Modeling and Simulation of Fluid-Particles Flows

This paper is concerned with models describing disperse particles interacting with a fluid. This work is motivated by the transport of pollutants [14, 39], the dispersion of smokes and dusts [18], the modeling of biomedical flows [7, 5] as well as combustion theory, with applications to Diesel engines or propulsors [1, 2, 20, 34, 40]. The basis of the models we are interested in assumes that the leading effect is due to the drag force exerted by the fluid on the particles. As a warm up, let us explain what is going on with the very simple example of a single particle, spherically shaped with radius a and mass density ρp, dropped in a fluid. The fluid is characterized by its mass density ρ f , its velocity u, and its dynamic viscosity μ. The drag force is supposed to be proportional to the relative velocity between the fluid and the particle so that the motion of the particle is described by the ODE system