Theoretical model of ice nucleation induced by inertial acoustic cavitation. Part 2: Number of ice nuclei generated by a single bubble.

In the preceding paper (part 1), the pressure and temperature fields close to a bubble undergoing inertial acoustic cavitation were presented. It was shown that extremely high liquid water pressures but quite moderate temperatures were attained near the bubble wall just after the collapse providing the necessary conditions for ice nucleation. In this paper (part 2), the nucleation rate and the nuclei number generated by a single collapsing bubble were determined. The calculations were performed for different driving acoustic pressures, liquid ambient temperatures and bubble initial radius. An optimal acoustic pressure range and a nucleation temperature threshold as function of bubble radius were determined. The capability of moderate power ultrasound to trigger ice nucleation at low undercooling level and for a wide distribution of bubble sizes has thus been assessed on the theoretical ground.

Theoretical model of ice nucleation induced by acoustic cavitation. Part 1: Pressure and temperature profiles around a single bubble.

This paper deals with the inertial cavitation of a single gas bubble in a liquid submitted to an ultrasonic wave. The aim was to calculate accurately the pressure and temperature at the bubble wall and in the liquid adjacent to the wall just before and just after the collapse. Two different approaches were proposed for modeling the heat transfer between the ambient liquid and the gas: the simplified approach (A) with liquid acting as perfect heat sink, the rigorous approach (B) with liquid acting as a normal heat conducting medium. The time profiles of the bubble radius, gas temperature, interface temperature and pressure corresponding to the above models were compared and important differences were observed excepted for the bubble size. The exact pressure and temperature distributions in the liquid corresponding to the second model (B) were also presented. These profiles are necessary for the prediction of any physical phenomena occurring around the cavitation bubble, with possible applications to sono-crystallization.

Prediction of the acoustic and bubble fields in insonified freeze-drying vials.

The acoustic field and the location of cavitation bubble are computed in vials used for freeze-drying, insonified from the bottom by a vibrating plate. The calculations rely on a nonlinear model of sound propagation in a cavitating liquid [Louisnard, Ultrason. Sonochem., 19, (2012) 56-65]. Both the vibration amplitude and the liquid level in the vial are parametrically varied. For low liquid levels, a threshold amplitude is required to form a cavitation zone at the bottom of the vial. For increasing vibration amplitudes, the bubble field slightly thickens but remains at the vial bottom, and the acoustic field saturates, which cannot be captured by linear acoustics. On the other hand, increasing the liquid level may promote the formation of a secondary bubble structure near the glass wall, a few centimeters below the free liquid surface. These predictions suggest that rather complex acoustic fields and bubble structures can arise even in such small volumes. As the acoustic and bubble fields govern ice nucleation during the freezing step, the final crystal's size distribution in the frozen product may crucially depend on the liquid level in the vial.