Beyond simple mass transfer models for polydisperse systems with fluidic interfaces: a population dynamics approach

In this work the limitations of the standard approaches to describe mass transfer in fluid-fluid systems are critically discussed. Emphasis is placed on polydisperse systems, such as liquid-liquid dispersions. In the simplest possible approach the fluid-fluid disperse system is supposed to be spatially homogeneous and monodisperse: namely all the elements of the disperse phase have the same properties. This very simple, albeit inaccurate, approach is the one typically employed for design, scale-up and optimization of unit operations and of the relative equipment. The adequacy of the model depends on the competition between four phenomena: spatial mixing (induced by convection and turbulent diffusion), coalescence, breakage and mass transfer (often triggered or enhanced by chemical reactions). When spatial mixing dominates the system can be considered spatially homogeneous, whereas when coalescence dominates the only polydispersity that one has to account for is in terms of size. On the contrary when mass transfer or breakage dominate the process, very often both spatial inhomogeneities and polydispersity with respect to size, composition and velocity (of the elements of the disperse phase) must be considered. This can be efficiently done by describing the dynamics of the entire population of elements of the disperse phase, by solving the so-called generalized population balance equation. This latter equation is in turn generally tackled by using quadrature-based moment methods, which can be easily implemented in computational fluid dynamics codes. In this work the governing equations will be analysed and made dimensionless by using characteristic time-scales. These time-scales will then be used to define different regimes, where the spatial homogeneous monodisperse model can be used and where the other models (of increasing complexity) have to be used.