Electrostatic adhesion of multiple non-uniformly charged dielectric particles

Charged particle adhesion measurements can be as much as one order of magnitude higher than theoretical calculations. This discrepancy has ignited a debate as to the nature of the physics occurring with microscopic particle adhesion. Attempts to bring calculations closer to measured results have produced models that include multiple particle interactions, dielectric polarization, and non-uniform charge. Individually, each of these models can only produce a 2× to 5× enhancement in predicted adhesion force over simple Coulombic attraction. In this correspondence, an analytical model of electrostatic particle forces is developed, which allows for independent assignment of dielectric constant and non-uniform surface charge distribution to an arbitrary number of particles. Because the model can include an image plane, it is ideal for electrostatic adhesion calculations. Application to a monolayer of printed toner particles predicts nearly an order of magnitude increase in adhesion force over Coulombic attraction. These results are the first analytical results to place predictions of charged particle adhesion on the same order of magnitude with measurements.