The effect of hydrodynamic interactions on self-organization of dilute assemblies of active rods in lipid membranes and viscous films.

Abstract

Many biological processes involve transport and organization of inclusions in thin fluid interfaces. The dissipative stresses applied from the inclusions to the fluid interface can result in long-range active interfacial flows. We study the effect of these flows on self-organization of active rod assemblies in thin fluid interfaces. Specifically, we consider a dilute assembly of Brownian rods of length <i>L</i>, embedded in a thin fluid interface of 2D viscosity <i>η</i>_m and surrounded on both sides with 3D fluid domains of viscosity <i>η</i>_f. The momentum transfer from the interface to 3D fluids occurs over the length ℓ₀ = <i>η</i>_m/2<i>η</i>_f, known as as Saffman-Delbrück length. We use zeroth, first and second moments of Smoluchowski equation to obtain the conservation equations for concentration, polar order and nematic order fields, and use linear stability analysis and continuum simulations to study the dynamic variations of these fields as a function of <i>L̂</i> = <i>L</i>/ℓ₀, the ratio of active to thermal stresses, and the dimensionless self-propulsion velocity of the embedded particles. We find that at sufficiently large activities, the active pusher suspensions (extensile stress) undergo a finite wavelength nematic ordering instability, with the number of the ordered domains increasing with increasing <i>L̂</i>. The ordering transition is ultimately hindered at larger values of <i>L̂</i>. In pusher suspensions of self-propelled particles, in addition to nematic ordering, the system undergoes large concentration fluctuations. Simulations and linear stability analysis show that the number of ordered domains is reduced with increasing self-propulsion velocity, with the extent of this reduction being dependent on <i>L̂</i>.