A New Bivariate Temom Method For The Fractal-Like Agglomerate Brownian Coagulation

A new bivariate TEMOM method for solving fractal-like agglomerate collision–coalescence dynamics was proposed, which is commonly present in atmospheric microphysics and chemical engineering processes. The Smoluchowski coagulation equation (SCE) is a highly nonlinear integral–differential equation and obtaining numerical solutions for it has been a challenging scientific problem since, especially when the SCE is extended from a single internal coordinate problem to a bivariate problem. Various researchers have already conducted studies in this area, with the most recent breakthrough being Jiang et al. (Bivariate Taylor-series expansion method of moment for particle population balance equation in Brownian coagulation, J. Aerosol Sci. 114 (2017) 94–106), who successfully proposed a new solution of the bivariate SCE by employing the Taylor-series expansion method of moments (TEMOM). However, Jiang et al.’s work is limited to the coagulation problem of spherical particles within a finite-sized regime. This paper further develops the work of Jiang et al. and takes into account the fractal of particles emphatically, extending it to the coagulation problem of bivariate agglomerates within any size regime, making the method a more general and universal research approach. As a validation, we selected the work of Jiang et al. and the log-normal distribution method of moments proposed by Lee et al. (Log-normally preserving size distribution for Brownian coagulation in the free-molecule regime, Aerosol. Sci. Technol. 3(1) (1984) 53–62) to verify the accuracy of the method developed in this paper.