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Mathematical Modelling Approach and Simulation in Food Drying Applications

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A special issue of Foods (ISSN 2304-8158). This special issue belongs to the section "Food Engineering and Technology".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 11437

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Special Issue Editors

Dr. Biljana Loncar

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Guest Editor

Faculty of Technology, University of Novi Sad, Novi Sad, Serbia
Interests: food processing and engineering; drying; freeze drying; osmotic dehydration; chemometrics

Dr. Lato Pezo

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Guest Editor

Institute of General and Physical Chemistry Serbia, Belgrade, Serbia
Interests: mathematical modelling; numerical modelling; discrete element modelling; computational fluid dynamics; statistics in food science and technology

Special Issue Information

Dear Colleagues,

In this Special Issue, readers will find research and review articles that explain the development of empirical, semi-empirical and theoretical mathematical models for food drying; the use of computational methods (such as artificial neural and convolutional networks, random forests, support vector machines, etc.) to analyse the effects of various drying conditions and methods on food quality and safety; and the potential mathematical modelling has to improve food drying performance. The issue also reviews recent advances in the application of mathematical models to food drying, as well as future trends in the field. This Special Issue summarizes traditional and advance drying techniques used to suggest the optimal drying parameters for the selected food material. Readers will also find an overview of the current state of the field so they can gain a better understanding of its potential applications. This Special Issue is an invaluable resource for researchers and practitioners in the field of food drying. It provides researchers with the latest research and insights into the mathematical modelling approach and machine learning algorithms for food drying, enabling them to make informed decisions and develop sustainable solutions.

Dr. Biljana Loncar
Dr. Lato Pezo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Foods is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2900 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

traditional drying techniques
advance drying techniques
mathematical modeling
empirical mathematical models
semi-empirical mathematical models
theoretical mathematical models
artificial intelligence
drying parameters optimization
drying kinetics

Published Papers (9 papers)

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Editorial

Jump to: Research

7 pages, 543 KiB

Open AccessEditorial

Mathematical Modeling Approach and Simulation in Food Drying Applications

by Biljana Lončar and Lato Pezo

Foods 2024, 13(3), 384; https://doi.org/10.3390/foods13030384 - 24 Jan 2024

Viewed by 725

Abstract

Recent developments in the branch of food drying involve advancements in the development of mathematical models [...] Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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Research

Jump to: Editorial

28 pages, 6231 KiB

Open AccessArticle

Unlocking the Potential of the ANN Optimization in Sweet Potato Varieties Drying Processes

by Olja Šovljanski, Biljana Lončar, Lato Pezo, Anja Saveljić, Ana Tomić, Sara Brunet, Vladimir Filipović, Jelena Filipović, Jasna Čanadanović-Brunet, Gordana Ćetković and Vanja Travičić

Foods 2024, 13(1), 134; https://doi.org/10.3390/foods13010134 - 29 Dec 2023

Viewed by 638

Abstract

This study explores the unexploited potential of Artificial Neural Network (ANN) optimization techniques in enhancing different drying methods and their influence on the characteristics of various sweet potato varieties. Focusing on the intricate interplay between drying methods and the unique characteristics of white, pink, orange, and purple sweet potatoes, the presented experimental study indicates the impact of ANN-driven optimization on food-related characteristics such as color, phenols content, biological activities (antioxidant, antimicrobial, anti-hyperglycemic, and anti-inflammatory), chemical, and mineral contents. The results unveil significant variations in drying method efficacy across different sweet potato types, underscoring the need for tailored optimization strategies. Specifically, purple sweet potatoes emerge as robust carriers of phenolic compounds, showcasing superior antioxidant activities. Furthermore, this study reveals the optimized parameters of dried sweet potato, such as total phenols content of 1677.76 mg/100 g and anti-inflammatory activity of 8.93%, anti-hyperglycemic activity of 24.42%. The upgraded antioxidant capability is presented through DPPH^●, ABTS^●+, RP, and SoA assays with values of 1500.56, 10,083.37, 3130.81, and 22,753.97 μg TE/100 g, respectively. Additionally, the moisture content in the lyophilized sample reached a minimum of 2.97%, holding favorable chemical and mineral contents. The utilization of ANN optimization proves instrumental in interpreting complex interactions and unlocking efficiencies in sweet potato drying processes, thereby contributing valuable insights to food science and technology. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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18 pages, 3511 KiB

Open AccessArticle

Mathematical Modeling of Thin-Layer Drying Kinetics of Tomato Peels: Influence of Drying Temperature on the Energy Requirements and Extracts Quality

by Mihaela Popescu, Petrica Iancu, Valentin Plesu, Costin Sorin Bildea and Fulvia Ancuta Manolache

Foods 2023, 12(20), 3883; https://doi.org/10.3390/foods12203883 - 23 Oct 2023

Viewed by 1211

Abstract

Tomato drying implies high energy consumption due to the high moisture content, and limiting drying temperatures is necessary to avoid carotenoid degradation. To explain the mechanism of moisture transport through the material and to scale up the drying process, drying experiments are needed and supported by mathematical modeling. For the Rila tomato peel drying process, ten thin-layer mathematical models were formulated based on experimental data for six temperatures (50–75 °C) and validated by statistical analysis. Considering the slab geometry of the peels sample and Fick’s second law of diffusion model, the calculated effective moisture diffusivity coefficient values D_eff varied between 1.01 × 10⁻⁹–1.53 × 10⁻⁹ m²/s with R² higher than 0.9432. From the semi-theoretical models, Two-term presents the best prediction of moisture ratio with the highest R² and lowest χ² and RMSE values. Using the experimental data on extract quality (carotenoid content), two degradation models were formulated. Increasing the drying temperature from 50 °C to 110 °C, a degradation of 94% for lycopene and 83% for β-carotene were predicted. From the energy analysis, a specific energy consumption of 56.60 ± 0.51 kWh is necessary for hot-air drying of 1 kg of Rila tomato peel at 50 °C to avoid carotenoid degradation. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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18 pages, 1373 KiB

Open AccessArticle

Prototype of an Innovative Vacuum Dryer with an Ejector System: Comparative Drying Analysis with a Vacuum Dryer with a Vacuum Pump on Selected Fruits

by Zdravko Šumić, Aleksandra Tepić Horecki, Vladimir Kašiković, Andreja Rajković, Lato Pezo, Tatjana Daničić, Branimir Pavlić and Anita Milić

Foods 2023, 12(17), 3198; https://doi.org/10.3390/foods12173198 - 25 Aug 2023

Viewed by 1500

Abstract

The following article describes new research about the design, construction and installation of the new prototype of a vacuum dryer with an ejector system. Moreover, the testing of this new prototype involved comparing the qualities of fruit dried in a vacuum drier with an ejector system to fruit dried in a convectional vacuum drier. The data obtained were then analyzed and presented. Due to their economic relevance and highly valuable nutritional value and sensory properties, sour cherries and apricots have been chosen to be the subjects for the testing. The most appropriate quality indicators for analyzing were moisture content, a_w value, share and penetration force, total phenol, flavonoid and anthocyanin content and antioxidant activity (FRAP, DPPH and ABTS test). The main results of this study were achieved by designing, constructing, installing and testing the usage of the innovative prototype of a vacuum dryer with an ejector system in the laboratory of the Technology of fruit and vegetable products of the Faculty of Technology Novi Sad, University of Novi Sad. Based on our analyses of the obtained data, it was concluded that vacuum dryer with an ejector system are similar to vacuum dryer with a vacuum pump in terms of all tested physical, chemical and biological properties of dried samples. We observed similarities in some of the most important parameters, including product safety and quality, such as the a_w value and the total phenol content, respectively. For example, in dried sour cherry, the a_w values ranged from 0.250 to 0.521 with the vacuum pump and from 0.232 to 0.417 with the ejector system; the total phenol content ranged from 2322 to 2765 mg GAE/100 g DW with the vacuum pump and from 2327 to 2617 mg GAE/100 g DW with the ejector system. In dried apricot, the a_w ranged from 0.176 to 0.405 with the vacuum pump and from 0.166 to 0.313 with the ejector system; total phenol content ranged from 392 to 439 mg GAE/100 g DW with the vacuum pump and from 378 to 428 mg GAE/100 g DW with the ejector system. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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22 pages, 6155 KiB

Open AccessArticle

Evaluating Kinetics of Convection Drying and Microstructure Characteristics of Asian Seabass Fish Skin without and with Ultrasound Pretreatment

by Mohammad Fikry, Soottawat Benjakul, Saleh Al-Ghamdi, Mohamed Tagrida and Thummanoon Prodpran

Foods 2023, 12(16), 3024; https://doi.org/10.3390/foods12163024 - 11 Aug 2023

Cited by 3 | Viewed by 1164

Abstract

Convection drying in combination with ultrasound pretreatment has emerged as a promising technology for seafood manufacturing. The primary objective of this research was to model the mass transfer process of Asian seabass (Lates calcarifer) fish skin without and with ultrasound pretreatment during convection drying at different temperatures (45, 55, and 65 °C). Additionally, the study aimed to examine the impact of ultrasound pretreatment and temperatures on the drying characteristics and specific energy consumption for drying of Asian seabass fish skin. Seven semi-theoretical models, namely Lewis, Page, modified Page, Vega-Lemus, Verma, Henderson and Pabis, and two-term models, were employed to characterize the moisture transfer process. The results of the study indicated a decrease in the moisture content as the drying time increased at different drying temperatures. Higher drying temperatures were associated with an increased drying rate. Among the mathematical models tested, the modified Page model provided a satisfactory description of the thin-layer drying characteristics of fish skin. Fick’s law of diffusion was utilized to determine the effective moisture diffusivities. Comparing the drying of fish skin without (SS) and with ultrasound pretreatment (US-SS), the drying of the latter generally showed higher D_eff values. The temperature dependence of the effective diffusivity coefficient was well described by the Arrhenius-type model. An increase in the drying temperature resulted in an increment of the effective moisture diffusivity. In general, the skin pretreated using ultrasound had a reduced drying time, by up to 28%. Additionally, this approach contributed to an approximate 22% reduction in the specific energy consumption, concurrently enhancing the energy efficiency. The microstructure analysis showed that fresh and dried US-SS samples had a more open structure and higher porosity, in comparison to the corresponding SS samples. These findings contribute to the knowledge on the application of ultrasound as the pretreatment of fish skin before drying and provide valuable insights for the development of potential drying techniques in the seafood industry. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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14 pages, 1024 KiB

Open AccessArticle

Thermal Characterisation and Isoconversional Kinetic Analysis of Osmotically Dried Pork Meat Proteins Longissimus dorsi

by Sanja Ostojić, Darko Micić, Snežana Zlatanović, Biljana Lončar, Vladimir Filipović and Lato Pezo

Foods 2023, 12(15), 2867; https://doi.org/10.3390/foods12152867 - 27 Jul 2023

Viewed by 810

Abstract

The kinetic properties and thermal characteristics of fresh pork meat proteins (Longissimus dorsi), as well as osmotically dehydrated meat proteins, were investigated using differential scanning calorimetry. Two isoconversional kinetical methods, namely the differential Friedman and integral Ortega methods, were employed to analyze the data. The obtained kinetic triplet, activation energy, pre-exponential factor, and extent of conversion, has been discussed. The resulting activation energy for proteins of fresh meat ranges between 751 kJ·mol⁻¹ for myosin, 152 kJ·mol⁻¹ for collagen and sarcoplasmic proteins, and 331 kJ·mol⁻¹ for actin at a conversion degree of 0.1 to 0.9. For osmotically dried pork meat proteins, the values range from 307 kJ·mol⁻¹ for myosin 272 kJ·mol⁻¹ for collagen and sarcoplasmic proteins, and 334.83 kJ·mol⁻¹ for actin at a conversion degree from 0.1 to 0.9. The proteins of the dry meat obtained by osmotic dehydration in molasses could be described as partly unfolded as they retain the characteristic protein denaturation transition. Concerning the decrease in enthalpies of proteins denaturation, thermodynamic destabilization of dried meat proteins occurred. On the contrary, dried meat proteins were thermally stabilized with respect to increase in the temperatures of denaturation. Knowledge of the nature of meat protein denaturation of each kind of meat product is one of the necessary tools for developing the technology of meat product processing and to achieve desired quality and nutritional value. The kinetic analysis of meat protein denaturation is appropriate because protein denaturation gives rise to changes in meat texture during processing and directly affects the quality of product. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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19 pages, 3004 KiB

Open AccessArticle

Effect of Temperatures on Drying Kinetics, Extraction Yield, Phenolics, Flavonoids, and Antioxidant Activity of Phaleria macrocarpa (Scheff.) Boerl. (Mahkota Dewa) Fruits

by Fatin Nurain Stephenus, Mohammad Amil Zulhilmi Benjamin, Adilah Anuar and Mohd Azrie Awang

Foods 2023, 12(15), 2859; https://doi.org/10.3390/foods12152859 - 27 Jul 2023

Cited by 5 | Viewed by 1617

Abstract

Phaleria macrocarpa (Scheff.) Boerl. or ‘Mahkota Dewa’ is a popular plant found in Malaysia as it is a valuable source of phytochemicals and therapeutic properties. Drying is an essential step in the storage of P. macrocarpa fruits at an industrial level to ensure their availability for a prolonged shelf life as well as preserving their bioactive compounds. Hence, this study evaluates the effect of different temperatures on the drying kinetics, extraction yield, phenolics, flavonoids, and antioxidant activity of P. macrocarpa fruits. The oven-drying process was carried out in this study at temperatures of 40 °C, 50 °C, 60 °C, 70 °C, and 80 °C. Six thin-layer drying models (i.e., Lewis, Page, Henderson and Pabis, two-term exponential, Logarithmic, and Midilli and Kucuk models) were evaluated to study the behaviour of oven-dried P. macrocarpa fruits based on the coefficient of determination (

R^{2}

), root mean square error (

R M S E

), and chi-square (

χ^{2}

). The quality of the oven-dried P. macrocarpa fruits was determined based on their extraction yield, total phenolic content (TPC), total flavonoid content (TFC), and antioxidant activity (2,2-diphenyl-1-picrylhydrazyl) using ultrasound-assisted extraction. The results showed that the time for moisture removal correspondingly increased in the oven-dried P. macrocarpa fruits. Apparently, the Midilli and Kucuk model is the most appropriate model to describe the drying process. The range of effective moisture diffusivity was 1.22 ×

10^{- 8}

to 4.86 ×

10^{- 8}

m^{2} / s

, and the activation energy was 32.33 kJ/mol. The oven-dried P. macrocarpa fruits resulted in the highest extraction yield (33.99 ± 0.05%), TPC (55.39 ± 0.03 mg GAE/g), TFC (15.47 ± 0.00 mg RE/g), and DPPH inhibition activity (84.49 ± 0.02%) at 60 °C based on the significant difference (p < 0.05). A strong correlation was seen between the antioxidant activity, TPC, and TFC in the oven-dried P. macrocarpa fruits. The current study suggests that the oven-drying method improved the TPC, TFC, and antioxidant activity of the P. macrocarpa fruits, which can be used to produce functional ingredients in foods and nutraceuticals. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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16 pages, 7474 KiB

Open AccessEditor’s ChoiceArticle

Application of Central Composite Design and Superimposition Approach for Optimization of Drying Parameters of Pretreated Cassava Flour

by Ellyas Alga Nainggolan, Jan Banout and Klara Urbanova

Foods 2023, 12(11), 2101; https://doi.org/10.3390/foods12112101 - 23 May 2023

Cited by 4 | Viewed by 1800

Abstract

The primary goals of this study were to identify the influence of temperature and drying time on pretreated cassava flour, as well as the optimal settings for the factors and to analyze the microstructure of cassava flour. The experiment was designed using the response surface methodology with central composite design and the superimposition approach in order to assess the effect of drying temperature (45.85–74.14 °C) and drying time (3.96–11.03 h) and the optimal drying conditions of the cassava flour investigated. Soaking and blanching were applied as pretreatments to freshly sliced cassava tubers. The value moisture content of cassava flour was between 6.22% and 11.07%, whereas the observed whiteness index in cassava flour ranged from 72.62 to 92.67 in all pretreated cassava flour samples. Through analysis of variance, each drying factor, their interaction, and all squared terms had a substantial impact on moisture content and whiteness index. The optimized values for drying temperature and drying time for each pretreated cassava flour were 70 °C and 10 h, respectively. The microstructure showed a non-gelatinized, relatively homogeneous in size and shape sample with pretreatment soaked in distilled water at room temperature. These study results are relevant to the development of more sustainable cassava flour production. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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15 pages, 2451 KiB

Open AccessArticle

A Comparative Analysis of Thin-Layer Microwave and Microwave/Convective Dehydration of Chokeberry

by Marko Petković, Vladimir Filipović, Biljana Lončar, Jelena Filipović, Nemanja Miletić, Zoranka Malešević and Darko Jevremović

Foods 2023, 12(8), 1651; https://doi.org/10.3390/foods12081651 - 15 Apr 2023

Cited by 2 | Viewed by 970

Abstract

Due to high water content, chokeberries (Aronia melanocarpa L.) are perishable. Therefore, energy-saving, combined drying technologies have been explored to improve the chokeberry drying. The combined microwave and the traditional convective drying method (MCD) have significantly enhanced the drying effectiveness, efficiency, and energy utilization rate and improved product quality. The MCD method, which implies the microwave power (MD) of 900 W for 9 s and the convective dehydration (CD) at 230 °C for 12 s, has the shortest dehydration time t (24 ± 2 min), has the maximum coefficient of diffusion (D_eff = 6.0768 × 10⁻⁹ ± 5.9815 × 10⁻¹¹ m² s⁻¹), and represents the most energy effective for dehydration process (E_min = 0.382 ± 0.036 kWh). A higher water-holding capacity (WHC) characterized the chokeberries obtained by the MCD method compared to the regular microwave method (MD). The mildest MCD (15 s of MD on 900 W, 7 s of CD on 180 °C) could dehydrate chokeberries with the highest WHC (685.71 ± 40.86 g H₂O g⁻¹ d.m.) and the greatest evaluations for sensory attributes in terms of all properties. The results of this study provide the drying behavior of chokeberries that can help develop efficient drying methods and improve existing ones. Full article

(This article belongs to the Special Issue Mathematical Modelling Approach and Simulation in Food Drying Applications)

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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Mathematical approach in determining optimal quality parameters for wild garlic biscuits.

Mathematical modelling of almond and hazelnut drying

A comparative analysis of thin-layer microwave and microwave/convective dehydration of chokeberry

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