Electric forces on conducting spheres in millimeter sized high-voltage gaps

Particles acting as contamination pose challenges in applications ranging from high-tech equipment to high-voltage switchgear. Although analytical models describe the motion of charged, conducting spherical particles well, they become inaccurate in the limiting case of two planar electrodes being closely spaced. The aim of this work is to quantify the deviation between analytical predictions and experimental observations in this regime. Through a combination of experiments and numerical simulations, the lift-off dynamics of a conducting solid sphere subjected to electric fields exceeding 1 MV/m were investigated in an electrode gap comparable to the sphere diameter (1 mm). From the lift-off acceleration measured using high-speed imaging, the electric force acting on the sphere was quantified and found to be in good agreement with numerical simulations and the analytical model of a single electrode and a single sphere by Felici (1966) when the sphere-to-gap ratio R / d was small. However, for a sphere approaching the size of the gap, the analytical model values were up to 20% lower than the experimental and numerical results, implying that the attractive electrostatic interactions between the sphere and the top electrode should be included in the analytical model in that limit case.