Can electrostatic precipitation work in reverse? An electrostatic precipitator captures particles by charging them so that they are attracted to a grounded precipitation plate.  Does that process work in reverse?  I.e., if we apply a voltage to a conductive plate will it repel all particles in contact with it?
(I'm doubting this is the case because if it were it would seem like a simple way to clean any conductive surface.)
 A: If the particles are not too heavy or too small then a charged plate can repel them.  For example, a paper confetti explosion is a classic Van de Graaff demonstration.
This repulsion can, indeed, be useful.
A recent study - "Electrostatic dust removal using adsorbed moisture–assisted charge induction for sustainable operation of solar panels" -
demonstrated that electrostatic forces can be used to clean solar panels. Using their notation, the forces acting on a spherical particle of radius $R$ and uniform density $\rho$ resting on a charged horizontal conducting plate with surface electric field $E$ are:

*

*Gravity pulling down,  $F_G= Mg=\rho\frac{4}{3}\pi R^3 g$

*Electrostatic repulsion from the plate, $F_E =QE =Q^* 4\pi R^2 \epsilon_0 \epsilon_r E^2$

*Van der Waals Attraction to the plate, $F_A=\frac{A}{6d_0^2}R$
The particle will levitate if $F_E > F_G+F_A$.
$Q^*$ is a constant that varies from $0$ for perfect insulator to $1$ for a perfect conductor. Mineral dust is typically 40-75% silica, so silica Arizona test dust was used in the study with $Q^*\approx 0.9$, $\rho\approx 2.7\,\mathrm{g/cm^3}$, surface atomic separation $d_0 \sim 0.4 \,\mathrm{nm}$, and a Hamaker constant $A\sim 6.3 \times 10^{-20} \mathrm{J}$.
Scanning a $12$ KV plate above a test solar panel sloped at 20° cleared most of the dust larger than 30 microns for air humidity above 30%. At lower humidity, the silica particles don't adsorb enough water for them to easily charge.  The slope is necessary for the levitated dust to flow off the plate, instead of just hovering in the air and continuing to block the sunlight.
There are, of course, limits on the effectiveness of electrostatic cleaning. The first large Van de Graaff generator was built in a large open airship hangar, and it famously could not initially reach the expected high voltage because of bird droppings on the top of the generator's dome.  Even Megavolts are insufficient to remove pigeon poop.
