Extended self-similarity in a 2D complex plasma with active Janus particles

Kurzfassung

Extended self-similarity (ESS) is a concept originally proposed by [R. Benzi et al., Phys. Rev. E 48, R29 (1993)] for a fully developed turbulence. ESS refers to the power-law scaling of the structure functions of the velocity field expressed through the structure functions of different orders rather than distance. Extended self-similarity of the velocity fields in fluids is particularly important because it can help to identify otherwise obscured scaling regimes and can even provide a more accurate method of measuring the scaling exponents. We experimentally studied a two-dimensional (2D) suspension of active Janus particles in a gas-discharge plasma. The Janus particles were micron-size plastic microspheres with a hemispherical metal coating. Plasma was produced by a capacitively coupled radio-frequency (rf) discharge in argon at 13.56 MHz in a modified Gaseous Electronics Conference (GEC) rf reference cell. The gas pressure was 0.66 Pa, the discharge rf power was 20 W. When injected in plasma, the Janus particles formed a single-layer suspension in the plasma sheath of the lower rf electrode. The particles were levitated by the balance of the sheath electric field and gravity. The suspension consisted of around 780 particles and had a diameter of approximately 40 mm. Due to the Janus particles’ self-propulsion, they acquired high speeds greatly exceeding the thermal speed, which prevented them from forming a regular lattice. Their trajectories, however, remained in the horizontal plane due to the strong vertical confinement. The self-propulsion force was balanced by the neutral gas drag force. To characterize how chaotic the Janus particles’ motion is, we utilized a tool widely used in the field of turbulence - the longitudinal velocity structure functions Sp(r). We showed that the velocity field of the system of active Janus particles features extended self-similarity, i.e. Sp(r) is proportional to (S3(r))^x, where x=p/3, even though the underlying structure functions Sp(r) lack respective power-law scaling. Given the extended self-similarity of its velocity field, the chaotic intermittent flow in the 2D system of active Janus particles can be regarded as active turbulence.