Particle diffusion in active fluids is non-monotonic in size

Abstract

We experimentally investigate the effect of particle size on the motion of passive polystyrene spheres in suspensions of Escherichia coli. Using particles covering a range of sizes from 0.6 to 39 microns, we probe particle dynamics at both short and long time scales. In all cases, the particles exhibit super-diffusive ballistic behavior at short times before eventually transitioning to diffusive behavior. Surprisingly, we find a regime in which larger particles can diffuse faster than smaller particles: the particle long-time effective diffusivity exhibits a peak in particle size, which is a deviation from classical thermal diffusion. We also find that the active contribution to particle diffusion is controlled by a dimensionless parameter, the Péclet number. A minimal model qualitatively explains the existence of the effective diffusivity peak and its dependence on bacterial concentration. Our results have broad implications on characterizing active fluids using concepts drawn from classical thermodynamics.

Collective motion of bacteria and their dynamic assembly behavior

“…Many people have studied influences of bacterial concentrations on particle diffusion in this field. For example, in the suspensions of E. coli, Deff was found to increase linearly with increasing bacterial concentration [45,46]. It was later found that this result was obtained at low concentrations and in the absence of cluster movement.…”

“…Also, researchers experimentally investigated the effect of particle size on their motion in the suspensions of bacteria. When 0.6 to 39 μm particles were mixed with E. coli bacteria [45], it was found that large particles moved faster, which were inconsistent with the principle that the speed of particle is inversely proportional to the radius of the particle according to the traditional Einstein-stokes Equation (Fig. 8).…”

Tracer diffusion in active suspensions

“…This theory predicts a net enhancement of tracer diffusivity arising from the fluid flow induced by the swimming bacteria, which was shown to be a nonmonotonic function of a Péclet number relating the strength of bacterial advection to the Brownian motion of the tracer. Experiments have also observed a nonmonotonicity in the Péclet number when varying the size of the tracer particle [16]. Other theory and experiments propose that the enhancement to the diffusivity is linear in the "active flux" due * jfbrady@caltech.edu to the swimmers' autonomous motion [6][7][8][9], and that, in close contact, entrainment of tracers in the swimmers' flow field is primarily responsible for this enhancement [13,14].…”

Dynamics of ellipsoidal tracers in swimming algal suspensions

“…Such an enhanced diffusion can be orders of magnitude stronger than the tracer's intrinsic Brownian motion at high bacterial concentrations. Following their pioneering work, the enhanced diffusion of passive spherical tracers has been reported and systematically studied in different active fluids including suspensions of swimming microorganisms such as prokaryotic cells E. coli [17][18][19][20][21][22]24], Bacillus subtilis [25] and Pseudomonas sp. [26] and eukaryotic cell Chlamydomonas reinhardtii [27,28] as well as synthetic colloidal microswimmers [19].…”

“…Although the dynamics of spherical passive tracers have been extensively studied [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the motion of asymmetric tracers that possess degrees of freedom beyond simple translation has not been investigated until very recently. 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].…”