A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions

A model for transitional breakage probability of droplets in agitated lean fiquid-liquid dispersions is proposed based on the mechanism of breakage of droplets due to their oscillations resulting from relative velocity fluctuations. A universal transitional breakage probability in terms of non-dimensionalized drop diameter is derived for all dispersed phases whose density and viscosity are almost the same as that of continuous phase. The maximum stable drop diameter d_s derived from the model, shows a dependence of N_We^?0.6. It is shown that a “power law” approximation Kvⁿ is valid for transitional breakage probability for d/d_s up to 2. The exponent 2.67, predicted by this model corresponds rather well with an estimate of 2, obtained from experimental observations. A functional relation for the rate constant K in terms of the parameters and physical properties of the system is derived. A universal non-dimensionalized equilibrium drop-size distribution for agitated lean liquid-liquid dispersions is derived by analytical solution of a population balance equation simplified by order of magnitude estimates. Interestingly enough, this analytical solution is the same as the Gaussian distribution suggested empirically by Chen and Middleman.