Seminar

Zoom Link

In this talk, I will present two mathematical models describing heat exchange in gas–particle mixtures. The starting point is a purely kinetic framework, coupling two collisional equations in which interactions between gas molecules and dispersed particles (such as dust grains) are modeled through a diffuse reflection mechanism. 

In the first model, we introduce an additional internal variable in the particle distribution function to enforce energy conservation at the collision level. By performing a formal asymptotic analysis in a double small-parameter regime, we derive a Vlasov–Euler type system. This limiting model explicitly contains terms accounting for drag forces and interphase energy transfer. This part of the work was carried out in collaboration with Laurent Desvillettes.

In the second model, the particle surface temperature is instead treated as a macroscopic field depending on time and space, whose evolution satisfies a balance law ensuring global conservation of total energy. A diffusive asymptotic limit then leads to a two-species cross-diffusion system, capturing the coupled thermal dynamics of the gas and particle phases. This second part is the result of joint work with Francesco Salvarani and Annamaria Massimini.

Derivation of Macroscopic Heat Exchange Models in sprays