Extracting barberry juice: Mathematical models describing loading stage, stress‐relaxation behavior, and momentary juice mass

Abstract

AbstractIn the present study, barberries were poured into a topless cylinder with a diameter of 55 mm and were subjected to axial compression force up to 440 kg (4,314.926 N). Effects of duration of water exposure, loading rate, and number of layers were investigated on momentary juice mass, Stress–strain behavior, and stress‐relaxation behavior. Considering momentary porosity, the momentary juice mass, stress–strain, and stress‐relaxation behaviors of the berries were modeled by inverse tangent function, exponential function, and One‐term Maxwell model, respectively. The extraction yield of juice (EYJ), specific absorbed energy by berries (SAEB), and efficiency index of energy (EIE) were calculated, and their analysis of variance and optimization were performed. The results showed that the R2 of the exponential model for the Stress–Strain diagram, Maxwell model for relaxation behavior, and inverse tangent model for momentary juice mass variation were more than 0.975, 0.985, and 0.995, respectively. The effects of the three operating parameters on the stiffness factor of springs and damping factor of dashpot were significant at 5%. Furthermore, the effects of the three input variables on the juice point force, juice point energy, EYJ, SAEB, and EIE were significant at 1%.Practical ApplicationsThe first step in producing barberry products in accordance with international food standards is barberry juice extraction. In the current study, the axial pressure method, one of the conventional barberry juicing methods, was investigated. This method has more ability to control the quality of juice than other methods. Traditionally, fruits are soaked in water for several hours before barberry juicing. Also, in the loading stage, rigid plates are placed between the fruit layers. Duration of water exposure, loading rate, and the number of layers are the three major influential factors in the juicing process. The information obtained from this article can help optimize the barberry juicing process using existing axial pressure devices. Besides, the results can be used in the optimal design of the barberry‐juicing device.