Effect of mass transfer on droplet breakup in stirred liquid‐liquid dispersions

Population balances represent an effective framework for the analysis of rate processes in dispersed phase systems. Mainly, they are able to account for the dynamics of the dispersed phase because of particle breakup and agglomeration while concurrently accounting for the rate processes in single particles. The effectiveness of this framework depends on whether particle phenomena (such as breakage and agglomeration) may be regarded as independent of the rate processes themselves. Thus, for example, in liquid-liquid dispersions one may ask if droplet breakup and coalescence rates may themselves depend on rate processes such as mass transfer. There is very little information in the literature on measurement of drop breakup and coalescence rates even in the absence of mass transfer. In this connection, recent work by Narsimhan et al. (1980, 1984) has reported drop breakup rates in lean liquid-liquid dispersions in which coalescence may be neglected. Their determination of the breakup rates has been accomplished with the aid of a similarity theory. In the present context, it is of interest to ascertain whether the foregoing similarity theory is applicable to dispersions in which mass transfer of a solute is occurring. The primary objective of this note is thus an investigation of droplet breakup when a solute is transferring into the continuous phase. Information about drop breakage pertains to the breakage rates of single droplets as well as the size distribution of daughter droplets arising out of a given breakage. Narsimhan et al. (1980) have formulated and applied a similarity theory to the population balance equation in order to recover the breakage rate of single drops as a function of drop sizes. In their latest work (1984) they have shown that their theory adapts reasonably well to data on transient drop size distributions obtained by direct photographic measurement. Narsimhan et al. (1984) have determined the transitional breakage probability as well as the daughter droplet size distribution from the breakage of a parent droplet. They have characterized the breakage rate as a function of drop sizes and other operational parameters in terms of generalized dimensionless groups. However, their experiments were limited to pure systems. The question then arises as to whether the similarity theory is also applicable for dispersed phase systems with solute in phase equilibrium with the continuous phase, as well as the effect of mass transfer, on drop breakage rate. The similarity theory proposed by Narsimhan et al. (1 984) can be applied more universally if the breakage frequencies do not strongly depend on the transfer rates between the dispersed particles and the containing medium. The main theme of this paper is to verify the applicability of the above similarity theory in the presence of rate processes in droplets.