Static electrification by laminar flows through artificially roughed pipes

The mechanism of static electrification of hydrocarbon liquids flowing through artificially roughed metallic pipes is analyzed. Only the case of a laminar flow is considered. The equations of motion of the liquid are computed in the case of circular pipes with periodic roughness of rectangular cross section in the axial direction. The results reveal the formation of eddies, which depend on the size and the period of the roughness and on the Reynolds number. After determining the charge convected in a smooth pipe and the velocity profile in a rough one, it is possible to predict the convected space charge in terms of the roughness characteristics. The experimental results obtained with different rough pipes and several Reynolds numbers are in good agreement with the predictions, making it possible to explain the observations made during previous experiments on static electrification in rough pipes