Is the kinetic equation for turbulent gas-particle flows ill-posed?

In a recent paper [6] Minier & Profeta (M&P) considered the relative merits of two ProbabilityDensity Function (PDF) based approaches that have been used extensively to model the dispersionof small particles in turbulent gas flows [15, 24]. A major conclusion of their analysis is that the PDFequation associated with the kinetic approach has the properties of a backward heat equation, and as a consequence is ill-posed and therefore an invalid description of dispersed particle flows. We show that the analysis leading to this conclusion is fundamentally flawed, the authors having neglected the coupling between the phase space variables in the kinetic equation and as a consequence incorrectlyidentified a density weighted variable with a convective rather than a diffusive contribution. Weshow that this contribution always outweighs the −ve diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numericalevaluation of analytic solutions of the +ve and −ve contributions to the particle diffusion coefficientin the transformed phase space considered by M&P in their analysis. We also examine numerous other erroneous claims and assumptions made by these authors that demonstrate the apparent superiority of the authors’ so called dynamic PDF approach over the kinetic approach. In so doingwe have drawn attention to the limitations of the ‘dynamic model’ which these authors have chosen to ignore, to give a more balanced appraisal of the benefits of both PDF approaches