Microscale modeling of coupled water transport and mechanical deformation of fruit tissue during dehydration

Numerical simulation and microtomography study for drying a deformable isodiametric-cellular food

The aim of this work is the simulation of volumetric strain of tuberous crop during drying. We propose a poroelastic model for predicting the drying kinetics and volume loss of potato cubes during convective drying. The Biot’s theory of poroelasticity was used, which considers the Lamé parameters, Young’s modulus and Poisson’s ratio. Drying kinetics and volumetric strain were modeled and compared versus experimental data. An X-ray microtomograph coupled with image analysis was used to visualize the shape and size of the samples during drying. Drying experiments were conducted at 50, 60 and 70 °C, 20% RH, with an air velocity of 1 and 2 m/s. The drying process was interrupted several times to perform tomographic acquisitions. We found a period of ideal shrinkage, nevertheless, the volumetric strain reveals a kinetic behavior over time. The model computes the volumetric strain, which describes correctly the experimental data obtained by microtomography.

Modelling Volume Change and Deformation in Food Products/Processes: An Overview

Volume change and large deformation occur in different solid and semi-solid foods during processing, e.g., shrinkage of fruits and vegetables during drying and of meat during cooking, swelling of grains during hydration, and expansion of dough during baking and of snacks during extrusion and puffing. In addition, food is broken down during oral processing. Such phenomena are the result of complex and dynamic relationships between composition and structure of foods, and driving forces established by processes and operating conditions. In particular, water plays a key role as plasticizer, strongly influencing the state of amorphous materials via the glass transition and, thus, their mechanical properties. Therefore, it is important to improve the understanding about these complex phenomena and to develop useful prediction tools. For this aim, different modelling approaches have been applied in the food engineering field. The objective of this article is to provide a general (non-systematic) review of recent (2005-2021) and relevant works regarding the modelling and simulation of volume change and large deformation in various food products/processes. Empirical- and physics-based models are considered, as well as different driving forces for deformation, in order to identify common bottlenecks and challenges in food engineering applications.

A three-dimensional (3-D) meshfree-based computational model to investigate stress-strain-time relationships of plant cells during drying

A better understanding of plant cell micromechanics would enhance the current opinion on “how things are happening” inside a plant cell, enabling more detailed insights into plant physiology as well as processing plant biomaterials. However, with the contemporary laboratory equipment, the experimental investigation of cell micromechanics has been a challenging task due to diminutive spatial and time scales involved. In this investigation, a three-dimensional (3-D) coupled Smoothed Particle Hydrodynamics (SPH) and Coarse-Grained (CG) computational approach has been employed to model micromechanics of single plant cells going through drying or dehydration. This meshfree-based computational model has conclusively demonstrated that it can effectively simulate the behaviour of stress and strain in a plant cell being compressed at different levels of dryness: ranging from a fresh state to an extremely dried state. In addition, different biological and physical circumstances have been approximated through the proposed novel computational framework in the form of different turgor pressures, strain rates, mechanical properties and cell sizes. The proposed computational framework has potential not only to study the micromechanical characteristics of plant cellular structure during drying, but also other equivalent, biological structures and processes with relevant modifications. There are no underlying difficulties in adopting the model to replicate other types of cells and more sophisticated micromechanical phenomena of the cells under different external loading conditions.

In silico study of the role of cell growth factors in photosynthesis using a virtual leaf tissue generator coupled to a microscale photosynthesis gas exchange model

Computational tools that allow in silico analysis of the role of cell growth and division on photosynthesis are scarce. We present a freely available tool that combines a virtual leaf tissue generator and a two-dimensional microscale model of gas transport during C3 photosynthesis. A total of 270 mesophyll geometries were generated with varying degrees of growth anisotropy, growth extent, and extent of schizogenous airspace formation in the palisade mesophyll. The anatomical properties of the virtual leaf tissue and microscopic cross-sections of actual leaf tissue of tomato (Solanum lycopersicum L.) were statistically compared. Model equations for transport of CO2 in the liquid phase of the leaf tissue were discretized over the geometries. The virtual leaf tissue generator produced a leaf anatomy of tomato that was statistically similar to real tomato leaf tissue. The response of photosynthesis to intercellular CO2 predicted by a model that used the virtual leaf tissue geometry compared well with measured values. The results indicate that the light-saturated rate of photosynthesis was influenced by interactive effects of extent and directionality of cell growth and degree of airspace formation through the exposed surface of mesophyll per leaf area. The tool could be used further in investigations of improving photosynthesis and gas exchange in relation to cell growth and leaf anatomy.

A coarse-grained multiscale model to simulate morphological changes of food-plant tissues undergoing drying

Numerical modelling has emerged as a powerful and effective tool to study various dynamic behaviours of biological matter. Such numerical modelling tools have contributed to the optimisations of food drying parameters leading to higher quality end-products in the field of food engineering. In this context, one of the most recent developments is the meshfree-based numerical models, which have demonstrated enhanced capabilities to model cellular deformations during drying, providing many benefits compared to conventional grid-based modelling approaches. However, the potential extension of this method for simulating bulk level tissues has been a challenge due to the increased requirement for higher computational time and resources. As a solution for this, by incorporating meshfree features, a novel coarse-grained multiscale numerical model is proposed in this work to predict bulk level (macroscale) deformations of food-plant tissues during drying. Accordingly, realistic simulation of morphological changes of apple tissues can now be performed with just 2% of the previous computational time in microscale and macroscale simulations can also be conducted. Compared to contemporary multiscale models, this modelling approach provides more convenient computational implementation as well. Thus, this novel approach can be recommended for efficiently and accurately simulating morphological changes of cellular materials undergoing drying processes, while confirming its potential future expansion to efficiently and accurately predict morphological changes of heterogeneous plant tissues in different spatial scales.

Modeling of Osmotic Dehydration of Apples in Sugar Alcohols and Dihydroxyacetone (DHA) Solutions

The purpose of this paper is twofold: on the one hand, we verify effectiveness of alternatives solutes to sucrose solution as osmotic agents, while on the other hand we intend to analyze modeling transfer parameters, using different models. There has also been proposed a new mass transfer parameter-true water loss, which includes actual solid gain during the process. Additional consideration of a new ratio (Cichowska et al. Ratio) can be useful for better interpretation of osmotic dehydration (OD) in terms of practical applications. Apples v. Elise were dipped into 30% concentrated solutions of erythritol, xylitol, maltitol, and dihydroxyacetone (DHA) to remove some water from the tissue. To evaluate the efficiency of these solutes, 50% concentrated sucrose solution was used as a control. All of the tested osmotic agent, except maltitol, were effective in the process as evidenced by high values in the true water loss parameter. Solutions of erythritol and xylitol in 30% concentrate could be an alternative to sucrose in the process of osmotic dehydration. Peleg's, Kelvin⁻Voigt, and Burgers models could fit well with the experimental data. modeling of mass transfer parameters, using Peleg's model can be satisfactorily supplemented by Kelvin⁻Voigt and Burgers model for better prediction of OD within the particular periods of the process.

Impact of drying methods on the changes of fruit microstructure unveiled by X-ray micro-computed tomography

Distinct evolution of fruit microstructure under different drying conditions were identified using a 3D imaging and Eulerian–Lagrangian analysis.

Multiscale Modeling for Food Drying: State of the Art

Plant-based food materials are mostly porous in nature and heterogeneous in structure with huge diversity in cellular orientation. Different cellular environments of plant-based food materials, such as intercellular, intracellular, and cell wall environments, hold different proportions of water with different characteristics. Due to this structural heterogeneity, it is very difficult to understand the drying process and associated morphological changes during drying. Transport processes and morphological changes that take place during drying are mainly governed by the characteristics of and the changes in the cells. Therefore, to predict the actual heat and mass transfer process that occurs in the drying process and associated morphological changes, development of multiscale modeling is crucial. Multiscale modeling is a powerful approach with the ability to incorporate this cellular structural heterogeneity with microscale heat and mass transfer during drying. However, due to the huge complexity involved in developing such a model for plant-based food materials, the studies regarding this issue are very limited. Therefore, we aim in this article to develop a critical conceptual understanding of multiscale modeling frameworks for heterogeneous food materials through an extensive literature review. We present a critical review on the multiscale model formulation and solution techniques with their spatial and temporal coupling options. Food structure, scale definition, and the current status of multiscale modeling are also presented, along with other key factors that are critical to understanding and developing an accurate multiscale framework. We conclude by presenting the main challenges for developing an accurate multiscale modeling framework for food drying.

Application of a coupled smoothed particle hydrodynamics (SPH) and coarse-grained (CG) numerical modelling approach to study three-dimensional (3-D) deformations of single cells of different food-plant materials during drying

Numerical modelling has gained popularity in many science and engineering streams due to the economic feasibility and advanced analytical features compared to conventional experimental and theoretical models. Food drying is one of the areas where numerical modelling is increasingly applied to improve drying process performance and product quality. This investigation applies a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) and Coarse-Grained (CG) numerical approach to predict the morphological changes of different categories of food-plant cells such as apple, grape, potato and carrot during drying. To validate the model predictions, experimental findings from in-house experimental procedures (for apple) and sources of literature (for grape, potato and carrot) have been utilised. The subsequent comaprison indicate that the model predictions demonstrate a reasonable agreement with the experimental findings, both qualitatively and quantitatively. In this numerical model, a higher computational accuracy has been maintained by limiting the consistency error below 1% for all four cell types. The proposed meshfree-based approach is well-equipped to predict the morphological changes of plant cellular structure over a wide range of moisture contents (10% to 100% dry basis). Compared to the previous 2-D meshfree-based models developed for plant cell drying, the proposed model can draw more useful insights on the morphological behaviour due to the 3-D nature of the model. In addition, the proposed computational modelling approach has a high potential to be used as a comprehensive tool in many other tissue morphology related investigations.

Contrast-enhanced 3D micro-CT of plant tissues using different impregnation techniques

BACKGROUND

X-ray micro-CT has increasingly been used for 3D imaging of plant structures. At the micrometer resolution however, limitations in X-ray contrast often lead to datasets with poor qualitative and quantitative measures, especially within dense cell clusters of plant tissue specimens. The current study developed protocols for delivering a cesium based contrast enhancing solution to varying plant tissue specimens for the purpose of improving 3D tissue structure characterization within plant specimens, accompanied by new image processing workflows to extract the additional data generated by the contrast enhanced scans.

RESULTS

Following passive delivery of a 10% cesium iodide contrast solution, significant increases of 85.4 and 38.0% in analyzable cell volumes were observed in pear fruit hypanthium and tomato fruit outer mesocarp samples. A significant increase of 139.6% in the number of analyzable cells was observed in the pear fruit samples along the added ability to locate and isolate better brachysclereids and vasculature in the sample volume. Furthermore, contrast enhancement resulted in significant improvement in the definition of collenchyma and parenchyma in the petiolule of tomato leaflets, from which both qualitative and quantitative data can be extracted with respect to cell measures. However, contrast enhancement was not achieved in leaf vasculature and mesophyll tissue due to fundamental limitations. Active contrast delivery to apple fruit hypanthium samples did yield a small but insignificant increase in analyzable volume and cells, but data on vasculature can now be extracted better in correspondence to the pear hypanthium samples. Contrast delivery thus improved visualization and analysis the most in dense tissue types.

CONCLUSIONS

The cesium based contrast enhancing protocols and workflows can be utilized to obtain detailed 3D data on the internal microstructure of plant samples, and can be adapted to additional samples of interest with minimal effort. The resulting datasets can therefore be utilized for more accurate downstream studies that requires 3D data.

Multi-scale model of food drying: Current status and challenges

For a long time, food engineers have been trying to describe the physical phenomena that occur during food processing especially drying. Physics-based theoretical modeling is an important tool for the food engineers to reduce the hurdles of experimentation. Drying of food is a multi-physics phenomenon such as coupled heat and mass transfer. Moreover, food structure is multi-scale in nature, and the microstructural features play a great role in the food processing specially in drying. Previously simple macroscopic model was used to describe the drying phenomena which can give a little description about the smaller scale. The multiscale modeling technique can handle all the phenomena that occur during drying. In this special kind of modeling approach, the single scale models from bigger to smaller scales are interconnected. With the help of multiscale modeling framework, the transport process associated with drying can be studied on a smaller scale and the resulting information can be transferred to the bigger scale. This article is devoted to discussing the state of the art multi-scale modeling, its prospect and challenges in the field of drying technology. This article has also given some directions to how to overcome the challenges for successful implementation of multi-scale modeling.

Food structure: Its formation and relationships with other properties

Food materials are complex in nature as it has heterogeneous, amorphous, hygroscopic and porous properties. During processing, microstructure of food materials changes which significantly affects other properties of food. An appropriate understanding of the microstructure of the raw food material and its evolution during processing is critical in order to understand and accurately describe dehydration processes and quality anticipation. This review critically assesses the factors that influence the modification of microstructure in the course of drying of fruits and vegetables. The effect of simultaneous heat and mass transfer on microstructure in various drying methods is investigated. Effects of changes in microstructure on other functional properties of dried foods are discussed. After an extensive review of the literature, it is found that development of food structure significantly depends on fresh food properties and process parameters. Also, modification of microstructure influences the other properties of final product. An enhanced understanding of the relationships between food microstructure, drying process parameters and final product quality will facilitate the energy efficient optimum design of the food processor in order to achieve high-quality food.

Integrating Physiology and Architecture in Models of Fruit Expansion

Architectural properties of a fruit, such as its shape, vascular patterns, and skin morphology, play a significant role in determining the distributions of water, carbohydrates, and nutrients inside the fruit. Understanding the impact of these properties on fruit quality is difficult because they develop over time and are highly dependent on both genetic and environmental controls. We present a 3D functional-structural fruit model that can be used to investigate effects of the principle architectural properties on fruit quality. We use a three step modeling pipeline in the OpenAlea platform: (1) creating a 3D volumetric mesh representation of the internal and external fruit structure, (2) generating a complex network of vasculature that is embedded within this mesh, and (3) integrating aspects of the fruit's function, such as water and dry matter transport, with the fruit's structure. We restrict our approach to the phase where fruit growth is mostly due to cell expansion and the fruit has already differentiated into different tissue types. We show how fruit shape affects vascular patterns and, as a consequence, the distribution of sugar/water in tomato fruit. Furthermore, we show that strong interaction between tomato fruit shape and vessel density induces, independently of size, an important and contrasted gradient of water supply from the pedicel to the blossom end of the fruit. We also demonstrate how skin morphology related to microcracking distribution affects the distribution of water and sugars inside nectarine fruit. Our results show that such a generic model permits detailed studies of various, unexplored architectural features affecting fruit quality development.

A two-dimensional microscale model of gas exchange during photosynthesis in maize (Zea mays L.) leaves

CO2 exchange in leaves of maize (Zea mays L.) was examined using a microscale model of combined gas diffusion and C4 photosynthesis kinetics at the leaf tissue level. Based on a generalized scheme of photosynthesis in NADP-malic enzyme type C4 plants, the model accounted for CO2 diffusion in a leaf tissue, CO2 hydration and assimilation in mesophyll cells, CO2 release from decarboxylation of C4 acids, CO2 fixation in bundle sheath cells and CO2 retro-diffusion from bundle sheath cells. The transport equations were solved over a realistic 2-D geometry of the Kranz anatomy obtained from light microscopy images. The predicted responses of photosynthesis rate to changes in ambient CO2 and irradiance compared well with those obtained from gas exchange measurements. A sensitivity analysis showed that the CO2 permeability of the mesophyll-bundle sheath and airspace-mesophyll interfaces strongly affected the rate of photosynthesis and bundle sheath conductance. Carbonic anhydrase influenced the rate of photosynthesis, especially at low intercellular CO2 levels. In addition, the suberin layer at the exposed surface of the bundle sheath cells was found beneficial in reducing the retro-diffusion. The model may serve as a tool to investigate CO2 diffusion further in relation to the Kranz anatomy in C4 plants.

The stiffening of the cell walls observed during physiological softening of pears

The Young's modulus of the primary cell walls of pears decreases linearly during the pre-harvest on-tree maturation and increases during postharvest storage, and does not correlate with firmness of fruit. The determination of mechanical properties of cell walls is indispensable for understanding the mechanism of physiological softening and deterioration of quality of fruits during postharvest storage. The Young's modulus of the primary cell walls from pear fruit (Pyrus communis L., cultivars 'Conference' and 'Xenia') during pre-harvest maturation and postharvest storage in an ambient atmosphere at 2 °C followed by shelf life was studied using atomic force microscopy (AFM). The results were related to the firmness of fruits, galacturonic acid content in water, chelator, sodium carbonate and insoluble pectin fractions, polygalacturonase and pectin methylesterase activities. The Young's modulus of the primary cell walls decreased linearly during the last month of pre-harvest maturation from 3.2 ± 1.8 to 1.1 ± 0.7 MPa for 'Conference' and from 1.9 ± 1.2 to 0.2 ± 0.1 MPa for 'Xenia' which correlated with linear firmness decrease. During postharvest storage the cell wall Young's modulus increased while firmness continued to decrease. Correlation analysis for the entire period of the experiment showed a lack of straightforward relation between the Young's modulus of primary cell walls and fruit firmness. The Young's modulus of cell walls correlated negatively either with galacturonic acid content in sodium carbonate soluble pectin ('Conference') or with insoluble pectin fractions ('Xenia') and positively with polygalacturonase activity. It was therefore evidenced that covalently linked pectins play the key role for the stiffness of fruit cell walls. Based on the obtained results, the model explaining the fruit transition from firm and crispy to soft and mealy was proposed.

Hyperelastic models for hydration of cellular tissue

In this paper we present hyperelastic models for swelling elastic shells, due to pressurization of the internal cavity. These shells serve as model systems for cells having cell walls, as can be found in bacteria, plants and fungi. The pressurized internal cavity represents the cell vacuole with intact membrane at a certain turgor pressure, and the elastic shell represents the hydrated cell wall. At pressurization the elastic shell undergoes inhomogeneous deformation. Its deformation is governed by a strain energy function. Using the scaling law of Cloizeaux for the osmotic pressure, we obtain approximate analytical expressions of the cell volume versus turgor pressure - which are quite comparable to numerical solutions of the problem. Subsequently, we have simulated the swelling of shells - where the cell wall material is embedded with microfibrils, leading to strain hardening and anisotropic cell expansion. The purpose of our investigations is to elucidate the contribution of cell membrane integrity and turgor to the water holding capacity (hydration) of plant foods. We conclude with a discussion of the impact of this work on the hydration of food material, and other fields like plant science and the soft matter physics of responsive gels.

Prediction of water loss and viscoelastic deformation of apple tissue using a multiscale model

A two-dimensional multiscale water transport and mechanical model was developed to predict the water loss and deformation of apple tissue (Malus × domestica Borkh. cv. 'Jonagold') during dehydration. At the macroscopic level, a continuum approach was used to construct a coupled water transport and mechanical model. Water transport in the tissue was simulated using a phenomenological approach using Fick's second law of diffusion. Mechanical deformation due to shrinkage was based on a structural mechanics model consisting of two parts: Yeoh strain energy functions to account for non-linearity and Maxwell's rheological model of visco-elasticity. Apparent parameters of the macroscale model were computed from a microscale model. The latter accounted for water exchange between different microscopic structures of the tissue (intercellular space, the cell wall network and cytoplasm) using transport laws with the water potential as the driving force for water exchange between different compartments of tissue. The microscale deformation mechanics were computed using a model where the cells were represented as a closed thin walled structure. The predicted apparent water transport properties of apple cortex tissue from the microscale model showed good agreement with the experimentally measured values. Deviations between calculated and measured mechanical properties of apple tissue were observed at strains larger than 3%, and were attributed to differences in water transport behavior between the experimental compression tests and the simulated dehydration-deformation behavior. Tissue dehydration and deformation in the high relative humidity range ( > 97% RH) could, however, be accurately predicted by the multiscale model. The multiscale model helped to understand the dynamics of the dehydration process and the importance of the different microstructural compartments (intercellular space, cell wall, membrane and cytoplasm) for water transport and mechanical deformation.

A particle based model to simulate microscale morphological changes of plant tissues during drying

Fundamental understanding on microscopic physical changes of plant materials is vital to optimize product quality and processing techniques, particularly in food engineering. Although grid-based numerical modelling can assist in this regard, it becomes quite challenging to overcome the inherited complexities of these biological materials especially when such materials undergo critical processing conditions such as drying, where the cellular structure undergoes extreme deformations. In this context, a meshfree particle based model was developed which is fundamentally capable of handling extreme deformations of plant tissues during drying. The model is built by coupling a particle based meshfree technique: Smoothed Particle Hydrodynamics (SPH) and a Discrete Element Method (DEM). Plant cells were initiated as hexagons and aggregated to form a tissue which also accounts for the characteristics of the middle lamella. In each cell, SPH was used to model cell protoplasm and DEM was used to model the cell wall. Drying was incorporated by varying the moisture content, the turgor pressure, and cell wall contraction effects. Compared to the state of the art grid-based microscale plant tissue drying models, the proposed model can be used to simulate tissues under excessive moisture content reductions incorporating cell wall wrinkling. Also, compared to the state of the art SPH-DEM tissue models, the proposed model better replicates real tissues and the cell-cell interactions used ensure efficient computations. Model predictions showed good agreement both qualitatively and quantitatively with experimental findings on dried plant tissues. The proposed modelling approach is fundamentally flexible to study different cellular structures for their microscale morphological changes at dehydration.