Instability in poroelastic media

Fluid flow in deformable porous materials, which play significant role in different biological and geological systems of wide range of scales, is a highly nonlinear problem. Feedback from the elastic deformation of the solid skeleton on the fluid flow and vice-versa gives rise to pattern formation in the porosity structure of the skeleton [1]. We view some of these patterns as instabilities of the coupled fluid-solid system. Due to highly nonlinear nature of the problem, very little has been understood about this instability. Here, we use a minimal poroelastic theory to understand the pattern formation in a fluid-saturated poroelastic material and discuss the similarities/differences with viscous fingering in non-deformable porous media.\newline $[1]$ C. M. MacMinn, E. R. Dufresne, and J. Wettlaufer, ``Fluid-driven deformation of a soft granular material," Phys. Rev. X 5, 011020 (2015).