Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer

We construct a coarse-grained effective two-dimensional (2d) hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy [Phys. Rev. Lett., 102, 118107 (2009)] to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.Comment: accepted in EPJ

Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid

We develop an effective two-dimensional coarse-grained description for the coupled system of a planar fluid membrane anchored to a thin layer of polar ordered active fluid below. The macroscopic orientation of the active fluid layer is assumed to be perpendicular to the attached membrane. We demonstrate that {\em activity} or nonequilibrium drive of the active fluid makes such a system generically linearly unstable for either signature of a model parameter $\Delta\mu$ that characterises the strength of activity. Depending upon boundary conditions and within a range of the model parameters, underdamped propagating waves may be present in our model. We discuss the phenomenological significance of our results.Comment: 13 pages, accepted in EPJ

Role of interfacial friction for flow instabilities in a thin polar ordered active fluid layer

We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient $\Gamma$. Being controlled by $\Gamma$, our model provides a unified framework to describe the long wavelength behaviour of a variety of thin polar-ordered systems, ranging from {\em wet} to {\em dry} active matters and free standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system, that can depend sensitively on $\Gamma$. Based on our results, we discuss estimation of bounds on $\Gamma$ in experimentally accessible systems.Comment: 23 pages, to be published in PR