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

Abstract

In 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 Applications The 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.

Physico‐mechanical properties of unripe grape berries relevant in the design of juicing machine

“…So, if skewness divided into 0.4269 was between −2 and +2, the population data would be neither positively nor negatively skewed. If kurtosis divided into 0.8328 was between −2 and +2, the population data would be neither positively nor negatively kurtosis (Mirzabe et al, 2021a; 2021b).…”

“…So, the basket press method was used to study the mechanical behavior of compression loading and stress‐relaxation of the bulk unripe grape berries. Loading rate, the diameter of baskets, and the height of pressurized materials are the most critical factors influencing the performance and efficiency of this method (Mirzabe et al, 2021a). Also, placing rigid plates between the bulk materials and creating different layers of materials can increase the amount of juice extracted.…”

“…Unripe grape berries were placed in the refrigerator (4°C and relative humidity of 80%) during the 31 days. Based on the standard hot air oven method (105 ± 1°C for 24 hr), the moisture content of the berries was measured (Mirzabe et al, 2021a; 2021b).…”

“…The Based on the standard hot air oven method (105 ± 1 C for 24 hr), the moisture content of the berries was measured (Mirzabe et al, 2021a;2021b).…”

“…Another application of image processing method in the agricultural and food industry is in the field of physical and mechanical properties of agricultural products. Although the application of image processing method in the field of physical and mechanical properties of agricultural products was more related to the determination of the dimensions and projected area (Mansouri, Mirzabe, & Ráufi, 2017; Mirzabe, Chegini, & Khazaei, 2018), there are reports of determining the angle of friction (Taheri, Mirzabe, Mansouri, & Aliakbari, 2015), angle of repose (Taheri et al, 2015), determining the terminal velocity (Mirzabe, Hajiahmad, & Asadollahzadeh, 2021a; 2021b). Also, although not found in the field of physical properties of agricultural products, in other engineering sciences, the application of image processing technique to determine the Poisson's ratio is prevailing (Farfán‐Cabrera, Pascual‐Francisco, Barragán‐Pérez, Gallardo‐Hernández, & Susarrey‐Huerta, 2017; Hursa, Rolich, & Ražić, 2009; Razbin, Jeddi, Semnani, & Ramzanpoor, 2020; Righetti, Srinivasan, Kumar, Ophir, & Krouskop, 2007).…”