Electrification in turbulent channel flows of liquid dielectrics

Abstract

Electrification of wall-bounded flows of liquid dielectrics occurs via the transport of electric-charge carriers (ions) from the electrical double layer at a liquid–solid interface to the bulk of the flow. This phenomenon is currently not well understood, but it has been proposed that flow turbulence plays a major role on it. However, conclusive studies about the role of turbulence and the underpinning mechanisms of flow electrification are still lacking. In this paper, we report on direct numerical simulations (DNS) of electrification in turbulent channel flow of liquid dielectrics and for friction Reynolds numbers ranging from 150 to 210. Our simulations confirm that turbulence increases dramatically the amount of charge transported in the bulk of the flow. Also, the electrification rate increases with the turbulence intensity. Nonetheless, ionic diffusion does not influence the electrification process, due to the large value of the ionic Schmidt number. Our simulations further predict that, upon electrification, the charge-density profile consists of three zones. In the first one, adjacent to the wall, the dominant mechanism is ionic diffusion, whereas in the second one, the dominant mechanisms are convective and conductive currents. In the third zone, the bulk of the flow, the charge density remains almost constant. Also, according to the budget of the charge-density variance, molecular transport counterbalances molecular dissipation in the first zone, and production counterbalances turbulent transport in the second one. Finally, we provide a closed-form expression for the mean charge-density profile based on the gradient assumption, which agrees well with our DNS results.