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

Abstract

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.

Sonocrystallisation: Observations, theories and guidelines

“…As most components show a decreased solubility at elevated pressures, these high pressures are thought to result in an increased supersaturation and hence enhanced nucleation [20]. The increase in supersaturation, defined as the difference between the liquid temperature and melting temperature (solid-liquid transition), was simulated by Cogné et al for different initial bubble radii and acoustic pressures for the nucleation of ice [63,64]. Significant local supersaturations of -370 K were obtained at the time of maximum pressure at the bubble wall.…”

“…The huge supersaturations are thought to trigger nucleation even though the high supersaturation domain (>-50 K) is very narrow in time ( around 1 ns after the collapse) and space (around 2 µm from the bubble wall). Simulations in the same papers suggested namely that nucleation could be triggered starting from a supersaturated solution of 5 K for bubbles with initial radius of 5 µm driven by an ultrasonic sinusoidal wave with a frequency of 29 kHz and acoustic pressure amplitude of 220 kPa [64]. Brotchie et al reported, however, conflicting results with this pressure hypothesis [59].…”

Antisolvent Sonocrystallisation of Sodium Chloride and the Evaluation of the Ultrasound Energy Using Modified Classical Nucleation Theory

“…It is well accepted that cavitation bubbles generated by the ultrasound influence the crystallisation process [4,[17][18][19][20][21][22]. However, the complexity of both the cavitation and crystallisation processes, which occur in extremely short time and length scales, makes it difficult to determine the precise mechanism behind sonocrystallisation.…”

Ultrasound cavitation induced nucleation in metal solidification: An analytical model and validation by real-time experiments

“…At bubble implosion, the pressure is assumed to propagate outwards spherically [26] and any heat transfer from the imploding bubble to its surrounding melt is ignored (i.e. an adiabatic process) [22] , [24] , [27] , The nucleation number at one-time implosion is calculated by where N i is the number of nucleus, and the subscript i indicates the bubbles size; I nuc is the nucleation rate in the undercooled volume V at time τ .

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“…It can calculate the pressure field in the vicinity of an imploding bubble, and the nucleation rate around the bubble. Cogne et al [23] , [24] recently derived a refined model that is able to incorporate the melt temperature profile and then calculate the nucleation rate around a single bubble in water. They found that the melt temperature at an imploding bubble wall is much closer to the ambient temperature than the inner bubble, due to heat conduction from the bubble centre or the latent heat release.…”