Edge instability in incompressible planar active fluids

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used in J. Zimmermann, M. Basan and H. Levine, Euro. Phys. J.: Special Topics 223, 1259 (2014), we perform a linear stability analysis on a two dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorise the stability of the model and find that for experimentally relevant parameters, fingering stability is always absent in this minimal model. Our results point to the crucial importance of density variation in the fingering instability in tissue regeneration.
Comment: 9 pages, 4 figures