Negative apparent viscosities, non-monotonic flow curves and multiple mechanical equilibria in the rheology of active suspensions*

Active suspensions, such as swarms of bacteria and the cytoskeleton of living cells, consist of anisotropic motile units interacting in a passive medium. Because these active units self-organize and collectively induce mechanical stresses in the bulk, they may, under shear, reduce the apparent viscosity of the suspension. Recently, using a highly sensitive rheometer, Lopez et al. (PRL 115, 2015) were able to measure zero and possibly negative values of the apparent viscosity in a suspension of E. Coli. In this talk, we will use a minimal model of an active liquid crystal to demonstrate that a negative apparent viscosity is realisable in this system and is associated with a negative slope in the steady-state stress vs. strain rate flow curve.
We will show that this latter feature, previously thought to represent mechanically unstable states, is peculiar to confined active fluids subject to an imposed strain rate, but is replaced by hysteresis in stress-controlled conditions. In other words, fixed stress and fixed strain rate ensembles are not equivalent for active fluids.