Charge relaxation due to surface conduction on an insulating sheet near a grounded conducting plane

Electrostatic charges are responsible for a variety of problems in industrial processes and customer equipment that use webs or sheets. Problems include particle contamination from attracting dust, sheets that stick to each other, and electrical discharges resulting in logic resets or damage to electrical components. These problems can be mitigated by increasing the surface conductivity of the insulating sheets by coating the surface with a conductive layer or by increasing the relative humidity. To mitigate problems, electrostatic charge must dissipate quickly compared with the mechanical transport time of the process. Reported here are the results of a model calculation of the charge relaxation time showing explicitly that the charge relaxation time depends on both surface conductivity and geometry. The charge relaxation time is found to increase as the distance to a nearby, grounded conducting plane decreases. Charge relaxation is slowed because the tangential electric field needed to drive surface current becomes smaller as the distance to the grounded plane decreases. Inferred from this analysis is the dependence of charging on the electric Reynolds number (ratio of the electrical charge relaxation time to the mechanical transport time). Web charging can be divided into three regimes: dissipation (R_e<0.1), transition (0.1e<10), and charging (10e). Only in the transition regime does charging depend strongly on surface conductivity and speed.