J. Non-Equilib. Thermodyn. Vol. 7 (1982), pages 253-258 A Model Describing Soret Diffusion and Convective Instability in a Closed Vertical Column M. G. Velarde, P. L. Garcia-Ybarra Dept. de Fisica Fundamental, Universidad Nacional de Educacion a Distancia, Ciudad Universitaria, Madrid, Spain Received 29 August 1981 Registration Number 217 Key Number 2301 128 Abstract Using Landau's theory of natural convection we describe the onset of Rayleigh- Benard instability in a closed vertical cylindrical column. For binary mixtures, and Soret-driven convection our predictions agree quite satisfactorily with recent experi- mental results reported by Abernathey and Rosenberger. Introduction The strong influence of natural convection on crystallization from vapors has re- cently been emphasized by Rosenberger [1, 2]. To understand thisjphenomenon he and his collaborators have conducted experiments on convective stability in non- reactive binary gas mixtures (Xe:He, Xe:Ar) in closed cylinders heated from below [3—5]. The comparison of their experimental findings with the available predictions for infinitely extended horizontal layers (Rayleigh-Benard convection) [6, 7], con- firmed the expected strong stabilizing effect of lateral boundaries. With mixtures, the effect was shown to be less strong than in experiments with single component fluid layers. The stabilizing effect of the boundaries can be associated with added viscous friction, and energy dissipation imposed by the presence of lateral walls. On the other hand the impervious character of these walls tends to compensate this effect. All fluctuations in composition that reach the impervious walls are rejected back into the fluid and this rejection causes destabilization in the layer [8—12]. In accordance with theoretical predictions for single-component fluid layers (see, for instance, [11 —13]) and the experimental evidence reported by Rosenberger and collaborators [1—5], we assume that natural convection in cylinders (height^ h; dia- meter, d; aspect-ratio 7 ~ d/h < 1) develops in the form of non-axisymmetric rolls (Fig. 1). The two-component gas mixture is confined between walls that are assumed to be rigid, perfect heat conductors and impervious to matter transfer. As the number of rolls, i.e., the wavenumber of the convective pattern is not known and has not been 0340-0204/82/0007-0253$02.00 © Copyright by Walter de Gruyter & Co. - Berlin · New York Brought to you by | The University of Auckland Library Authenticated Download Date | 6/3/15 10:37 PM