A chemical reaction-based boundary condition for flow electrification

A physical model is developed for the charge transfer boundary condition in semi-insulating liquids. The boundary condition is based upon interfacial chemical reactions and extends established relations for the interface by including the effects of interfacial surface charge and charge desorption at the interface. A steady state model for flow electrification in a rotating cylindrical electrode apparatus incorporated this boundary condition and described polarity changes in the open-circuit voltage and short-circuit current as a function of the fluid velocity, the volume charge density dependence an the terminal constraints, and the charge density dependence on applied dc voltages. Previously used boundary conditions are shown to be special cases of the chemical reaction rate boundary condition. A general methodology is developed for combining the volume charge density and voltage/current terminal measurements to estimate the parameters describing the interfacial charge transfer kinetics. Volume charge densities ρ^w on the liquid side of the interfaces of 1 to 20 mC/m ³ were estimated from the open-circuited electrode measurements, with the stainless steel ρ^w typically larger than that of copper but smaller than that of transformer pressboard. Activation energies for an Arrhenius temperature dependence of ~0.16 eV for pressboard, 0.25 eV for stainless steel and 0.28 eV for copper were obtained. Interfacial adsorption reaction velocities, estimated to be 10^-5 m/s, were not large enough to make the terminal current transport limited which contradicts the often used assumption that the reaction velocities can be considered `infinite´. Estimated surface reaction rates at a 70°C stainless steel/oil interface of ~20 μm/s for adsorption and ~0.5 s^-1 for desorption were obtained. The additive BTA reduced the ρ^w for pressboard and stainless steel at concentrations >8 ppm in transformer oil