An empirical model to estimate the growth of ice crystals for storage of Tilapia at variable temperature conditions

Abstract Empirical models can be used to represent the recrystallization process in frozen food as a simple strategy (limited by the complexity of the process). Anyway, the empirical model has a better fit when used within the range of experimental values from which they were generated. In this work, an empirical mathematical model derived from the Arrhenius equation was proposed, since in previous publications it was shown that there is a direct relation between the growth of ice crystals and the temperature oscillations that occur during the storage of frozen products. Equivalent diameter data of ice crystals obtained from the storage of frozen Tilapia analyzed in the optical microscope was used as a database for the formulation of the empirical model. The developed model was acceptable to predict ice crystal growth during recrystallization in frozen Tilapia samples and had the advantage of being simple and robust enough to estimate this growth in the flotation range from -18 to -11 °C After the first 30 days of storage. The average equivalent diameter (Deq) values predicted by the model indicated that the model provides a satisfactory description of the growth of the crystals with R2 equal to 0.930.

摘要 经验模型可作为一种简便策略，用于表征冷冻食品的重结晶过程，但该方法受限于该过程的复杂性。不过，当经验模型在其构建所基于的实验值范围内使用时，拟合效果更佳。本研究提出了一种源于阿伦尼乌斯方程（Arrhenius equation）的经验数学模型，因为已有前期研究表明，冷冻制品储存过程中出现的温度波动与冰晶生长存在直接关联。本研究以光学显微镜（optical microscope）对冷冻罗非鱼（Tilapia）储存过程中采集的冰晶当量直径（equivalent diameter）数据，作为构建该经验模型的数据集。所构建的模型可有效预测冷冻罗非鱼样品重结晶过程中的冰晶生长情况，其优势在于结构简便且鲁棒性较强，能够在储存30天后的-18℃至-11℃的温度区间内对冰晶生长进行估算。模型预测得到的平均当量直径（Deq）数值表明，该模型对冰晶生长的描述效果良好，决定系数（R²）为0.930。