Penetration of a supersonic particle at the interface in a binary complex plasma

The penetration of a supersonic particle at the interface is studied in a binary complex plasma. Inspired by the experiments performed in the PK-3 Plus Laboratory on board the International Space Station, Langevin dynamics simulations were carried out. A Mach cone structure forms in the lateral wave behind the supersonic extra particle, where the kink of the cone flanks is observed at the interface. The propagation of the pulse-like perturbation along the interface is demonstrated by the evolution of the radial and axial velocity of the small particles in the vicinity of the interface. The decay of the pulse strength is determined by the friction, where the propagation distance can reach several interparticle distances for small damping rate. The dependence of the dynamics of the background particles in the vicinity of the interface on the penetration direction implies that the disparity of the mobility may be the cause of various interfacial effects.

Figure 1

The setup of PK-3 Plus on board the International Space Station. The red arrow represents the trajectory of the extra particle, penetrating the phase separated binary complex plasma. The region of interest is highlighted by a dashed rectangle.

Figure 2

Snapshot of the penetration of an extra particle across the interface ($x\sim 0$ mm) of a binary complex plasma in the experiment (a) and velocity of the extra particle (b). The area of the panel (a) corresponds to the dashed rectangle in Fig. 1. 15 consecutive images are overlaid, where the trajectory of the penetrating particle is shown as a straight white line. Three locations are highlighted by the white solid rectangles, corresponding to the insets in Fig. 3. In (b), the velocity is measured by tracking the positions of the extra particle (circles) or measuring the length of its elongated shape in each recorded frame (squares), see also the insets in Fig. 3. The blue dashed rectangle highlights the region of interface.

Figure 3

Distribution of the density (a–c) and the velocity in $z$ direction (d–f) and in radial direction (g–i) of the background particles in a binary complex plasma in the Langevin dynamics simulation. The penetration velocity of the extra particle (shown as a grey semicircle) is set as 50 mm/s. The left, middle, and right panels correspond to the moment where the extra particle is in the big particle cloud, in the vicinity of the interface, and in the small particle cloud, respectively. For comparison, the experiment images at a similar moment are shown in the inset of (a–c), correspondingly. The cone structure is highlighted by dashed lines in (d–i).

Figure 4

Mach cone behind the supersonic particle. (a) Relation of the particle velocity $v_e$ and sound speed $c_s$ to the cone angle $\theta$. (b) The Mach cone structure observed behind the extra particle in the small particle cloud in the experiment. The image is produced by subtracting two consecutive frames to highlight the structure. The flanks of the cone are highlighted by yellow dashed-dotted lines and the trajectory of the extra particle is highlighted by the red-solid line.

Figure 5

The evolution of the pulse-like perturbation at the interface for radial locations $r\sim 0.5$ mm (a), $r\sim 0.68$ mm (b), and $r\sim 0.86$ mm (c) in the experiment. The bump highlighted by the orange arc represents the axial motion of big particles in (b,c), excited by the penetration of extra particle at $r=0$ mm. Since the temporal resolution (20 ms) of the experiment is much larger than the characteristic time scale of the propagation of the pulse $\sim 10$ ms, one sees the pulse for both $r\sim 0.5$ mm (a) and $r\sim 0.68$ mm (b) at $t\approx 0$ ms. The axial perturbation vanishes for $r\sim 0.86$ mm (c). The blue dashed rectangle highlights the region of interface and $t=0$ ms represents the moment that the extra particle reaches the interface.

Figure 6

The propagation of the pulse-like perturbation along the interface in terms of the radial velocity (a,c,e) and axial velocity (b,d,f) of the small particles in the simulations. The three selected pressures are $P=20$, 15, 7.5 Pa, corresponding to the damping rates of big particles ${\nu }_b=50.7$, 39.6, 19.0 ${\mathrm{s}}^{-1}$ and small particles ${\nu }_s=91.3$, 71.0, 34.0 ${\mathrm{s}}^{-1}$, respectively. The cavity is left blank. The first and third pulse with positive radial velocity are highlighted by the red and green ellipses, respectively, while the second pulse with negative radial velocity is highlighted by the blue ellipse.

Figure 7

Comparison of the maximal radial velocity in the first (a), second (b), and third (c) pulse propagating along the interface, corresponding to the area highlighted by the red, blue, and green ellipses in Fig. 6. The velocities for pressures $P=20$, 15, 7.5 Pa are represented by pink, purple, yellow symbols, respectively.

Figure 8

Trajectories of background particles for two cases where the penetration directions of the extra particle are opposite. The green arrows represent the penetration direction of the extra particles. The penetration velocity is $v_e=30$ mm/s for (a) and $v_e=-30$ mm/s for (b). The colored curves represent the trajectories of particles at different times $\mathrm{\Delta }t$, counting from the moment that the extra particle crossed the interface with a distance of 0.5 mm. Thicker lines represent big particles while the thinner lines represent small particles. The red-dashed line is the position of the interface.

Figure 9

Dependence of the number of small particles $N$, which refill the cavity and move across the interface, on the penetration velocity $v_e$ of the extra particle. Three types of small particles are considered, whose mass are $m_s=3.60\times {10}^{-15}$ kg (red bars), $m_s=2.68\times {10}^{-15}$ kg (blue bars), and $m_s=1.75\times {10}^{-15}$ kg (green bars).

Figure 10

The dependence of the maximal penetration depth $\zeta$ of small particles on the speed of the extra particle $v_e$, where the interface position is marked by a dashed line. Similar to Fig. 9, three types of small particles are considered whose masses are $m_s=3.60\times {10}^{-15}$ kg (red symbols), $m_s=2.68\times {10}^{-15}$ kg (blue symbols), and $m_s=1.75\times {10}^{-15}$ kg (green symbols). The errors signify the standard deviation across ten simulations with the same parameters.