In this work two major hydrodynamic parameters: the holdup of the dispersed phase
and the Sauter diameter are considered. In the first part, this is done for describing
the hydrodynamics of interacting liquid–liquid dispersions with using different drop
breakup, coalescence and growth models in a droplet population balance model. Based
on the variational iteration method, different process cases have been performed and, it
is possible to find the exact solution or a closed approximate solution of a problem. For
the simultaneous growth and the coalescence terms a comparison between the present
method and projection method which include discontinuous Galerkin and collocation
techniques are made respectively. The results are encouraging and the new method has
proven to be suitable to predict holdup and Sauter diameter profiles.
In the second part, we extended the dual quadrature method of generalized moments
(DuQMoGeM) to solve the population balance model for the hydrodynamics of liquidliquid
extraction columns using a multi-compartment model. The DuQMoGeM results
were compared to analytical solutions for batch and continuous well-mixed vessels and
extraction columns, showing that it is accurate for predicting the evolution of the low
order moments and the drop number distribution along with the column height. We
also modeled a K¨ uhni column for which the simulation accurately predicted the steadystate
experimental holdup, encouraging the DuQMoGeM usage to solve the population
balance equation for heterogeneous systems and different columns