An efficient approach to obtain analytical solution of nonlinear particle aggregation equation for longer time domains

Population balances commonly incorporate physical kernels such as polymerization, generalized bilinear, and Brownian aggregation kernels, which have found widespread application in aerosol physics, astrophysics, chemical engineering, mathematical biology, and pharmaceutical sciences to monitor the dynamics of particles. However, finding analytical solutions for physical relevant kernels over longer time domains in order to validate these models remains a challenging task. The aim of this note is to enhance the semi-analytical solutions obtained from the Adomian decomposition method (ADM) for solving the nonlinear aggregation population balance equation. The applicability of ADM is limited to shorter time domains, and the accuracy of its results decreases as the time domain increases, thereby restricting its potential applications. Therefore, a hybrid approach based on ADM and Padé approximant is proposed to find the solutions of the non-linear aggregation equation. The accuracy of the new technique is evaluated by considering Brownian, polymerization and generalized bilinear kernels for which new generalized series solutions are obtained and compared against the finite volume scheme [Kumar et al. (2015), Kinet. Relat. Models 9(2), 373–391]. In addition, the new series solutions for the sum kernel are computed corresponding to a Gamma initial distribution. Quantitative errors in the number density functions are calculated for sum and product aggregation kernels and shown in tables to assess the accuracy of the proposed technique. The results indicate that the new approach provides more accurate analytical solutions for longer time domains while using fewer terms in the truncated series than the ADM and Homotopy perturbation method [Kaur et al. (2019), J. Phys. A: Math. Theor. 52(38), 385201].

Subjects

Adomian decomposition method

Brownian kernel

Finite volume scheme

Nonlinear equation

Padé approximant

DDC Class

600: Technology

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An efficient approach to obtain analytical solution of nonlinear particle aggregation equation for longer time domains