Flagella-induced transitions in the collective behavior of confined microswimmers

Bacteria are usually studied in free-swimming planktonic state or in sessile biofilm state. However, little is known about intermediate states where variability in the environmental conditions and/or energy supply to the flagellar propulsive system alter flagellar activity. In this Rapid Communication, we propose an idealized physical model to investigate the effects of flagellar activity on the hydrodynamic interactions among a population of microswimmers. We show that decreasing flagellar activity induces a hydrodynamically triggered transition in confined microswimmers from turbulentlike swimming to aggregation and clustering. These results suggest that the interplay between flagellar activity and hydrodynamic interactions provides a physical mechanism for coordinating collective behaviors in confined bacteria, with potentially profound implications on processes such as molecular diffusion and transport of oxygen and nutrients that mediate transitions in the bacteria physiological state.

Figure 1

Strongly confined microswimmers create potential dipolar far-field flows.

Figure 2

(a) Time-averaged flow field created by a beating flagellum with $A=0.5$, $k=\pi$, and $U=1$. Inset: Snapshots of the flagellum-induced flow field at different times. (b) Dipolar field created by a circular disk of effective radius $R_{\mathrm{tail}}$ fitted to the average flow field in (a). (c) Change in $R_{\mathrm{tail}}$ with $A$ and $k$ of the traveling wave via the flagellum. (d) Reduction of a flagellated swimmer to a dumbbell swimmer.

Figure 3

(a) Swirling motion in vigorously beating flagellated swimmers; (b) orientational order; and (c) aggregation in weakly beating flagellated swimmers. Probability distributions of velocity of the swimmers are depicted in the lower row.

Figure 4

(a) Swimmers with vigorously beating flagella orient with local flow and thus tend to chase each other. (b) Swimmers with weakly beating flagella orient in the opposite direction to local flow and thus tend to aggregate together.

Figure 5

Statistics associated with swirling (top row) and orientational order (bottom row): polar order parameter $\langle P\rangle$, velocity and angular correlations $C_{\mathrm{v}},C_{\theta }$, and probability distribution of rotational activity parameter $\kappa$, all computed based on data corresponding to the shaded time range.

Figure 6

(a) The time-averaged mean and standard deviation of $\kappa$ and (b) the sample-averaged mean and standard deviation of long-time developed $\langle P\rangle$ over various initial conditions.

Figure 7

Phase diagrams showing the three different collective modes swirling, orientational order, and aggregation, as a function of ${\nu }_1$, ${\nu }_2$, and ${\Phi }_A$. Regions of transitional behavior for which no clear pattern is identified are left in white.