Onset of Rayleigh−Bénard−Marangoni Convection in Gas−Liquid Mass Transfer with Two-Phase Flow:  Theory

Abstract

Rayleigh and Marangoni instabilities in solute transfer between a gas phase and a liquid phase which are in parallel, laminar, stratified flow between two horizontal plates have been investigated theoretically. The effects of nonlinear velocity profiles of fluid flows and the nonlinear concentration profiles on the onset of RayleighBénard-Marangoni convection in gas-liquid mass transfer of practical importance have been considered in the linear analysis of the general Rayleigh-Bénard-Marangoni problem. In addition, the effect of surface convection and surface diffusion and the effect of surface viscosity of the surface active solute in the Gibbs adsorption layer, which were investigated separately by previous authors, have been combined together. To obtain the variations of the critical Rayleigh number and Marangoni number with the downstream distance of fluid flows, the restriction of the "frozen profile" has been released in the present study. For simplicity, the gas-liquid interface is assumed to be nondeformable.

Transient Rayleigh-Bénard-Marangoni Convection Enhanced Gas-Liquid Solute Transfer in Thin Layers

“…Using reasonably estimated values for the surface viscosity and the surface dilational viscosity of the Gibbs adsorption layers, the calculated values of the overall-system critical concentration are in satisfactory agreement with the measured data (Sun, 2006). In the stationary gas-liquid system where convective patterns are not limited to rolls as is the case in parallel flow systems (Davis and Choi, 1977;Sun and Fahmy, 2006), one would seek normal mode solutions of the form,…”

“…then, after introducing the non-dimensionalising scales h for distance, 2 / l h D for time and 0 i C C C    for concentration, the linearised and non-dimensionalised governing equations for the perturbation fields in the liquid bulk phase 0 1 z   , can be written as follows (here we only reproduce final model equations and we refer the reader to Sun and Fahmy (2006) for further details):…”

“…Since the main objective of this paper is to investigate the effect of the non-diffusing boundaries on the critical parameters and the mass transfer enhancement behaviour of RBM convection, Gibbs adsorption effects have been neglected in the present analysis (Brian, 1971;Brian and Ross, 1972;Palmer and Berg, 1972;Sun and Fahmy, 2006).…”

“…However, in gasliquid solute transfer system with thin liquid layers, the quasi-static analysis is known to predict critical thresholds that are in satisfactory agreement with experiment if the effect of surface viscosity in the Gibbs adsorption layer is considered (Sun, 2006). In thin layer parallel flow gas-liquid solute transfer systems, a quasi-static analysis together with the simplification of flow velocity treatment under penetration conditions show that the critical Rayleigh and Marangoni numbers will continue to monotonically decrease with time (Sun and Fahmy, 2006).…”

“…The stability of such systems have been extensively studied (e.g., Kim et al, 2007;Pearson, 1959;Scriven and Sternling, 1964;Sun and Fahmy, 2006;Lu et al, 1997). Most of these studies have focused on various stability analyses of systems with penetration type concentration profile to determine critical onset time, when the system first becomes unstable.…”