Impact of hydrodynamics on effective interactions in suspensions of active and passive matter

Passive particles exhibit unique properties when immersed in an active bath of self-propelling entities. In particular, an effective attraction can appear between particles that repel each other when in a passive solution. Here we numerically study the effect of hydrodynamics on an active-passive hybrid system, where we observe qualitative differences as compared to simulations with excluded volume effects alone. The results shed light on an existing discrepancy in pair lifetimes between simulation and experiment, due to the hydrodynamically enhanced stability of coupled passive particles.

Figure 1

Fluid flow around a swimmer (green) alongside a passive particle (red). Blue vectors indicate the velocity of the fluid at each location, and the swimming direction is directly downward. The force centers of the swimmer are also shown (black circles). The distance between field vectors is 1 $\mu \mathrm{m}$.

Figure 2

Mean squared displacement of the HDMD (red solid line) simulation as a function of time, with ($\Delta r^2\propto t^{\alpha }$) ballistic (blue dashed line) and simple diffusive (green dotted line) curves also shown. At short times the spheres exhibit superdiffusive motion, owing to correlated interactions with the swimmer fluid flows and collisions, but this eventually transitions into simple diffusion for $t>1$ s (due to reduced correlation). Inset: Same plot for MD simulations, where the same characteristics can be seen, but the shift occurs on a shorter timescale, at a much lower magnitude.

Figure 3

Radial distribution function $g\left(r\right)$ for HDMD (red solid curve) and MD (blue dashed curve) simulations, with the distance in units of sphere diameter $d$. Adjacent graphics indicate the typical formation leading to the shown peaks. MD peaks are narrow due to the relatively low rate of collisions for a close pair. It takes a long time for particles to get knocked out of the tightly bound state, and they are generally pushed directly out to the secondary peaks upon splitting. The two separate MD peaks at $1.2d$ are due to different angles and local rod formations when a swimmer splits a pair, and the distinction is not significant. Inset: Same plot zoomed out to see the full range.

Figure 4

Average number of spheres (coordination number) within a distance $r$ of a given sphere (units in terms of sphere diameter $d$) for HDMD (red solid curve) and MD (blue dashed curve) simulations. Inset: HDMD results divided by MD results, showing significant changes close to the sphere.

Figure 5

NOS (red solid curve) and NOT (blue dashed curve) coordination number (see Fig. 4) divided by HDMD results. NOS lacks a $g\left(r\right)$ peak at $1.2d$ (since no steric collision gives rise to it), which gives it a much higher coordination number at low $r$. NOT is higher around $2d$, signifying somewhat greater mid-range interaction between passive spheres. Inset: NOS coordination number divided by NOT results, showing the relative areas of higher and lower coordination.

Figure 6

Ratio of the MSD of the NOT case to the NOS and HDMD case. At short times, the absence of tumbling means a net increase in the strength of the fluctuating field (more swimmers swimming), yielding greater diffusion. The lack of tumbling also causes the system to take longer to change, thus giving a larger increase at longer times. Inset: MSD for NOS and HDMD (red solid curve) and NOT (blue dashed curve) conditions.