On Existence and Uniqueness of Positive Solutions to Population Balance Models for Column Crystallizers

In this article, we prove the existence and uniqueness of positive/nonnegative solutions on $[0,\infty )$ of population balance models for column crystallizers. These solutions represent the crystal size distributions in the stages of the column. We first investigate a system of ODEs model for a column with no particle agglomeration. Then we consider a system of integrodifferential equations (IDEs) model that accounts for particle agglomeration. In this case, we turn a boundary value problem for a Fredholm-Volterra system of IDEs into an initial value problem of Volterra type IDEs coupled with a system of algebraic equations. We obtain our results employing some algebraic facts along with the Brouwer and the Schauder's fixed point theorems.