Active Particles Powered by Quincke Rotation in a Bulk Fluid

Dielectric particles suspended in a weakly conducting fluid are known to spontaneously start rotating under the action of a sufficiently strong uniform dc electric field due to the Quincke rotation instability. This rotation can be converted into translation when the particles are placed near a surface providing useful model systems for active matter. Using a combination of numerical simulations and theoretical modeling, we demonstrate that it is possible to convert this spontaneous Quincke rotation into spontaneous translation in a plane perpendicular to the electric field in the absence of surfaces by relying on geometrical asymmetry instead.

Figure 1

Schematic representation of the problem considered in this Letter. A solid particle of volume $V^{-}$, surface $S$, and outward unit normal vector $\mathit{n}$ is suspended in an infinite fluid of volume $V^{+}$ and subject to a uniform dc electric field, ${\mathit{E}}_0=E_0\widehat{\mathit{z}}$. The electric permittivities and conductivities of the suspending fluid and particle are denoted as ${ϵ}^{+},{\sigma }^{+}$ and ${ϵ}^{-},{\sigma }^{-}$, respectively, and the dynamic viscosity of the fluid is $\mu$. The translational and angular velocity of the particle are $\mathit{U}$ and $\mathbf{\Omega }$, respectively.

Figure 2

(a)–(c) Snapshots of a cylinder and a helix having an aspect ratio of $a/L=0.0167$ under Quincke rotation due to an applied electric field ${\mathit{E}}_0^{*}=2.5\widehat{\mathit{z}}$ with $R=Q=2$. The helix has $N=3$ turns, pitch angle $\alpha =0.2\pi$, and pitch $\lambda /L=0.236$. The particles are slightly tilted with respect to the $x$ axis at an angle $0.1\pi$ at time $t^{*}=0$. The cylinder performs pure rotation while the helix undergoes rotation as well as translation perpendicular to the $z$ axis. (d) Rotated view of snapshot (c) showing the positively charged side of the particles. The particles move out of the $x-z$ plane due to their initially titled configuration. The colorbar indicates surface charge distribution. Associated movies are available in the Supplemental Material [26].

Figure 3

Three-dimensional trajectories of the centroid of the cylinder (cl) and the helix (hl).

Figure 4

(a) Critical electric field of a helix with three different cross-sectional radii but fixed number of turns, $N=1$, plotted against the pitch angle. Red, blue, and green indicate $a/\lambda =0.10$, 0.05, 0.02, respectively. Open and filled symbols indicate no swimming and swimming, respectively, computed using numerical simulations based on boundary element method while solid and dashed lines represent $E^{*}/\sqrt{1+G}$. (b) Swimming speed versus pitch angle for a helix with aspect ratio $a/L=0.0167$ for two different electric field strengths, $E^{*}=2.5$ (red circle and solid line indicate theory and simulations, respectively) and $E^{*}=5.5$ (blue square and dashed line indicate theory and simulations, respectively). (c) Swimming speed versus cross-sectional radius of a helix keeping the electric field $E^{*}=2.5$, number of turns $N=3$, pitch angle $\alpha =0.2\pi$, and pitch $\lambda /L=0.27$ fixed (red circle and solid line indicate theory and simulations, respectively). Movies associated with (c) are available in the Supplemental Material [26].