Author:

Abstract:

The rapidly growing interest in the field of population balances, especially for applications involving complex chemical, biochemical and metallurgical processes need proper scientific attention. This is particularly important for process intensification which helps to optimize a given process. Simultaneous understanding of particulate phenomena like nucleation, growth, aggregation and breakage are needed to build a framework for understanding a range of natural and manufacturing phenomena. A population balance equation (PBE), typically a mass conservation equation, is mathematically a hyperbolic partial integro-differential equation which is used to describe the nonlinear evolution of a density function or the population behavior of a state vector such as size or volume of a particle, droplet or bubble. The evolution of this density function has four different processes that control the population namely, nucleation, growth, aggregation, breakage and adjective transport of the state vector. It is this equation that must be used in systems where there is dependence on spatial position. If however the system is well mixed to be spatial dependence, then the PBE can be averaged over the extent of the external coordinates. In general, the choice of the particle state is determined by the variables needed to specify (i) the rate of change of those variables with direct interest to the application, and (ii) the birth and death processes. Due to the absence of exact analytical solution of this equation, typically referred to as the Population Balance Equation (PBE), numerical methods are often employed to obtain a solution. To overcome the limitation of exact solution, often modified form of semi-analytical solutions such as homotopy methods or auxiliary equation method are preferred. Under various conditions of nucleation, growth, aggregation and breakage, several case studies have been simulated by using the solution(s) of such methods with appropriately chosen parameters and by using homotopy methods. The analytical solutions obtained are compared with numerical or existing semi-analytical solutions from the literature. The proposed talk thus encompasses the various applications and solution strategies to solve population balances in complex process systems.