Cassandre Lebot "Introduction to the low-Mach-number limit for compressible two-phase flows"
Abstract : This presentation provides an introduction to the low-Mach-number limit for compressible two-phase flows. Such models describe the coupled evolution of a liquid and a gas phase and are widely used in geophysical and industrial contexts. When the characteristic flow velocity is small compared with the speed of sound in the mixture, the governing equations are expected to simplify and approach an incompressible or quasi-incompressible regime.
The core of the talk focuses on the formal derivation of this asymptotic limit. Starting from a general compressible two-phase system with one single velocity, we introduce the nondimensional formulation and analyse how the pressure and velocity terms behave as the Mach number tends to zero. This formal process highlights the constraints imposed by the incompressibility condition, the evolution of phase fractions, and the modifications to the momentum and mass equations.
Charlotte Tonnelier "Modeling problems around the Poisson-Nernst-Planck equations"
Abstract: The movements of charged particles can be modeled by the Poisson-Nernst-Planck equations, completed with a Stokes equation for hydrodynamic behavior. These dynamics are necessary for understanding the methods of energy recovery from saline gradients. We are interested here in modeling these phenomena in a nanofluidic exchanger. We then wish to understand how to model the different scales present in the geometry of the system, as well as the influence of the boundary conditions.