Charge relaxation in partially filled vessels

Abstract

The decay of electrostatic charge within a conducting vessel partially filled with charged powder is influenced by the geometry of the vessel and the fill level within. As it decays, some of the volume charge temporarily accumulates at the surface of the powder heap. This surface charge is capacitively coupled to the conducting vessel walls and, therefore, its (extrinsic) rate of decay is always slower than the (intrinsic) relaxation rate of the volume charge. If the percent fill is close to 100%, the decay rate can be significantly prolonged. To exemplify this geometry-dependent behavior, a transient solution to Poisson's equation is obtained for the case of a grounded cylindrical tank partially filled with charged powder under the assumption that the uniform initial volume charge decays according to an exponential charge relaxation law. The dominant (extrinsic) time constant which governs decay of the surface charge is identified and its dependence upon the vessel geometry and the percent fill is studied. Because of the lingering presence of surface charge, the electric fields near the powder/air boundary can remain at hazardous levels for an extended period of time. The practical implication of these results is that the probability of electrostatic discharge during and after filling operations is increased.