Implementation of a fragmentation–coagulation–scattering model for the dynamics of stirred liquid–liquid dispersions

The model for the evolution of a liquid–liquid dispersion including the so-called volume scattering effect introduced by the authors in [A. Fasano, F. Rosso, A new model for the dynamics of dispersions in a batch reactor, in: H.J. Bungartz, R.H.W. Hoppe, C. Zenger (Eds.), Proceedings of the Symposium Organized by the Sonderforschungsbereich 438 on the Occasion of Karl-Heinz Hoffman’s 60th Birthday, in: Lectures in Applied Mathematics, Springer Verlag, Berlin, 2000, pp. 123–141] and incorporating multiple breakage–see [A. Fasano, F. Rosso, Dynamics of droplets in an agitated dispersion with multiple breakage. I. Formulation of the model and physical consistency, Math. Methods Appl. Sci. 28 (6) (2005) 631–659; A. Fasano, F. Rosso, Dynamics of droplets in an agitated dispersion with multiple breakage. II. Uniqueness and global existence, Math. Methods Appl. Sci. 28 (9) (2005) 1061–1088]–is considered from a viewpoint closer to applications. The choice of kernels is discussed on the basis of the technical literature (not just using very abstract kernels like in most mathematical papers) and simulations are performed utilizing data from different sources.