In this work, the advantages of the generalized fixed pivot technique as extended to mass transfer and the quadrature method of moments are utilized to reduce the bivariate spatially distributed population balance equation describing the coupled hydrodynamics and mass transfer in liquid-liquid extraction columns. The proposed reduction technique is found to reduce the discrete system of partial...

This paper presents our preliminary effort in predicting particle size distributions in particulate processes in turbulent flow systems. The focus has been on processes of pure aggregation, occurring in a turbulent environment. A remarkably simple strategy has been used to solve the population balance equation (PBE) for spatially dependent pure aggregation with insignificant diffusive transport...

This paper presents a comparative study on the application of different numerical methods for the solution of the dynamic bi-variate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the combined action of particle aggregation and/or particle growth are examined. In order to solve the bi-variate PBE the Galerkin finite element me...

Manufacturing processes in which the desired product takes the form of individual particles are ubiquitous in the chemical, pharmaceutical and agricultural industries. Particulate processes often are modeled using a form of the population balance equation (PBE) which describes the evolution of the particle distribution. In many applications, control of the particle distribution is necessary to ...

The population balance equation (PBE) is an integro-partial differential equation, which admits analytical solutions only for a few simple cases. We propose for the first time a novel converging sequence of continuous approximations to the number concentration function as a solution to the PBE. The uniqueness and convergence of such a sequence are assured by being an optimal solution to a const...

Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0, ) ∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluat...

Computational fluid dynamics (CFD), micromixing modeling, and the population balance equation (PBE) are coupled to simulate the crystal size distribution in a confined impinging jet crystallizer. For the antisolvent crystallization of lovastatin in confined impinging jets, the simulation results show varying degrees of inhomogeneity in the supersaturation and the nucleation and growth rates in ...

Aggregation-fragmentation equations arise in many different contexts, ranging from cell division, protein polymerization, biopolymers, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest to develop theoretical and numerical methods to recover reaction rates and parameters of the equation from indirect observation of the solution. Following th...