Exact solution for the Darcy law of yield stress fluids on the Bethe lattice

Statistical Physics and Complexity Group meeting

Exact solution for the Darcy law of yield stress fluids on the Bethe lattice

  • Event time: 3:00pm until 4:00pm
  • Event date: 17th January 2023
  • Speaker: (University Paris-Saclay)
  • Location: Zoom - see email invite.

Event details

In a series of experiments during the nineteenth century, Henry Darcy studied the flow of water in a cylinder filled with sand and established a famous empirical law: the flow of the liquid grows linearly with  the pressure gradient. Today we know that Darcy's law governs the underground flow of all Newtonian fluids such as water, oil or natural gases, but its simplicity is completely broken in presence of yield stress fluid such as cement, mud or foams. Experiments and extensive numerical simulations  report a non-linear Darcy's law because the number of open channels supporting a non-vanishing flow increases with the pressure gradient. Statistical physics provides the tools to describe the complex landscape of these channels thanks to a mapping with the directed polymer with disordered bond energies. Here we consider this problem on a Cayley tree and use travelling wave equations to derive  the  exact pressure-dependence of the number of open channels and of the total flow. Our predictions are confirmed by extensive numerical simulations.

Event resources