The side view (a) and the top view (b) of the experimental setup. In a bottom view image (c) of a real droplet, the direction of the flow vortices is shown. The distance between the vortex center and the pinning site Lvc is represented by the red arrow. The orange rectangle represents the electrode where the contact line of the droplet is pinned.
(a) The bottom view images of the droplets with colloidal polystyrene particles of diameter 5 μm, 0.5 μm, and 0.02 μm. The top and the bottom rows represent droplets in the beginning (t = 0 and fAC = 1 kHz) and at the end (t = tfin and fAC = 40 kHz) of the frequency sweep, respectively. The bright rim of the droplets is due to reflection. The orange rectangles represent the position of the pinning site, i.e., the electrode (enhanced online). (b) The intensity profile for the droplet containing 0.5 μm particles before (black) and after (red) the frequency sweep. The intensity is normalized with respect to its maximum value. Distance is normalized with respect to the total profiling length. The inset is a cartoon of the droplet with the dashed line indicating the location of the intensity profile. [URL: http://dx.doi.org/10.1063/1.4815931.1]doi: 10.1063/1.4815931.1.
The intensity at the vortex-center as a function of time for a frequency sweep from 1 to 40 kHz at a rate of 1 kHz/s. The amount of particles accumulated reaches a maximum and does not increase any further. Larger particles reach this maximum amount quicker (marked by the arrows) than the smaller ones. The normalization is performed with respect to the average initial intensity for each type of particles. The error bar is the standard deviation in the intensity values for the four vortices in two different droplets of volume 0.7 μl each.
The displacement of the vortex-center Lvc versus frequency for droplets of different volume (shown in the figure). The arrows indicate the onset frequency above which the vortices start to shift. Below this onset frequency, the size of the vortex is comparable to the radius of the droplet. Smaller the droplet the larger the onset frequency. The error bar is the standard deviation in the values of Lvc for the four vortices in two different droplets, for each droplet volume.
Cartoon of an AC electrowetting droplet (electric connections are not shown). (a) and (b) are side view and (c) is 3D view. (a) Capillary waves on the surface of the droplet create internal flows (marked by the red, curved arrows) by a Stokes drift like mechanism (see Refs. 29 and 32 ). (b) When the symmetry is broken by a pinning site, there are no waves and hence no upward flows in the regions near the pinning site. All the upward flows as illustrated by red arrows in (c) sink in the pinning region. Due to mass conservation fluid flows back, creating vortices illustrated by the red dashed lines.
Azimuthal flow velocity in the vortices at the liquid-air interface as a function of the radial distance from the center of the vortex. The velocity is zero at the center and increases to a large value near the outer boundary (represented by the arrows) of the vortex. As the frequency fAC (shown in the figure) increases, the radius of the vortex decreases and the shear rates increase sharply at the edge of the vortex. The solid lines are guide to the eyes.
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