Modelling the freezing of butter Amsha Nahid a, *, John E. Bronlund a , Donald J. Cleland a , Bruce Philpott b a Institute of Technology and Engineering, Massey University, Private Bag 11222, Palmerston North 5103, New Zealand b Fonterra Research Centre, Private Bag 11029, Palmerston North 5103, New Zealand article info Article history: Received 10 February 2006 Received in revised form 27 June 2007 Accepted 8 July 2007 Published online 6 August 2007 Keywords: Butter Freezing Modelling Simulation Freezing time Temperature Nucleation Crystallization abstract Butter is a water-in-oil emulsion so its behaviour during freezing is very different from that of most food products, for which water forms a continuous phase. The release of latent heat during freezing is controlled as much by the rate of crystallization of water in each of the water droplets as by the rate of heat transfer. Measurements of the freezing of butter show that the release of latent heat from the freezing water depends on the degree of supercooling, which, in turn, depends on the cooling medium temperature, the size of the butter item, the packaging and the type of butter. Four modelling approaches were tested against the experimental data collected for a 25 kg block of butter. A ‘‘sensible heat only model’’ accurately predicted the butter temperature until temperatures at which water freezing becomes significant were reached. An ‘‘equilibrium thermal properties model’’ predicted a temperature plateau near the initial freezing point of the butter in a manner that was inconsistent with the measured data. A third model used a stochastic approach to ice nucleation based on supercooling using classical homogeneous nucleation theory. The predicted temperatures showed that supercooling-driven nucleation alone is not sufficient to predict the freezing behaviour of butter. A fourth approach took account of time-dependent nucleation and ice crystal growth kinetics using classical Avrami crys- tallization theory. The relationship between the ice crystal growth rate and the supersatu- ration was assumed to be linear. The model predicted the experimental data accurately, particularly by predicting the slow rebound in the temperature following supercooling that is found when freezing butter under some conditions. ª 2007 Elsevier Ltd and IIR. All rights reserved. Mode ´ lisation de la conge ´ lation de beurre Mots cle ´s : Beurre ; Conge ´lation ; Mode ´ lisation ; Simulation ; Temps de conge ´lation ; Tempe ´ rature ; Nucle ´ ation ; Cristallisation 1. Introduction Butter is a water-in-oil emulsion. Approximately 16% of water in butter exists in the form of tiny spherical or oval droplets embedded in the continuous fat phase. There are approximately 10 10 –3  10 10 droplets per millimeter in butter (Precht, 1988; Walstra, 2003; Mulder et al., 1956). Butter is commonly frozen and stored in bulk before thaw- ing and further processing into consumer packs or use by the food processing industry. Accurate predictions of the rates of * Corresponding author. Tel.: þ64 6 350 5799x7439; fax: þ64 6 350 5604. E-mail address: a.nahid@massey.ac.nz (A. Nahid). www.iifiir.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/ijrefrig 0140-7007/$ – see front matter ª 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.07.012 international journal of refrigeration 31 (2008) 152–160