calculations. The numerical calculations were on the basis of a
three-dimensional hard-sphere model of the distinct element
method (DEM). Details of the numerical method are reported in the
literature [21,33,35]. The electrostatic field that determines the
Coulomb force and the dielectrophoresis force applied to the sand
particles is calculated by a two-dimensional differential element
method in a cyclic domain. Although the dynamic motion of the
particles cannot be conveyed by still images as shown in Fig. 4, we
confirmed the calculated and observed motions are in qualitative
agreement by comparing calculated and measured movies. As
described later, the calculated performance agrees well with the
measured results, not only qualitatively but also quantitatively.
Fig. 5 shows the cleaning efficiency, i.e., the ratio between the
weight of the sand fed onto the panel for 30 s and that after the
cleaning operation of the system, versus the inclination of the plate.
A cleaning experiment using a four-phase traveling wave was also
conducted for comparison with single-phase cleaning. High performance
was achieved even when the plate was only slightly inclined,
and the performance achieved by standing wave cleaning
was almost the same as that for traveling-wave cleaning when the
inclination was greater than 20. This suggests that the system
would even be effective at low latitudes at which solar panels are
installed at low inclinations.
Effects of pitch, applied voltage, and frequency
Figs. 6 and 7 show the cleaning efficiency versus the averaged
electrostatic field strength determined by the applied voltage
divided by the pitch of the parallel electrodes and the frequency of
the applied voltage, respectively. The solid curves in Figs. 6 and 7
show the calculated results, which agree well with the measured
results. We observed that producing a high field strength achieved
high performance; however, saturation occurred at a high value.
Because the applied voltage is limited by the insulation breakdown,
which is determined by the electrostatic field, the system performance
is almost independent of the electrode pitch at the threshold