Simulations and experiments of phase separation in binary dusty plasmas

Molecular dynamics simulations of binary dusty plasmas have been performed and their behavior with respect to the phase separation process has been analyzed. The simulated system was inspired by experimental research on phase separation in dusty plasmas under microgravity on parabolic flights. Despite vortex formation in the experiment and in the simulations the phase separation could be identified. From the simulations it is found that even the smallest charge disparities lead to phase separation. The separation is due to the force imbalance on the two species and the separation becomes weaker with increasing mean particle size. In comparison, experiments on the phase separation have been performed and analyzed in view of the separation dynamics. It is found that the experimental results are reproduced by the simulation regarding the dependency on the size disparity of the two particle species.

Figure 1

Experimental setup used for the measurements under microgravity: (a) side view, (b) top view.

Figure 2

Different quantities that are either provided directly by the SIGLO code or deduced from those quantities; see text for details. The gray boxes depict the location of the two electrodes. Shown are (a) the electron density, (b) the electron temperature, (c) the electric field force, (d) the ion streaming velocity, (e) the ion drag force on particles with $a=3.5\mu \mathrm{m}$, and (f) the total force on those particles. The arrows indicate the direction of the ion streaming velocity and the forces. Their length is normalized. Panels (g) and (h) show the ion drag force along the horizontal $x$ and vertical $z$ axis; note the different scales. Panels (i) and (j) represent zoomed-in views of the total force on particles with $\overline{a}=3.5\mu \mathrm{m}$ and $\varepsilon =0.2$.

Figure 3

(a) Drift velocity of the two species of particles, averaged over all particles in each time step. The force disparity is $\mathrm{\Delta }F=5\times {10}^{-14}\mathrm{N}$ in this example. (b) Drift speed (red circles) versus force disparity $\mathrm{\Delta }F$. For the smallest forces, there is hardly any drift. From about $\mathrm{\Delta }F={10}^{-14}\mathrm{N}$ on, the drift speed starts to approach the Epstein friction limited drift speed (dashed line), but does not reach it.

Figure 4

Simulation with a cylindrical geometry that was constructed from the force along the $z$ axis. The two species of particles have radii of $a_1=3.15\mu \mathrm{m}$ and $a_2=3.85\mu \mathrm{m}$. (a) snapshot of the system after initialization. Particles of species 1 (black) and species 2 (red) are mixed. (b) Snapshot after running for 5 more seconds with force disparity. The populations are separated and a phase boundary can be seen. [(c) and (d)] Radial particle distributions for the situations shown in (a) and (b), respectively. (e) Evolution of the radial positions and (f) ratio of the radial positions of the two populations. All these quantities show an increasing separation of the two populations with time.

Figure 5

Temporally averaged mean distance ratio $B$ vs. relative size disparity $\varepsilon$ for all simulation runs of a radial geometry with the force profile taken from the $z$ axis (see text for details).

Figure 6

Example of a simulation run for particles with $a_1=3.15\mu \mathrm{m}$ and $a_2=3.85\mu \mathrm{m}$: (a) Trajectories of particles of both species from $t=0$ to $t=5\mathrm{s}$. For clarity, only every ${10}^{\mathrm{th}}$ trajectory is shown. (b) Particle positions of species 1 (black) and species 2 (red) at the beginning of the phase separation. Here every third particle is shown. (c) Same as in (b), but situation at the end of the simulation run. Particles of the larger species mainly accumulate at the top and bottom of the discharge while particles of the smaller species accumulate closer to the void. [(d) and (e)] Distribution $f\left(b\right)db$ of the radial positions of both populations at $t=0$ and $t=5\mathrm{s}$, respectively. (f) Mean radial positions ${\overline{b}}_{1/2}$ of the two populations and (g) their ratio ${\overline{b}}_2/{\overline{b}}_1$. At $t=0$, a ratio of 1 and identical distributions indicate a mixed system. A progressively increasing ratio as well as a shift of the distributions in opposite direction correspond to the increasing separation of the two populations.

Figure 7

Temporally averaged mean distance ratio $B$ of all simulation runs using the realistic geometry vs relative size disparity $\varepsilon$.

Figure 8

Snap shots of (a) camera 1 (all particles) and (b) camera 2 (RhB particles) at a progressed state of the phase separation in data set 1. (c) Reconstructed particle positions of the RhB species seen in camera 2 (red) and the pure MF species (black). Every other particle is shown. The snap shots were inverted and their contrast enhanced.

Figure 9

Mean radial distance $\overline{b}$ of two measurements versus time. For data set 1, the RhB particles are the larger species (${\overline{d}}_{\mathrm{RhB}}>{\overline{d}}_{\mathrm{MF}}$). For data set 2, the RhB particles are the smaller species (${\overline{d}}_{\mathrm{RhB}}<{\overline{d}}_{\mathrm{MF}}$). In both cases, the curve for ${\overline{b}}_{\mathrm{all}}$ lies between ${\overline{b}}_{\mathrm{RhB}}$ and ${\overline{b}}_{\mathrm{MF}}$.

Figure 10

Temporally averaged mean distance ratio $B$ of all measurements vs. relative size disparity $\varepsilon$.

Figure 11

Mean distance ratio $B$ versus different parameters: (a) temperature, (b) particle number, (c) neutral gas pressure, and (d) rf voltage.