Simulation of streaming electrification phenomenon

The streaming electrification tends to occur in transformers when the oil flow velocity increases. This is due to the ionic double layer formed at the duct wall adjacent to the oil flow. The simulations of this phenomenon are attempted based on the diffusion of ions in the oil-flowing space. A simple solution is found for the ion density or charge density in the case the velocity is uniform. The solution is modified to obtain the approximate charge density in the case that the velocity has a quadratic distribution in the duct. The charge distributions calculated by the too solutions are compared. The value of diffusion constant is discussed in order to explain an experimental current level by these models.