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<p>For this study, we re-analyzed previously published ice crystal size data in commercial ice cream during long-term storage. Ice crystal growth during frozen storage is a major factor determining the texture and sensory quality of ice cream. Historically, based on the Ostwald ripening theory, ice crystal growth rates in ice cream and sugar solutions have been predicted using a mean particle size power law equation, e.g. the average radius cubed is proportional to time. However, the ice crystal growth in commercial ice cream stored at low temperatures for more than a year could not be fitted accurately using conventional equations. We therefore developed a novel equation incorporating anomalous diffusion of water molecules to predict ice crystal growth rates. Unlike conventional ice crystal growth equations, which assume a fixed growth exponent, the proposed model allows the exponent to vary as a function of storage conditions. Importantly, this exponent is not an empirical fitting parameter but reflects the diffusion regime of water molecules in the frozen matrix, thereby providing a physically interpretable link between molecular mobility and macroscopic ice crystal growth. The obtained data were re-analyzed using previously published datasets reporting the time evolution of average ice crystal diameter in ice cream stored at − 12&#xa0;°C to − 70&#xa0;°C for periods of up to one or two years, where the growth kinetics were re-examined by fitting the proposed model to the original diameter–time data. Ice crystal growth kinetics are consistent with an effective sub-cubic coarsening exponent that varies systematically with storage conditions and can be parameterized using an anomalous-transport-inspired form. These results provide a new perspective on the theory of ice crystal growth rates.</p>

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A Hypothesis-Based Framework for Ice Crystal Growth Kinetics in Ice cream Incorporating Anomalous Diffusion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月18日

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  • Misaki Shiba,
  • Younju Lee,
  • Mario Shibata,
  • Tomoaki Hagiwara,
  • Toru Suzuki

摘要

For this study, we re-analyzed previously published ice crystal size data in commercial ice cream during long-term storage. Ice crystal growth during frozen storage is a major factor determining the texture and sensory quality of ice cream. Historically, based on the Ostwald ripening theory, ice crystal growth rates in ice cream and sugar solutions have been predicted using a mean particle size power law equation, e.g. the average radius cubed is proportional to time. However, the ice crystal growth in commercial ice cream stored at low temperatures for more than a year could not be fitted accurately using conventional equations. We therefore developed a novel equation incorporating anomalous diffusion of water molecules to predict ice crystal growth rates. Unlike conventional ice crystal growth equations, which assume a fixed growth exponent, the proposed model allows the exponent to vary as a function of storage conditions. Importantly, this exponent is not an empirical fitting parameter but reflects the diffusion regime of water molecules in the frozen matrix, thereby providing a physically interpretable link between molecular mobility and macroscopic ice crystal growth. The obtained data were re-analyzed using previously published datasets reporting the time evolution of average ice crystal diameter in ice cream stored at − 12 °C to − 70 °C for periods of up to one or two years, where the growth kinetics were re-examined by fitting the proposed model to the original diameter–time data. Ice crystal growth kinetics are consistent with an effective sub-cubic coarsening exponent that varies systematically with storage conditions and can be parameterized using an anomalous-transport-inspired form. These results provide a new perspective on the theory of ice crystal growth rates.