Hydrodynamics-Induced Long-Range Attraction between Plates in Bacterial Suspensions

We perform optical-tweezers experiments and mesoscale fluid simulations to study the effective interactions between two parallel plates immersed in bacterial suspensions. The plates are found to experience a long-range attraction, which increases linearly with bacterial density and decreases with plate separation. The higher bacterial density and orientation order between plates observed in the experiments imply that the long-range effective attraction mainly arises from the bacterial flow field, instead of the direct bacterium-plate collisions, which is confirmed by the simulations. Furthermore, the hydrodynamic contribution is inversely proportional to the squared interplate separation in the far field. Our findings highlight the importance of hydrodynamics on the effective forces between passive objects in active baths, providing new possibilities to control activity-directed assembly.

Figure 1

(a) Snapshot of two plates trapped by optical tweezers in the bacterial suspension. The particles with black edges are the plates, and the small rodlike particles are bacteria. Scale bar: $5\mathrm{\mu }\mathrm{m}$. (b) In simulation, the bacterium is modeled as a dimer connected by two beads via a rigid spring. Here, an impulse $\mathrm{\Delta }P$ is imposed on the dimer, meanwhile, an opposite impulse is applied on fluid elements in the red circle during the dimer moving. (c) Schematic of two parallel plates fixed in the bacterial solution in simulation.

Figure 1

(a) Snapshot of two plates trapped by optical tweezers in the bacterial suspension. The particles with black edges are the plates, and the small rodlike particles are bacteria. Scale bar: $5\mathrm{\mu }\mathrm{m}$. (b) In simulation, the bacterium is modeled as a dimer connected by two beads via a rigid spring. Here, an impulse $\mathrm{\Delta }P$ is imposed on the dimer, meanwhile, an opposite impulse is applied on fluid elements in the red circle during the dimer moving. (c) Schematic of two parallel plates fixed in the bacterial solution in simulation.

Figure 2

(a) The PDFs of deviation $\mathrm{\Delta }d$ for $d_f/l=4.80$ without E.coli and for four different $d_f/l$ at $\varphi =0.13$. The solid lines are Gaussian fits. (b) The relation between the effective force $F_{\mathtt{eff}}$ and $\varphi$ at different $d_f/l$. A positive $F_{\mathtt{eff}}$ represents an attractive force between two plates. (c) $F_{\mathtt{eff}}$ as a function of $d_f/l$ at different $\varphi$. The symbols and error bars represent the mean and standard deviation calculated over 4–16 independent measurements, respectively.

Figure 2

(a) The PDFs of deviation $\mathrm{\Delta }d$ for $d_f/l=4.80$ without E.coli and for four different $d_f/l$ at $\varphi =0.13$. The solid lines are Gaussian fits. (b) The relation between the effective force $F_{\mathtt{eff}}$ and $\varphi$ at different $d_f/l$. A positive $F_{\mathtt{eff}}$ represents an attractive force between two plates. (c) $F_{\mathtt{eff}}$ as a function of $d_f/l$ at different $\varphi$. The symbols and error bars represent the mean and standard deviation calculated over 4–16 independent measurements, respectively.

Figure 3

The distributions of bacterial ${\rho }_r$ and $Q$ around two plates at four different separations of (a) $d_f/l=0.48$, (b) 2.29, (c) 4.80, and (d) 8.60. The solid black diamonds and hollow red circles represent the bacterial ${\rho }_r$ and $Q$, respectively. The positions of plates are indicated by blue shaded regions. Inset of (b): Sketch of bacterium-induced hydrodynamic attraction between two plates.

Figure 4

Simulation results: (a) The effective force $F_{\mathtt{eff}}$ as a function of $d_f/l$ for different bacterial concentration $\varphi$. (b) The relation between $F_{\mathtt{eff}}$ and $\varphi$ at different $d_f/l$. (c) The contributions of the bacterial flow field and direct bacterium-plate collisions to $F_{\mathtt{eff}}$ as a function of $d_f/l$ at $\varphi =0.08$. Inset: The red solid line represents a power-law fit.