A mathematical treatment of the effect of particle size distribution on mass transfer in dispersions



A mathematical model is proposed that takes into account interaction between drops or bubbles in a swarm as well as the effect of particle size distribution. The model is used to solve the equations for unsteady state mass transfer with and without chemical reaction when the drops or bubbles are suspended in a nonextraordinarily purified agitated fluid. Steady state diffusion to a family of moving drops with clean interface and without interaction and chemical reaction has been also analyzed. The model demonstrates the sort of error that may arise when one applies uniform drop size assumptions to drop populations. It is shown quantitatively that this error is usually small when one replaces the variable particle size by the mean. By using variables that can be determined and predicted, the equations presented permit the estimation of diffusion rate per unit area of interface, as well as the average concentration and the total average rate of mass transfer in the disperser under pseudo steady state conditions.