A physicochemical explanation for flow electrification in low-conductivity liquids in contact with a corroding wall

Electrification during flow of insulating liquids in pipes has been studied for a long time. Its dependence on flow parameters and pipe geometry has been modeled for many different cases and is quite well known. Even though different laws of flow electrification have been obtained empirically in terms of the pipe length, a complete analysis taking into account the electrochemical reactions at the pipe wall-liquid interface is lacking. In this paper, we present a model of the process in the case of a corroding wall and a liquid containing additives or impurities partially dissociated into positive and negative ions. We treat the case of laminar flow and an interfacial reaction whose conversion is small compared to the concentrations of positive and negative ions in the bulk solution. We compute the evolution of the space charge density in terms of the axial and radial coordinates, and the flow velocity. The boundary conditions on the wall are deduced from the kinetics of the wall surface reactions with the additives. Thus, analysis of these chemical reactions allows us to compute the net flux of electrical charge from the wall to the liquid. This flux is a function of the axial distance along the pipe and the mean flow velocity. Finally, comparison is made between our model and experiments on flow electrification for hydrocarbons liquids.