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We perform the linear stability analysis for a new model for poromechanicalprocesses with inertia (formulated in mixed form using the solid deformation,fluid pressure, and total pressure) interacting with diffusing and reactingsolutes convected in the medium. We find parameter regions that lead tospatio-temporal instabilities of the coupled system. The mutual dependencesbetween deformation and diffusive patterns are of substantial relevance in thestudy of morphoelastic changes in biomaterials. We provide a set ofcomputational examples in 2D and 3D (related to brain mechanobiology) that canbe used to form a better understanding on how, and up to which extent, thedeformations of the porous structure dictate the generation and suppression ofspatial patterning dynamics, also related to the onset of mechano-chemicalwaves.

Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue