The electric field in porous materials calculated with the grain consolidation model

We have used the grain consolidation model (GCM) to study the spatial variation of the electric field inside a porous medium such as oil impregnated cellulose. The calculations were primarily performed in order to determine the maximum electric field within the composite, which is important for the overall dielectric strength of the material. In the composite as a whole, the maximum field may be considerably higher than in a homogeneous medium under the same applied external field. The contacts between the solid particles in the composite material are more realistically described in the GCM than in effective-medium models, and a comparison shows that the GCM yields higher maximum fields than effective-medium theory. Two different 3-dimensional geometries have been used in the GCM calculations and the results indicate that the exact geometry is of minor importance. These models are isotropic, while many important insulation materials are highly anisotropic. In order to illustrate the effects of different geometries, we have also performed calculations on a 2-dimensional geometry. In this case, it appears as if the lack of contacts between the solid particles mainly influences the maximum field in the phase which has the highest complex conductivity. If the conductivities of both phases are almost equal, the maximum field is close to the applied field. Increasing the difference in conductivity between the oil and the solid increases the maximum electric field. We have also shown that the GCM can be used to estimate the electric field in the presence of interface effects.