The effect of Gibbs adsorption on Marangoni Instability

Abstract

An investigation has been performed to determine the conditions at the onset of surface tension-driven instability, in gas-liquid systems, as characterized by the critical value of a dimensionless Marangoni number. A theoretical analysis, for the case in which a surface tension-lowering solute transfers from a liquid according to penetration theory, shows that adsorption of the solute in the Gibbs layer, at the gas-liquid interface, has a strong ability to retard convective instability. Theories which ignore Gibbs adsorption predict the onset of convection at Marangoni numbers as much as ten thousand times higher than the values found experimentally. With Gibbs adsorption included in the new theory, the discrepancy is very substantially reduced, to a factor of ten or less. Frequently, the residual disagreement has been blamed on the presence of minute amounts of impurities, adsorbed in the Gibbs layer, in the experimental liquids. The revised theory confirms that this influence can be strong under some circumstances. However, new experimental determinations of the critical Marangoni number, during triethylamine desorption from water, show that in typical systems the presence of trace contaminants is inconsequential. It is suggested that further efforts, to resolve the data-theory discrepancy, should focus on the relation between predictions of the critical Marangoni number and assumptions made in the stability theory concerning the size of the convective disturbance cells.