A poroelastic model for wave propagation in partially frozen orange juice

We use a poroelastic model to describe the propagation of ultrasonic waves through orange juice, which is subjected to a freezing process. The theoretical results are compared with those obtained by ultrasound methods used to monitor the freezing of orange juice. The ultrasonic properties of partially frozen orange juice, specifically, are characterized by the P-wave and S-wave velocities and their respective attenuation coefficients, which are related to the amount of water in the juice in the liquid state. Kelvin’s model is used to obtain the amount of unfrozen water in the juice as a function of temperature, and the Biot’s poroelastic theory provides the ultrasonic properties of orange juice as a function of temperature, below the eutectic point. A model similar to the Kelvin’s model is used in the food literature to describe the crystallization of ice as a function of temperature. In concurrence with the Kelvin’s model describing the formation of ice crystals, the frame moduli of the ice-crystal matrix are obtained by a percolation model of ice formation. The model shows a good agreement with the experimental data, regarding the wave velocities, and a qualitative agreement with the experimental attenuation values. A critical temperature, at nearly 50% saturation, is related to the maximum attenuation of the fast P-wave, and maximum velocity and minimum attenuation of the slow P-wave.