Two-phase flow of a yield-stress fluid in a porous medium
Contact: Laurent Talon (laurent.talon@universite-paris-saclay.fr), Alex Hansen (alex.hansen@ntnu.no)
Context: Complex fluid flows play a key role in many industrial processes. Among non-Newtonian rheological behaviors, we focus here on yield-stress fluids, which only flow when the applied stress exceeds a critical value. Below this threshold, the material behaves like a solid. This property is common in many industrial fluids, such as injected cements used to stabilize soils or foams used for soil decontamination or to contain the spread of pollutants.
Single-phase flows of yield-stress fluids in porous media have been relatively well studied in recent years [1,2]. An important property is that, depending on the disorder and the applied pressure, some paths flow more easily than others.
Objectives: The objective of this internship is to study dispersed two-phase flows of yield-stress and Newtonian fluids. First, we aim to characterize the different flow regimes. Second, we would like to analyze these regimes from a statistical perspective. In particular, we want to assess the relevance of using a spin-glass model, as recently proposed by Hansen et al. [3] for Newtonian flow.
Co-supervision : The project will be done in collaboration with Alex Hansen (NTNU) and Alberto Rosso (LPTMS, Saclay, France)
[1] Liu, C., De Luca, A., Rosso, A. and Talon, L. Phys. Rev. Lett. 2019
[2] L. Talon, A.A. Hennig A. Hansen and A. Rosso, Phys. Rev. Fluids 2024
[3] A. Hansen, S. Sinha, arXiv:2603.09658
Figure 1: Two phase flow of a yield stress (blue) displaced by a Newtonian fluid (red). The flow is from left to right. The solid state of the fluid is represented in light blue, and the fluid state in dark blue.