Numerical Simulations of Activity-Driven Mechanical Instabilities in Gels

Biological systems allow for the generation of active stresses, which can lead to instability and pattern formation. These phenomena often stem from material fluxes induced by active stress, and hence many systems are frequently described using a single, fluid-like phase. However, this description is not sufficient for modeling poroelastic systems such as cartilage, bone, gels, or developing tissue, and the effect of differential activity on the stability of biphasic systems such as these remains largely unstudied. In this talk, we describe a generic hydrodynamic description of active poroelastic media and apply it to an incompressible mixture of solid- and fluid-like phases with varying levels of active stress generation. Simulations are carried out using a custom implementation of Chorin's projection method to enforce incompressibility, and the large linear system resulting from the projection is solved at each time step using a geometric multigrid method. We find this differential activity can drive mechanical instabilities leading to condensation of solid patches and macroscopic contractions. Our results indicate that differential activity, like differential adhesion, size and shape, acts as a generic mechanism for instability.