [1], it has been found that the separation ratio in the fluid investigated here takes a high value of c ¼ 1850: This opens for the future the possibility to perform an experimental proof of the square roll flow pattern which has been predicted in Ref. [1].…”

“…Again it is clearly observed that a strong convective flow appears below DT Ã 0 : The solid line is a fit of the theoretical dependence of the amplitude on as is given in Ref. [1]. The free fit parameter is the separation ratio c which is determined from the fit to be c ¼ 1850 AE 100: It should be noted that long-term measurements have shown that the convective flow is stable over time and that no oscillations of the convection amplitude can be observed.…”

“…[1], Fig. 5 shows the amplitude of convectionmeasured over a wide range of temperature differences-as a function of the reduced Rayleigh number ; which is defined by…”

“…For such high values of c; remarkably large convection amplitudes have been predicted in Refs. [1] and [4].…”

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

“…This extended model incorporates the Soret and Dufour effects. However, the Dufour effect is exceedingly weak in liquids and can be safely neglected [9], while the Soret effect can be significant and will be taken into account hereafter. Therefore, in what follows the heat J h and mass J m fluxes are given by…”