Superfluid Behavior of Active Suspensions from Diffusive Stretching

The current understanding is that the non-Newtonian rheology of active matter suspensions is governed by fluid-mediated hydrodynamic interactions associated with active self-propulsion. Here we discover an additional contribution to the suspension shear stress that predicts both thickening and thinning behavior, even when there is no nematic ordering of the microswimmers with the imposed flow. A simple micromechanical model of active Brownian particles in homogeneous shear flow reveals the existence of off-diagonal shear components in the swim stress tensor, which are independent of hydrodynamic interactions and fluid disturbances. Theoretical predictions from our model are consistent with existing experimental measurements of the shear viscosity of active suspensions, but also suggest new behavior not predicted by conventional models.

Figure 1

Schematic of active particles with swimming speed $U_0$ and reorientation time ${\tau }_R$ in simple shear flow with fluid velocity $u_x^{\infty }=\dot{\gamma }y$, where $\dot{\gamma }$ is the magnitude of shear rate. The unit vector $\mathit{q}(t)$ specifies the particle’s direction of self-propulsion. Diffusion of active particles along the extensional axis of shear acts to “stretch” the fluid and reduce the effective shear viscosity, similar to the effect that the hydrodynamic stress plays for pusher-type microorganisms.

Figure 2

Swim diffusivity as a function of shear Péclet number for two different values of geometric factor $B$ ($B=0$ sphere; $B=0.8$ ellipsoid). Solid and dashed curves are theoretical solutions, and the symbols are Brownian dynamics (BD) simulation results. Dash-dotted curve for $D_{xy}$ is the small-Pe solution for $B=0.8$.

Figure 3

Comparison of our model, Eq. (4), with shear experiments of López et al. [29] with motile E. coli bacteria at different concentrations. Horizontal dashed lines for small Pe are the analytical solutions of Eq. (6).

Figure 4

Effective suspension viscosity of spherical active particles at dilute concentrations and reorientation Péclet number ${\mathrm{Pe}}_R\equiv a/(U_0{\tau }_R)=0.035$. Filled circles and crosses at large Pe are experimental data of Rafaï et al. [31] using “puller” microalgae C. Reinhardtii. The solid curve is the analytical theory of Eq. (5), and the open circles are BD simulation results. Inset: Magnification at large Pe to show agreement with experiments.