Effect of gibbs adsorption on marangoni instability

Abstract

SCOPEIn the transfer of mass from one fluid phase to another, solute concentration gradients or temperature gradients may produce surface tension gradients, resulting in cellular convection at the interface. In liquid-liquid extraction systems the convection may become so intense that it causes the break-up of the interface, resulting in "spontaneous emulsification." Often referred to as Marangoni instability, convection driven by surface tension gradients also occurs frequently in gas-liquid mass transfer systems and has been known to enhance the mass transfer rate more than tenfold.A theoretical understanding of Marangoni instability should lead ultimately to the prediction of its occurrence and of its effect upon the mass transfer rate when it occurs, permitting this important phenomenon to be properly accounted for and perhaps even exploited in the design and development of processes involving interphase mass transfer.Previous workers have made substantial progress toward defining the conditions under which the instability occurs, usually measured by the critical value of the Marangoni number. These workers have employed small disturbance hydrodynamic stability theory to predict the point of convective instability. Recent experimental measurements of the critical Marangoni number in desorbing surface tensionlowering solutes from water, however, were found to be several orders of magnitude greater than the theoretical predictions. One speculation offered to explain the discrepancy involved the Gibbs adsorption layer. Because previous theoretical work had not considered the effect of Gibbs adsorption, the present study was undertaken to evaluate the effect of Gibbs adsorption on the theoretically predicted critical Marangoni number. SUMMARYThe influence of Gibbs adsorption has been incorporated into a small disturbance hydrodynamic stability analysis of Marangoni convection. The model used was the first and perhaps the simplest model studied by previous workers, the mass transfer analog of the problem studied by Pearson (9). In this model, the unperturbed state is a horizontal liquid layer at rest, from which a surface tensionlowering solute is desorbing into a gas phase above. The concentration gradient within the liquid layer is linear, and it is assumed that the planar gas-liquid interface is not deformed. The fluid mechanics of the gas phase are not considered, mass transfer in the gas phase being represented by a constant mass transfer coefficient which is unaffected by convection in the liquid phase. These simplifications appear to be adequate for gas-liquid systems, and in any event they are appropriate for this initial analysis of the effect of Gibbs adsorption.The present theory, therefore, involves the incorporation of the effect of Gibbs adsorption into Pearson's hydrodynamic stability analysis. The influence of Gibbs adsorption enters the problem in the boundary condition which Correspondence concerning this article should be addressed to Profes-represents a solute material balance on a small elemen...

Convective instabilities in concurrent two phase flow: Part I. Linear stability

“…Our treatment here will be for instabilities driven by energy transport between the two phases. Recent work by Palmer and Berg (1972) and Brian (1971) has shown that in the case of mass transfer accumulation of mass in the Gibbs layer may have profound stabilizing effects on surface tension driven instabilities. In cases for which the instability arises primarily as the effect of buoyancy or shear, however, the two transport mechanisms are analogous.…”

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

“…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).…”

Visualization and analysis of adsorption behavior of alcohols on aqueous alcohol solution surfaces utilizing Brewster angle videomacrography and digital image processing

“…Such motions sometimes called interfacial turbulence or Marangoni convection (Brian 1971;Bragard et al 1994) are, if adequately controlled, quite effective to promote heat and/or mass transfer across the surfaces. For developing advanced heat/mass transfer technology utilizing surfactant solutions, dynamic as well as static properties of adsorbed surfactant films covering the solution surfaces should be well known.…”