On the charge of a moving particle within a parallel electrodes in viscous fluid

The conductive spherical particle in viscous fluid (silicone oil) under a uniform electric field shows both up-and-down motion and resting on the electrode between motions. In order to analyze the motion of a conductive particle under electric field theoretically, the charge amount of particle must be known. It can be achieved with several methods. When the conductive particle is on the electrode experiencing the uniform field, there is a well-known equation for the charge amount of a spherical particle. The second way is to estimate the electrostatic force acting on the particle in the motion through viscous fluid by using dynamic equation. The third method is to integrate a pulsed current when the charge exchange process is occurring between the particle and the electrode. The value of particle charge by integrating the current is much smaller than the others. The width of the current pulse is less than 100 μs, which is much shorter than the resting time. This suggests that the acquired charge from the integration of pulse might not be the whole charge, but several small discharges might follow the first one during the time the particle is resting on the electrode