A contribution towards predicting the evolution of droplet size distribution in flowing dilute liquid/liquid dispersions

Abstract

There is growing experimental and theoretical evidence that in common flow fields, such as stirred vessels and pipelines, the steady state of the dispersed phase size distribution (including the maximum stable size X m ) may be unattainable over a time period of practical interest. Therefore, computation of the temporal evolution of the dispersion (through the breakage population balance equation) is indispensable. The necessary breakage rate and breakage kernel can be determined from experimental data by solving the so-called inverse problem. To tackle the latter, an improvement of the method originally developed by Sathyagal et al. (Comput. Chem. Eng. 19 (1995) 437) is presented in this paper. The method is based on the concept of self-similarity of size distributions, which is shown here to hold even if the evolving maximum particle size is relatively close to an existing maximum stable size X m . The proposed improved inversion procedure relies on the observation that the form of the breakage kernel can be inferred from the form of the self-similar distribution representing the experimental data. The new method is very stable with respect to noise in the experimental data.