Flows in porous media with erosion of the solid matrix
Leda Bucciantini, Angiolo Farína, Antonio Fasano · Networks and Heterogeneous Media · 2010
We consider the flow of an incompressible Newtonian fluid through anidealized porous medium consisting of an array of identical solid symmetriclamellae, whose profile varies in space and time due to a stress inducederosion process. The focus is on the influence of mass exchange betweensolid and fluid on the macroscopic flow. By means of the upscaling procedureillustrated in [6] we derive the governing system ofequations for the macroscopic flow, encompassing various physicalsituations. We show that Darcy's law no longer applies in the classicalsense. The corresponding mathematical problem turns out to be surprisinglycomplicated. Existence and uniqueness are proved. Numerical simulations arepresented.