Coupled Population Balance and Species Balance Models of Crystallization: Analytic Solutions and Data Fits

Abstract

Obtaining kinetic constants in rate laws for nucleation and growth is challenging and essential to the design of the crystallization processes. Starting from the coupled species and population balance equations, we linearize the equations by expanding around the steady state. We then develop analytic solutions that describe the response to a step change in the feed flow rate. We use the analytic solution to extract parameters in the rate laws for nucleation and growth from experimental crystal size distribution data. Specifically, the response of the crystal size distribution to a step change in the feed flow rate, as fitted to the analytic solution, reveals the rate constants and supersaturation dependence in rate laws for growth and secondary nucleation.