Spontaneous chiralization of polar active particles

Polar active particles constitute a wide class of active matter that is able to propel along a preferential direction, given by their polar axis. Here, we demonstrate a generic active mechanism that leads to their spontaneous chiralization through a symmetry-breaking instability. We find that the transition of an active particle from a polar to a chiral symmetry is characterized by the emergence of active rotation and of circular trajectories. The instability is driven by the advection of a solute that interacts differently with the two portions of the particle surface and it occurs through a supercritical pitchfork bifurcation.

Figure 1

Schematics of the spontaneous chiralization mechanism; the translational velocity is not shown for clarity. (a) and (c) An active particle with attractive ($\varphi <0$) and repulsive ($\varphi >0$) solute-surface interactions on the two hemispheres generates a concentration dipole through an active mechanism. The solute-surface interactions generate a body force $\mathit{f}$ in the fluid. (b) and (d) A perturbation of the polar axis changes $\mathit{f}$, which applies a torque to the fluid. The torque on the fluid must be balanced by an opposite torque on the particle. In (b), this leads to a clockwise rotation, which reinforces the initial perturbation possibly breaking the left-right symmetry if the solute diffusion is slower than the advection due to the rotating flow. In (d), the torque is reversed and the rotation restores the initial configuration.

Figure 2

(a) The rotation rate of a chemically active particle made dimensionless using the characteristic time $QM/RD$ in the case of $f(y/R)=y/R$ and $\tilde{M}(y/R)=My/R$. At small values of $\overline{Q}$, the concentration profile is left-right symmetric and aligned with the polar axis of the particle. At large values of $\overline{Q}$, the polar symmetry breaks and the particle starts to rotate. Insets: The distribution of solute and the streamlines in the symmetry plane $z=0$. (b) Phase diagram of the behavior of a chemically active Janus particle as a function of $Pe$ and of $M_1/M$. The upper figures show the steady-state solute distribution and the streamlines in the symmetry plane $z=0$.

Figure 3

Propulsion regimes of a squirmer moving through a solution of concentration $c_{\infty }$. The solute-surface interactions are given by $\varphi ={\varphi }_0(y/r-1/2)exp[-\lambda (r-R\left)\right]$, which is repulsive for $y/r>-1/2$ and attractive for $y/r<-1/2$. (a) Short-ranged potential $\lambda =5/R$ and ${\varphi }_0=1.5k_{B}T$ and (b) range of the potential comparable to the particle size $\lambda =1/R$ and ${\varphi }_0=k_{B}T$. The upper figures display the deviation of $c$ from its equilibrium distribution $c_{\text{eq}}$ and the flow streamlines in the symmetry plane $z=0$.