(Color online) Experimental setup. An additional four-electrode box is placed on the lower rf electrode of a capacitively coupled rf discharge in a modified GEC chamber. The ITO coating on the internal surfaces of the glass plates is conducting yet transparent; each plate is powered by a separate function generator (not shown here). Polymer microspheres are suspended inside the box. The lower rf electrode is heated by running water; this creates a vertical gradient of gas temperature and upward thermophoretic force on particles.
Horizontal “equatorial” (left column) and vertical central (right column) cross-sections of spheroidal cluster, for three settings of heating water temperature T W = 60 °C (upper row), 75 °C (middle row), and 90 °C (lower row). The equatorial cross-sections were chosen by the maximum size, their vertical positions are indicated by arrows in Fig. 5(a). The same cluster of about 1500 microparticles was used in these three runs. Note the development of a conical cluster top for higher T W .
(Color online) Velocity components of particles as a function of their position: (a) v x vs y and (b) v y vs x, all measured in the equatorial cross-section of particle cluster (see Fig. 2). Each particle in every frame of a 6.7 s movie is represented by a data point. Assuming linear fits in (a) and (b), their slopes were measured as Ω1 = −0.20 ± 0.004 s−1 and Ω2 = 0.24 ± 0.004 s−1, respectively, and the particle cluster rotation speed was calculated as (see Ref. 18) The pressure of argon was 4 Pa, the rf power was 2 W, the manipulation voltage and frequency were 20 V peak-to-peak and 5.19 kHz, respectively. The heating water temperature was 90 °C.
(Color online) Rotation speed of a 3D particle cluster measured at its “equator” (see Fig. 2) as a function of the frequency of applied manipulation voltage. Same cluster was studied at three different settings of the heating water temperature as indicated. (a) The open symbols illustrate the case when the direction of the field rotation is reversed from counterclockwise to clockwise. (b) “Residual” cluster rotation, i.e., the sum of rotation speeds (sign included) from (a). The residual rotation is virtually independent of the applied frequency. The pressure of argon was 4 Pa, the rf power was 2 W, the manipulation voltage was 20 V peak-to-peak.
(Color online) Height scan of the cluster rotation speed in two different regimes. (a) The pressure of argon was 4 Pa, the rf power was 2 W, the manipulation frequency was 5.19 kHz, the heating water temperature was set to three different values as indicated. Arrows indicate the heights of the equatorial cross-sections (see Fig. 2) where the frequency scan, Fig. 4(a), was taken. (b) The pressure of argon was 6 Pa, the rf power was 1 W, the manipulation frequency was 5.19 kHz or 10 kHz as indicated, the heating water temperature was 60 °C. In both (a) and (b), the manipulation voltage was 20 V peak-to-peak. Zero height corresponds to the lowest edge of the cluster at 60 °C. A common trend is for the rotation speed to decline with height. At the top and bottom, cluster cross-sections have few particles (see Fig. 2, right column) and hence large error bars.
(Color online) (a) Horizontal and (b) vertical position of a single particle trapped inside the glass box as a function of dc bias on one glass plate, for different heating water temperatures. The measurements were performed at argon pressure of 6 Pa and rf power of 1 W. The horizontal displacement is zero when all four plates are grounded. The vertical position is relative to the electrode surface.
(Color online) Vertical resonance frequency of a single particle, for different values of dc bias on one electrode and different heating water temperatures. The measurements were performed for the discharge conditions of Fig. 6.
(Color online) Rotating 3D cluster with N = 66 particles observed in the Kiel experiment. Particle trajectories during 10 s show cluster rotation in response to the rotating electric field with the amplitude of 20 V peak-to-peak and frequency of 5.19 kHz (particle positions at different times are color-coded and superposed). The pressure of argon was 4 Pa and rf power was 2 W. The particles were imaged using a stereoscopic in-line holography (see Ref. 17).
(Color online) Sequence of particle clusters that leads to a single particle suspended in the glass box. Four panels show side view of clusters of four to one particles. Particles are dropped one by one by temporarily de-tuning the plasma matching network. After restoring the matching conditions, the remaining particles almost re-occupy their previous positions. The horizontal position of particles is shown relative to the average position in the cluster of four particles. The pressure of argon was 4 Pa, the rf power was 2 W.
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