Speaker
Description
The flow of yield stress fluids in porous media is interestingly complex due to the interplay between the medium's heterogeneity and non-linear rheology. For instance, a non-linear Darcy law emerges as the number of flowing paths increases with the applied pressure difference.
In this talk, we will discuss some of the statistical aspects of this problem. In particular, we will explore how the directed polymer problem — which minimises the energy of a path in a random field — introduced by Kardar, Parisi and Zhang (KPZ) in 1987, relates to the limits of small flow rates and affects nonlinear Darcy's law. An interesting aspect is the influence of the boundary condition on the flow field.
In contrast to the Newtonian case, the type of boundary condition applied to the system significantly affects the flow over a large distance. We will therefore discuss how this distance is controlled by the KPZ universality class, as well as avalanches of a pinned interface.
| Country | France |
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