Poroviscoelasticity: Governing model and fundamental solutions*

Poroviscoelastic flows can be observed in many natural phenomena. Recent evidence suggest that large volumes of volcanic melt are disseminated in large crystal mush regions that may span the length of the crust. Furthermore, current studies also suggest that ground surface deformation in these mushy magmatic systems may be caused by both poroelastic and viscoelastic deformation. Some other important examples of coexisting poroelastic and viscoelastic behaviour include boreholes, soil consolidation and hydrocephalic brain tissue.

In this work we aim to combine existing poroelastic and viscoelastic models to present a unified model of poroviscoelasticity and explore its fundamental solutions. In order to do this, we first identify the intrinsic scales and dimensionless control parameters of the problem. We then explore the resulting deformation regimes and asymptotic limits of the system.