Modeling and Predicting the Drying Kinetics of Apple and Pear: Application of the Weibull Model

Ripening induced degradation of pectin and cellulose affects the medium-and short-wave infrared drying characteristics of mulberry

Mulberries were categorized into five stages of ripening (D1-D5, 0.905-1.055 g/cm3) based on their density, and their physicochemical properties, tissue structure, cell wall polysaccharide properties, and drying characteristics were investigated. As mulberry ripening progressed, the TSS and water-soluble pectin content rapidly increased, while the contents of TA, hardness, chelate-, sodium carbonate-soluble pectin, hemicellulose, and cellulose decreased gradually. Pectin nanostructure and monosaccharide composition indicated that both the main and side chains of pectin undergo depolymerization. Medium- and short-wave infrared drying time initially decreased and then increased during mulberry ripening, with D4 fruits exhibiting the shortest drying time. Compared with D4 fruits, the collapse of cell structure in D5 fruits prolongs their drying time. The results demonstrate that ripeness significantly affects mulberry drying characteristics, which is related to changes in cell structure and pectin properties. Utilizing mulberry density to determine ripeness and grading is an effective approach to achieving optimal drying.

Effective drying processes for Taikor (Garcinia pedunculata Roxb.) fruit by ultrasound-assisted osmotic pretreatment: Analysis of quality and kinetic models

The present study aimed to analyze and establish an effective combination of ultrasound and immersion pretreatment processes for drying Taikor (Garcinia pendunculata Roxb.) fruits. Taikorslices were first immersed in 10 % sucrose, fructose, and glucose solution. Then, the immersed slices were treated in an ultrasonic bath at 30 °C for 10, 20, and 30 min. Drying operations were carried out at 50, 60, and 70 °C, with a fixed relative humidity of 30 %. The Page, Newton, Henderson and Pabis, and Weibull distribution models were fitted to the obtained drying data to determine the best kinetic model that effectively describes the drying properties ofTaikor. After drying operations, changes in quality parameters, e.g., β-carotene, vitamin C, B vitamins, color, antioxidant activities, and microbial loads, were measured to obtain the best drying temperature and the most effective pretreatment combination with minimum loss of nutrients of the sample. Among different kinetic models, both Page and Weibull distribution models showed the best R2 values of 0.9867 and 0.9366, respectively. The chemical properties were preserved to the greatest extent possible by drying at 50 °C with glucose pretreatment. The color parameters were better preserved by fructose pretreatment. Sonication time also had profound effect on the quality parameters of dried Taikor slices. However, higher temperature drying required a shorter time for drying and exhibited better performance in microbial load reduction. This study's findings will help to establish an effective drying condition forGarcinia pedunculatafruits.

Drying of Chinese medicine residues (CMR) by hot air for potential utilization as renewable fuels: drying behaviors, effective moisture diffusivity, and pollutant emissions

High moisture in Chinese medicine residues (CMR) can decrease the energy efficiency of thermochemical conversion, which necessitates the pre-drying. Owing to the complex constituents and decoction, CMR may possess distinct drying characteristics. It is necessary to understand its drying behaviors, effective moisture diffusivity, and pollutant emissions for future design and optimization of an industrial-level dryer. In this study, the drying of four types of typical CMR in hot nitrogen was performed. Their condensate and exhaust gas were collected and characterized. The results indicated that their drying process was dominated by internal moisture transport mechanism with a long falling rate stage. Drying temperature influenced their drying process more greatly than N2 velocity did. Residual sum of squares, root mean square error, and coefficient of determination indicated that Weibull model demonstrated their drying process best. Their effective moisture diffusivity was in the range of 1.224 × 10-8 to 4.868 × 10-8 m2/s, while their drying activation energy ranged from 16.93 to 30.39 kJ/mol. The acidic condensate had high chemical oxygen demand and total nitrogen concentration and yet low total phosphorus concentration. The concentration of total volatile organic compounds, non-methane hydrocarbons, H2S, and NH3 in the exhaust gas met the national emission limitation, while the deodorization of exhaust gas was required to remove odor smell.

Supplementary information

The online version contains supplementary material available at 10.1007/s13399-022-03722-4.

Reparameterization of the Weibull model for practical uses in food science

The reparameterization of the Weibull cumulative distribution function and its survival function was performed to obtain meaningful parameters in food and biological sciences such as the lag phase (λ), the maximum rate ( μ max ${\mu _{{\rm{max}}}}$ ), and the maximum increase/decrease of the function (A). The application of the Lambert function was crucial in order to achieve an explicit mathematical solution. Since the reparameterized model is applicable only when the shape parameter (α) is greater than one, the Weibull model was modified with the introduction of a new parameter ( μ β ${\mu _\beta }$ ) that represents the model rate at time β (scale parameter). All models were applied to literature data on food technology and microbiology topics: Microbial growth, thermal microbial inactivation, thermal degradation kinetics, and particle size distributions. The Weibull model and the reparameterized versions showed identical fitting performance in terms of coefficient of determination, residual mean standard error, values of residuals, and estimated values of the parameters. Some faults in the datasets used in this study permitted to re-mark the criticality of a good experimental plan when data modeling is approached. The parameter μ β ${\mu _\beta }$ resulted in an interesting new rate parameter that is not correlated with the scale parameter ( | r ¯ | $| {\bar{r}} |$ = 0.64 ± 0.37) and highly correlated with the shape parameter ( | r ¯ | $| {\bar{r}} |$ = 0.90 ± 0.11). Also, the reparameterization of the Weibull probability density function was performed by using both the standard and new parameters and applied to experimental data and gave useful information from the distribution curve, such as the value of the mode ( μ max ${\mu _{{\rm{max}}}}$ ) and a measure of the curve skewness (λ).

Reassessment of Thin-Layer Drying Models for Foods: A Critical Short Communication

Modeling the thin-layer drying of foods is based on describing the moisture ratio versus time data by using a suitable mathematical model or models. Several models were proposed for this purpose and almost all studies were related to the application of these models to the data, a comparison and selecting the best-fitted model. A careful inspection of the existing drying data in literature revealed that there are only a limited number of curves and, therefore, the use of some models, especially the complex ones and the ones that require a transformation of the data, should be avoided. These were listed based on evidence with the use of both synthetic and published drying data. Moreover, the use of some models were encouraged, again based on evidence. Eventually, some suggestions were given to the researchers who plan to use mathematical models for their drying studies. These will help to reduce the time of the analyses and will also avoid the arbitrary usage of the models.

A novel ultrasound-assisted vacuum drying technique for improving drying efficiency and physicochemical properties of Schisandra chinensis extract powder

Schisandra chinensis (S. chinensis) extract powder is an important intermediate for the preparation of many prepared medicines and health products. The physicochemical properties of S. chinensis extract powder have been found to vary tremendously and this has been attributed to the long drying time in the traditional drying method. In this study, S. chinensis specimens were authenticated as the dry fruit of S. chinensis (Turcz.) Baill. S. chinensis were extracted twice with 8 L kg-1 (liquid to solid ratio) distilled water. The extracts were mixed and concentrated under reduced pressure to 1.24 g cm-3. Ultrasound-assisted vacuum drying (UAVD) was employed as a new approach to improve the efficiency in drying S. chinensis extract powder and produce a higher quality product. The effects of drying temperature (70, 80, 90°C), ultrasonic power (40, 120, 200 W), and ultrasonic application time (4, 12, 20 min every 20 min) on the kinetics and quality of S. chinensis extract were investigated and compared with the conventional vacuum drying (CVD). It was shown that, with the increase in drying temperature, ultrasonic power, and time of UAVD, the drying time for S. chinensis extract to reach the equilibrium moisture decreased. The drying time was reduced by more than 25% when utilizing UAVD compared to the CVD method. The effective moisture diffusivity (D eff) values for CVD and UAVD were 3.48 × 10-9 m2·s-1 and 7.41 × 10-9 m2 s-1, respectively, at the drying temperature of 80°C, indicating an increase of 112.93%. It was also found that a Weibull distribution model was suitable for predicting the moisture content of S. chinensis extract (R 2 > 0.95). Furthermore, the content of Schisandrol A in the extracts obtained from UAVD was 12.79% higher than that obtained using CVD at 90°C. This demonstrates that UAVD is an efficient drying technique for S. chinensis extract.