Experimental investigation of phase separation in binary dusty plasmas under microgravity

Three-dimensionally extended dusty plasmas containing mixtures of two particle species of different size have been investigated under microgravity conditions. To distinguish the species even at small size disparities, one of the species is marked with a fluorescent dye, and a modified two-camera video microscopy setup is used for position determination and tracking. Phase separation is found even when the size disparity is below $5\%$. Particles are tracked to obtain the diffusion flux, and resulting diffusion coefficients are calculated to be about $-{10}^{-6}{\mathrm{mm}}^2/\mathrm{s}$, which is in the expected range for a phase separation process driven by plasma forces. Additionally, a measure for the strength of the phase separation is presented that allows us to quickly characterize measurements. There is a clear correlation between size disparity and phase separation strength.

Figure 1

(a) Side view and (b) top view of the experimental setup. The field of view of the cameras is denoted by FoV. The coordinate system introduced here will be used throughout the following analysis.

Figure 2

The four panels show snapshots of both cameras at the start and at the end of a typical measurement. The images have been inverted and optimized to enhance the visibility of the particles. (a) and (c) Camera 1 (all particles); (b) and (d) camera 2 (fluorescent particles only). (a) and (b) Directly after stabilization of the dust cloud; (c) and (d) 16 s later.

Figure 3

Exemplary results of particle detection and tracking. The same data set as in Fig. 2 is shown, and the images of camera 2 (RhB particles) have been used. (a) Velocity field on a $2\times 2{\mathrm{mm}}^2$ grid, temporally averaged over the whole data set. (b) Curl of the velocity field, calculated on the same grid as in (a) and averaged over the whole data set as well. The overlaid contour of the cloud was obtained from the particle density of camera 1.

Figure 4

Vertical component (a) of the flux $J_z$ and (b) of the gradient of the particle number density. (c) Linear regression to obtain the diffusion coefficient. All data have been averaged over a $0.5\mathrm{s}$ interval in the middle of the measurement. (d) Diffusion coefficient from the linear regressions.

Figure 5

(a) Definition of the radial position parameter $b$ as given in the text. (b) Example for one frame from the beginning of the sequence. The detected particles of camera 2 are color-coded according to $b$. The solid lines denote $b=0$ and $b=1$, respectively.

Figure 6

Radial distribution of particles for (a) data set 1 and (b) data set 2. For each data set, six points in time are shown. The fluorescent particles ($f\left(b_{\mathrm{RhB}}\right)$, red) accumulate at high $b$ (data set 1) or low $b$ (data set 2), respectively, whereas the overall distribution of particles ($f\left(b_{\mathrm{all}}\right)$, black) nearly stays constant.

Figure 7

Separation parameter averaged over all particles in each frame ${\overline{b}}_{\mathrm{all}}$ (all particles) and ${\overline{b}}_{\mathrm{RhB}}$ (fluorescent particles only) for (a) data set 1 and (b) data set 2 and (c) and (d) their respective ratio ${\overline{b}}_{\mathrm{RhB}}/{\overline{b}}_{\mathrm{all}}$.

Figure 8

Space- and time-averaged separation parameter of all analyzed data sets. (a) Individual data points. Red circles show mixtures with a mean diameter in the $4\mu \mathrm{m}$ range, whereas blue crosses show data sets with a mean diameter in the $7\mu \mathrm{m}$ range. (b) Mean values and standard deviations of $\varepsilon$ and $B$ for each mixture. There is a clear correlation between the two quantities. The dashed lines indicate the expected center of symmetry.