Recent new models for multiphase flow: coal-water suspensions and oil-water dispersions

In theoretical papers about the dynamics of liquid dispersions, the integral kernels appearing in the evolution equation for the droplet size distribution functions are usually given some generic properties, leaving their analytic structure unspecified. Moreover breakage is always described as a cumulative effect with no reference to the influence of the various breakage modes. Here we want to show how the effort of better understanding these integral kernels, guided by their physical meaning, helps significantly to identify a set of rather simple hypotheses guaranteeing the well posedness of the problem.