Mathematical modeling and experimental validation of the mass transfer during unidirectional progressive cryoconcentration of skim milk

• Mathematical modeling of a unidirectional cryoconcentration of skim milk
• Experimental validation of the theoretical model
• High solute entrapment in the ice fraction

A mathematical model has been developed and experimentally validated to explain the process of unidirectional progressive cryoconcentration of skim milk. The capture coefficient determining the process efficiency was freezing rate dependent and the solute flow at the ice/liquid boundary layer was dependent of the competition between the heat and mass transfer phenomena. The dependence of the solute capture coefficient on the freezing velocity and the velocity of the ice/liquid interface zone was the key to understand the quantitative mass transfer to the bulk of the solution or the solute entrapment into the ice matrix. The experimental data for skim milk unidirectional progressive cryoconcentration showed that in a wide range of the ice/liquid interface velocity, and except for its smallest values, physical entrapment of the solute into the ice matrix during ice crystal growth is the predominant phenomenon. For practical purposes, it has been shown that the use of unidirectional progressive cryoconcentration for skim milk concentration is not efficient. Skim milk was cryoconcentrated from 8.50 ± 0.25% up to approximately 18% but the process efficiency significantly decreased as the ice thickness was increased. The highest process efficiency with an average value of 80% has been obtained up to 2 cm ice thickness. This efficiency drastically decreased after that to around of 3–4%. This decrease of the process efficiency was confirmed by the high solute entrapment into the ice matrix, a phenomenon that yielded in similar solute concentration in the liquid fraction and in the ice matrix.Industrial relevanceCryoconcentration (freeze concentration) is the best technological approach to concentrate liquid food with maintaining high quality of the concentrate. Cryoconcentration preserves the taste, aroma, color and high nutritive value of the product. Nowadays, this technique is still under used in the food industry. This is due to the serious lack of information on the mechanism and economic aspects of this technology. Several efforts have been made to improve the cryoconcentration process efficiency. The results obtained in this paper which are based on mathematical modeling followed by experimental validation showed that progressive cryoconcentration is not effective to concentrate liquid foods. The main reason is the high solute entrapment in the ice fraction. Thus, more detailed studies on other types of cryoconcentration techniques are required.