Marangoni instability in non-isothermal first order gas—liquid reactions—evaluations of Cl 2—toluene and CO 2—sodium hydroxide systems

Abstract

A necessary condition for surface tension driven interfacial convection in non-isothermal gas—liquid reaction processes is that the interface be at a higher temperature than the adjacent liquid. In many important practical applications the interface is, however, hotter than the liquid, unless the liquid looses heat to the gas. The magnitude of the dimensionless quantity Biot number, ( Bi), is a measure of the rate of this heat transfer. Its critical value Bi crit is defined as that value which makes the temperature gradient at the interface vanishes. Thus when Bi ⪢ Bi crit the temperature gradient at the interface is positive. It is assumed here that Bi crit constitutes a lower bound of the Biot number below which Marangoni type instability is not possible. Bi crit is evaluated here from the governing unperturbed state equations. This analysis is presented for liquids of both finite and infinite depths. For system conditions which result in a positive temperature gradient at the gas—liquid interface, the results for critical Marangoni number are obtained using small perturbation analysis. Stationary neutral stability curves for chlorine—toluene systems and the relation between independent system parameters and the critical Marangoni number are outlined. The critical Marangoni number shows a curious U-type relation with Biot number. Practical significance of the stability results to the chlorine—toluene system is discussed.