Thermodynamics of ultra-sonic cavitation bubbles in flotation ore processes

Ultra-sonic enhanced flotation ore process is a more efficient technique for ore recovery than classical flotation method. A classical simplified analytical Navier-Stokes model is used to predict the effect of the ultrasonic waves on the cavitations bubble behaviour. Then, a thermodynamics approach estimates the temperature and pressure inside a bubble, and investigates the energy exchanges between flotation liquid and gas bubbles. Several gas models (including ideal gas, Soave-Redlich-Kwong, and Peng-Robinson) assuming polytropic transformations (from isothermal to adiabatic) are used to predict the evolution of the internal pressure and temperature inside the bubble during the ultrasonic treatment, together with the energy and heat exchanges between the gas and the surrounding fluid. Numerical simulation illustrates the suggest theory. If the theory is verified experimentally, it predicts an increase of the temperature and pressure inside the bubbles. Preliminary ultrasonic flotation results performed on a potash ore seem to confirm the theory.