Percolation and Creeping Flows

Dispersion of solid particles carried by a creeping flow is the outcome of the competition between stresses/pressure imparted by the fluid and the cohesion stresses/pressure of the solid particles. We consider a two-dimensional creeping flow inside a rectangular cavity. Close to the corner adjacent to a moving wall and a stationary wall, the pressure is negative and it diverges as the corner is approached. This negative pressure extends the solid particle and is responsible for its rupture. Using the mean-field percolation model, we determine the distribution of fragments and their average size. We determine the percolation threshold line. Inside the non-percolating region, we determine a line beyond which the particles are completely dispersed.