The experimental setup. Grains freely fall inside a vacuum chamber from the hopper/nozzle through a region between two parallel copper plates held at a potential difference V ( points into the page). A camera connected to a carriage-rail system falls with the grains while simultaneously recording video. A vertical reference string hangs in front of the chamber to correct for camera yaw and roll.
Particle tracking. (a) Color-inverted still from experiment. Circled particles are positive particle identifications, while the few remaining particles are rejected on basis of size, shape, proximity to the string, or being far out of focus. The fuzzy vertical black strip is the string, and the thin white line is its calculated center position. (b) Example uncorrected particle position (black line), string position (dotted black line), and corrected particle position (red points) vs. time (particle and string are measured relative to their initial positions). The green data are the residuals from fitting the corrected trajectory to a parabola, which have a rms deviation of ∼0.5 pixels. (c) Sampling of the corrected horizontal deflection (i.e., x − v 0 t − x 0) for a few particles of different charges at V = 2250 V ( V/m).
Filtering procedure to reject colliding and crossing particles. (a) Example particle trajectory (x − x 0 vs. t) of a particle involved in a collision/crossing. The event leads to a perceived acceleration of ∼0.5 m/s2, although it is clear from either leg of the trajectory that the actual acceleration is much smaller than this. (b) Errors on acceleration fits σ a vs. particle lifetime τ. Most measurements (blue data) fall into a band σ a ∝ τ−2, while the colliding/crossing particles lie above this trend. These tracks (red data) are rejected by binning along τ, finding the average σ a in each bin by fitting to a Gaussian, and then rejecting particles whose σ a lies three sigma above their bin mean.
Relating acceleration distributions to charge measurements. (a) Particle acceleration distributions P(a) (weighted by ) for voltages V =0, 1500, and 4000 V ( = 0, 30 000, and 79 000 V/m, respectively). (b) Change in distribution width Δ a (red squares), mean (blue circles), and mean acceleration error (green dots) vs. V. Calculations for Δ a and are also weighted by , and the error bars are the standard deviations as calculated from N = 1000 bootstrap resamples of the original measurement population. Dashed line fits for and Δ a correspond to Eqs. (1) and (2) , respectively. (c) Particle size distribution P(d) as calculated from imaging particles with optical microscope. Inset: microscope image (color inverted). Using these data to calculate the mean diameter and particle mass , we can use Eqs. (1) and (2) to calculate the mean charge = −(6 ± 1) × 104 e and width Δ q = (4.5 ± 0.4) × 105 e of the particle charge distribution.
Independent measure of average charge per particle with Faraday cup. Plot of total charge in cup Q vs. time t. Data are smoothed to remove 60 Hz noise (∼10 nC peak to peak). We calculate the charge flow rate dQ/dt and mass flow rate dM/dt from this graph.
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