(199d) Exact Solutions of Population Balances Equations Via An Auxiliary Equation Method for Growth, Nucleation, Breakage and Aggregation Processes

There has been a growing interest in the field of population balance equations (PBEs), especially for applications in processes such as granulation and crystallization (Immanuel and Doyle III, 2005; Ma et al., 2002), in aerosol science and biochemical research (Kim and Seinfeld, 1992; Roussos and Kiparissides, 2012). A continuous population balance equation (PBE) involving particulate growth and aggregation, growth, aggregation and breakage, aggregation, nucleation, breakage and growth are investigated in this study. Usually numerical methods are employed to solve these PBEs, because of the absence of an analytical solution. However,  to overcome this, a new technique based on auxiliary equation method (AEM) with a sixth-degree (Pınar and Öziş, 2013a,b) even-power polynomial is proposed to obtain the exact solutions of PBEs under various conditions of growth, nucleation, aggregation and breakage. The proposed method is already applied to growth, nucleation and aggregation processes by Dutta et al. (2013). The proposed method has been found superior to standard numerical methods as it provides analytical solutions for a wide range of initial and boundary conditions. To illustrate the validity and efficiency of the proposed method, analytical solutions obtained with AEM are compared with the numerical solutions, and with the analytical solution as found in the standard literature.

References:

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