Transport limited currents close to an ultrasonic horn: Equivalent Flow Velocity Determination

The effect of changing the distance of an ultrasonic horn tip from a stationary platinum disk electrode on limiting current density at various electroanalyte concentrations, ultrasonic frequencies (20 and 40 kHz), and ultrasonic intensities was studied in an attempt to find the optimum position required for maximum sonoelectrochemical effect in "face-on" mode. Our findings were compared to mathematical models available in the literature, for the mass transport of electroactive species to the electrode under hydrodynamic flow conditions normal to the ultrasonic horn. A good fit with experimental results was found and confirmed the dependence of limiting current to operating parameters such as ultrasonic power, electrode-to-horn distances and electroactive species diffusion coefficient, and also highlighting the importance of ultrasonic frequency. From mass balance equations, it was then possible to develop an approach by analogy to an electrode subjected to pure hydrodynamic flow. A Levich-like equation relating the limiting current density, the square root of ultrasonic intensity, and the inverse square root of the electrode-horn distance was generated for ultrasonic frequencies of 20 and 40 kHz, allowing the generation of an "equivalent" flow velocity under sonication, an important and useful parameter in chemical engineering.