Title:
Consideration of a disjoining pressure model in the interface front capturing method (level-set) for direct numerical simulations of sheared foams.

Context and Motivation:
The rich and complex dynamics of two-phase flows represent a real numerical challenge when simulating them. Specific methods dedicated to the monitoring of the interface between phases (level-set, VOF) and to the consideration of discontinuities at the interface have been developed for several years. However, some mechanisms remain numerically inaccessible, especially when the nature of the flow is strongly multiscale. This is the case, for example, for the stability mechanism of foams, which is ensured by the development of repulsive forces at the level of the liquid film containing the network of gas bubbles, in order to prevent the interfaces from making contact. The difficulty lies in the diversity of the length scales involved, from the radius of action of the repulsive forces (a few dozen nm), to the diameter of the bubbles (a few mm) and the thickness hf of the liquid films (a few µm).

Internship objective:
In order to prevent the coalescence of two bubbles that are too close to each other, we propose to use a disjoining pressure model. The objective of the internship is to include this disjoining pressure model in a computational code dedicated to the direct numerical simulation (DNS) of interfacial incompressible two-phase flows with a level-set function as front capturing method. This model is based on the normal propagation of information from the maximum of the level-set function to the interfaces. This new algorithm aims to be parallelized and tested on realistic configurations.

Skills required:
Master students. Strong interest in numerical methods and CFD in general.