Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes

Abstract

Please cite this article as: A. Hasseine, H.-J. Bart, Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes, Appl. Math. Modelling (2014), doi: http:// dx. AbstractThe dynamic behavior of particulate processes under the influence of the nonlinear aggregation term, nucleation, growth and breakup is studied. Analytic solutions are obtained from the integro-differential population balance equation governing the particle size distribution density function for special cases by the Adomian decomposition method (ADM) and are compared with other analytical solutions available in the literature. It avoids the difficulty numerical stability that often characterizes general numerical techniques in this area. It generates an infinite series which converges uniformly to the exact solution of the problem. For the case where there are no previous results a comparison between the present method and projection method which include collocation techniques is made.The results obtained indicate that the Adomian decomposition method is highly accurate, efficient and are useful for further work.

On the expedient solution of the magneto-hydrodynamic Jeffery-Hamel flow of Casson fluid

“…Figure ( 1) shows the geometry of the MHD Jeffery-Hamel flow. The walls stretch/shrink at a rate s with radial distance of r and the velocity at the walls is: The constitutive equation describing an incompressible non-Newtonian Casson fluid is written as follow 22 : In Eq. ( 2 ), where μ B denotes the plastic dynamic viscosity of the non-Newtonian fluid, P y is the yield stress of the fluid, π is the product of the component of deformation rate with itself, namely, π = e ij e ij where e ij is the ( i , j ) th component of the deformation rate and π c is a critical value of this product based on the non-Newtonian model.…”

GPU‐accelerated simulation of polydisperse multiphase flows using dual‐quadrature‐based moment methods

“…Polydisperse multiphase flows are present in several industrial technologies, such as spray combustion, bubble column reactor, fluidized bed reactor, and so on . This is one of the reasons why the academia has been devoting a significant amount of effort on this topic . Basically, there are three main approaches to predict the polydisperse multiphase flow behaviour: the fully resolved, the Lagrangian point‐particle, and the Eulerian‐Eulerian (E‐E) models …”

Numerical study on fractal-like soot aggregate dynamics of turbulent ethylene-oxygen flame

“…[21]. Considerable research studies on particle dynamics are carried out by many researchers [7,[24][25][26][27][28][29][30][31] to overcome the complexity and difficulty in theoretical and experimental studies on PBE. Generally, PBE proposed by Friedlander [22] is adequate to describe typical aerosol dynamic processes including nucleation, condensation, and coagulation etc.…”

“…The popular numerical methods for the solution of PBE mainly include sectional methods [32][33][34][35], Monte Carlo methods [30,[36][37][38][39][40], and moment methods [7,[41][42][43][44]. On the other hand, the exact and analytical solutions of PBE can also be obtained by e.g., the group analysis [28,31] and the separate variable method [45]), respectively. As far as fractal aggregates are concerned, a modified coagulation kernel including a pre-specified fractal dimension for the entire aggregate population is often used due to the computing limitations [46].…”