Charge and force on a conductive sphere between two parallel electrodes: A Stokesian dynamics approach

Abstract

We present an accurate and efficient method to compute the electrostatic charge and force on a conductive sphere between two parallel electrodes. The method relies on a Stokesian dynamics-like approach, in which the capacitance tensor is divided into two contributions: (1) a far field contribution that captures the long range, many body interactions between the sphere and the two electrodes and (2) a near field contribution that captures the pairwise interactions between nearly contacting surfaces. The accuracy of this approach is confirmed by comparison to "exact" numerical results obtained by finite element modeling. From the capacitance tensor, we derive the charge and dipole moment on the sphere, the electrostatic free energy of the system, and the electrostatic force on the sphere. These quantities are used to describe the dynamics of micron-scale particles oscillating within a viscous dielectric liquid between two parallel electrodes subject to constant voltage. Simulated particle trajectories agree quantitatively with those captured experimentally by high speed imaging. V C 2014 AIP Publishing LLC. [http://dx.

Modeling of conductive particle motion in viscous medium affected by an electric field considering particle-electrode interactions and microdischarge phenomenon

“…Indeed, the competition between λ e and λ S determines the position of the reverse point in the particle trajectory. It is clear from Figure 13 that ∆h pmdm decreases significantly with decreasing s md , and ∆h pmdm ≈ 0 for s md ≤ 1 µm which conforms to the assumption of Drews et al 28 Generally, Figure 13 gives s min = f (s md ), where f is a function between the microdischarge point position, s md , and the possible minimum particle-electrode separation, s min . This function can be used as the initial position of the particle in using the proposed model as…”

“…In other words, since S → 0 implies λ S → ∞, it is essential to use a minimum distance for the particle-wall gap, say s min . This strategy has been used by many researchers, for example, Drews et al 28 used s min = 0.0247R (0.7 µm) in their modeling approach based on the assumption that the microdischarge takes place when the particle-electrode gap reduces to 0.7 µm (i.e., s md = 0.7 µm). Indeed, they assumed that the particle motion is immediately reversed after the microdischarge.…”

Crater Formation on Electrodes during Charge Transfer with Aqueous Droplets or Solid Particles

“…Provided the electric field is strong enough, the conducting object will move away to the opposite electrode, acquire the opposite charge, and repeat the process, effectively bouncing back and forth between the electrodes [3][4][5][6][7]. Although this qualitative behavior has been well established, experimental measurements of the amount of charge transferred have been marked for decades by irreproducibility [8][9][10][11] and significant deviations [10][11][12][13][14][15] from the theoretical prediction first derived by Maxwell [1]. Experimental work indicates general agreement with the theory, but close examination of the data shows that the charge transferred to the same object from the same electrode can vary up to 200% [8][9][10][11].…”

Metallic nanowires and mesoscopic networks on a free surface of superfluid helium and charge-shuttling across the liquid–gas interface

“…[23][24][25][26][27] The phenomenon is referred to as a contact charge electrophoresis 27,28 or a charge-shuttling 23 …”