I am interested in the mathematical analysis and modelling of suspension of particles in a viscous fluid. Precisely, it consists in the rigorous derivation of mesoscopic models (kinetic description) by performing a mean-field analysis of the microscopic model (ODEs system for a large number of particles). This asymptotic analysis is related to the homogenization of Stokes equation in a perforated domain. I am also interested in the analysis of the limit model which is a Stokes-transport coupled system. The main interesting aims are existence and uniqueness results for irregular data, analyticity and controllability. Another interesting issue is the long time behaviour and quantitative/qualitative properties of wave equilibria. The modelling of sedimentation of particles in a Stokes flow involves also the rigorous justification of some effective phenomena such as the effective viscosity. A challenging issue is to extend the well-known Einstein's effective viscosity formula for high order terms of the suspension volume fraction. I also collaborated on a work regarding fluid-kinetic modelling for respiratory aerosols that takes into account the radius growth of aerosol particles due to humidity in the respiratory system. This work includes 2D numerical simulations of aerosol deposit in the trachea in order to investigate the hygroscopic effects on the aerosol.
Sedimentation of a droplet in a viscous fluid
link video 1 : fall of a spherical droplet in a cynlindrical container
link video 2 : fall of a spherical droplet in unbounded domain