Hydrodynamics Determines Collective Motion and Phase Behavior of Active Colloids in Quasi-Two-Dimensional Confinement

We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multiparticle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as between squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gaslike and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.

Figure 1

(a) Sketch of a spherical squirmer. The prescribed surface velocity field ${\mathbf{v}}_s^{(i)}$ generates a swimming velocity along the unit vector ${\mathbf{e}}^{(i)}$. (b) Squirmers at positions ${\mathbf{r}}^{(i)}$ and with orientations ${\mathbf{e}}^{(i)}$ move in a quasi-2D geometry bounded by two parallel planar walls.

Figure 2

Typical snapshots of the collective motion of squirmers in a quasi-2D geometry depending on the area fraction $\varphi$ and the squirmer type ($\beta$). Also shown are active Brownian spheres moving in quasi-2D (BD Q-2D) and active Brownian disks moving in 2D (BD 2D). The view is from the top and the colors indicate the local bond-orientational order $|q_6{|}^2\in [0,1]$.

Figure 3

Distributions of local bond parameter $|q_6{|}^2$ and swimmer velocities $v_e$ (insets) at low ($\varphi =0.21$), medium ($\varphi =0.57$) and high ($\varphi =0.83$) density for pushers ($\beta =-3$), neutral squirmers ($\beta =0$), and pullers ($\beta =3$).

Figure 4

Bond-orientational order parameter $⟨|q_6{|}^2⟩$ plotted versus area fraction $\varphi$ for pushers ($\beta <0$), pullers ($\beta >0$) and neutral squirmers ($\beta =0$). Inset: Order parameter fluctuations $\mathrm{\Delta }|q_6{|}^2/⟨|q_6{|}^2⟩$.

Figure 5

(a) Rotational diffusion coefficient in units of its thermal value $D_r^0$ versus area fraction $\varphi$ and squirmer parameter $\beta$. (b) Distributions of squirmer orientations for two area fractions $\varphi$. $\theta$ is the angle with respect to the wall normal.