Numerical simulation of ice crystal growth of liquid food freeze concentration based on phase-field method

Abstract: The quality of products produced through freeze concentration is better than that produced through evaporation concentration and has lower energy consumed. But freeze concentration has been limited for industrial production because of the loss of soluble solids caused by ice crystal entrainment. Reducing the ice crystal entrainment and losses is critical for industrial production of freeze concentration. The breakthrough is to control ice crystal growth behavior. In order to develop a freeze concentration process mathematical model for simulating the evolution of ice crystal growth from the microscopic structure, through regarding liquid food as water and solute in binary system, the phase-field model theory was applied, liquid food system was treated as water and solute in binary system. The effects of ice crystal growth and solute concentration distribution over crystallized time were studied. Results showed that the crystallized time could affect the growth of lateral branch. Ice crystal growed gradually when the main branch become thinner and the secondary dendritic arms were well-developed. Solute field and phase field profiles were consistent. The solute concentration of ice crystals contained was greater, and the regional solute concentration distribution also changed. The precipitatied solute by crystallization was not completely dissoluted into the liquid phase since the solute diffusion velocity was much less than the ice crystal growth rate. The solute concentrated on the ice front of solid liquid interface. The solute concentration distribution was different in different parts of the solid-liquid interface. The solute concentration between crystal branches was the highest since the well-developed lateral dendritic branch captured the partion of the solute. The solute of lateral interface of ice crystals was enriched. The speed in the lateral ice crystals was slower than in the tip of ice crystals, which caused not sufficiently diffusion of the solute in lateral crystals. The solute concentration of ice crystals on cutting-edge solid-liquid interface showed the peaks and troughs by the solute redistribution. The solute concentration peak was formed because the growth rate of ice crystal tips was quickly enough to fully diffuse the solute. The trough corresponded to the ice crystal's solid phase. The simulation results were consistent with the experiment observation. The entrainment rate of ice crystals increased when the freeze concentrated time reached at a certain time. The entrainment rate of ice crystal could be reduced with properly controlling the crystallized time during freeze concentration process. In this study, we ignored the latent heat released and used an isothermal simulation. The simulation system was treated as dual components with water and solute. The influencing factors such as cooling rate, convection, super-cooling degree need to be further investigated. The non-isothermal algorithm and multiple structure of liquid food also need to be considered in the future research.