Diffusion of Ellipsoids in Bacterial Suspensions

Abstract

Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems.

Dynamics of ellipsoidal tracers in swimming algal suspensions

“…2(a)). The construction of the adjustable wire-frame device is similar to those used in previous experiments on enhanced diffusions of passive tracers [10,28,39,42]. To stabilize the thin liquid film, a trace amount of surfactant (Tween 20, 0.03 vol%) was added into the algal suspensions.…”

“…Particle displacements in the body frame were obtained through rotation of particle displacements in the laboratory frame ( Fig. 2(b)) [39,54,55]. Specifically, the displacement of an ellipsoid in the laboratory frame, δx(t n ) = x(t n+1 ) − x(t n ), in a small time interval δt = t n+1 − t n was transformed into its displacement in the body frame, δx(t n ), via δx(t n ) = R(t n )δx(t n ), where R(t n ) is a 2D rotation matrix with R(t n ) = cos θ n sin θ n − sin θ n cos θ n .…”

“…The ellipsoids were obtained by stretching monodispersed micron-sized PS spheres at 150 • C above the glass transition temperature of PS [52]. The lengths of the semi-principal axes of the ellipsoids were fixed at a = b = 2.8 ± 0.2 µm and c = 14.2 ± 0.5 µm, the same as the ellipsoids used in the previous study on pusher-type E. coli suspensions [39]. The aspect ratio of ellipsoids is p ≡ c/a = 5.1.…”

“…Peng et al studied the dynamics of isolated ellipsoids in E. coli suspensions and showed that both the translational and rotational diffusion of ellipsoids are enhanced with increasing bacterial con-centrations [39]. More importantly, they found an abnormal anisotropic diffusion in the body frame of ellipsoids, where an ellipsoid diffuses fastest along its minor axis at high bacterial concentrations.…”

“…The arrows indicates the direction of the flow. E. coli is a typical pusher-type microswimmer [39], whereas C. reinhardtii we study here is a typical puller-type microswimmer.…”