Onset of oscillatory binary fluid convection in three-dimensional cells

Abstract

Abstract. The purpose of this work is to investigate the influence of the transverse walls on the onset of convection in a horizontal rectangular cavity of infinite length filled with a binary mixture when heated from below. For the first time we take into account the effect of the third dimension without making any approximation and considering realistic boundary conditions. In previous numerical works the width of the cell was either taken to be infinity (bulk mixtures) or different approximations usually valid in the narrow cell limit were assumed (i.e. Hele-Shaw and non-ideal Hele-Shaw approximations). The results we find show that the presence of the walls has a considerable effect on the onset of convection even for intermediate transverse aspect ratio cells. They also show that the approximations generally assumed fail to reproduce the correct behaviour of the critical parameters in an important range of aspect ratio values when the primary bifurcation is oscillatory. We have compared the critical values of the Rayleigh number and the frequency that we obtain with those reported in the literature (Ohlsen et al., 1990) and we find a quantitative agreement within the experimental error.

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

“…First, the characteristic Rayleigh numbers in the experiments are higher. This is already known from the suppression of oscillatory or steady convection instabilities in narrow channels [22,52,89]. The no-slip conditions at the side-walls generate a nontrivial y-variation of the velocity field that introduces additional internal friction and that has to be compensated by a higher heating rate [18,90,91].…”

“…These stuctures can efficiently be described in the two dimensional vertical x − z cross section in the middle of the channel perpendicular to the roll axes ignoring variations in axis direction. Furthermore, these convection structures have relevant phase gradients only in x-direction thus causing effectively one dimensional patterns [22].…”

A Characteristic-based Solution of Forced and Free Convection in Closed Domains with Emphasis on Various Fluids

“…The different characteristics of the above-mentioned simulation is reported in this work. Alonso and Batiste [13] work on the convection flow in cavity and the influence of the transverse walls on the onset of convection is surveyed. The down wall of the cavity is heated in this work.…”

Collisions of localized convection structures in binary fluid mixtures

“…Thus, the convection structures have relevant phase variations only in the x-direction. One can well describe them by ignoring variations in the y-axis direction and by considering only the two-dimensional vertical x-z cross section in the middle of the channel perpendicular to the roll axes [33].…”