Modelling of mechanical deformation of apple fruit tissue due to hygrostresses

During postharvest storage at low relative humidity, water from fruit cells is lost, which is accompanied by hygrostresses. This leads to a decrease of the volume of the cells and thus of the total volume, shape and mass of the fruit. Water loss of fruit during storage has a large impact on fruit quality and shelf life, and is essential to fruit drying processes. The main objective of this thesis is to investigate the dynamics of dehydration of apple tissue during drying. For this purpose, a multiscale water transport and mechanical model was developed to predict the water loss and deformation of apple cortex tissue during dehydration. Maturation and senescence could influence the dehydration process but were not included in this study.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. The Mooney-Rivlin and Yeoh hyperelastic potentials with three parameters were effective to reproduce the nonlinear behavior during the loading region. The Maxwell model was successful to quantify the viscoelastic behavior of the tissue during stress relaxation. The sensitivity of different model parameters using the nonlinear viscoelastic model using Yeoh hyperelastic potentials was studied. The model predictions proved to be more sensitive to water transport parameters than to the mechanical parameters. One-dimensional water transport and large deformation of cylindrical samples of apple tissue during dehydration was modeled by coupled mass transfer and mechanics and was first validated by calibrated X-ray CT measurements. The accuracy of the 2D model was further verified with quantitative neutron radiography experiments. Both model simulations and experiments showed that the largest moisture gradients occurred at the air-tissue interface. The corresponding shrinkage behavior was similar. Furthermore, the Biot number was quite large, indicating that the drying kinetics were dominated by the water transport in the tissue rather than by the convective flow at air-tissue interface. In addition, the performance of a 3D model was checked, based on a comparison of the total water loss, the transient water distribution profiles and the mechanical deformation profiles, measured using quantitative neutron tomography. The simulated results showed a good agreement with experimental observations. Although access to facilities which produce neutrons is limited, neutron imaging also showed large potential for studies on fruit dehydration, as accurate quantification of the water content was possible. At the microscopic level, a model which took into account the water exchange between different microscopic structures of the tissue (intercellular space, the cellwall network and cytoplasm) was developed using transport laws, which consider 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 a good agreement with the experimentally measured values.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. The validated model can be employed to better understand postharvest storage and drying processes of apple fruit and thus improve product quality in the cold chain.status: publishe

A 3D Fruit Tissue Growth Algorithm Based on Cell Biomechanics

A 3D fruit tissue growth algorithm is presented based on the biomechanics of plant cells in tissues. The algorithm is able to generate realistic virtual fruit tissues. It was used to produce cell architectures of pome fruits with intercellular air spaces. The cell size and shape differences in pear cortex tissue and apple cortex tissue are obtained by implementing different maximum resting length of the cell walls and different cell wall stiffness (e.g., by including a degree of anisotropy) in the model. In addition to cell size and shape, the difference in the size of the intercellular air spaces and their connectivity is recognized in our model by implementing different pore formation mechanisms. The arrangement of different tissue layers which are observed from the skin to the cortex (epidermis, hypodermis and cortex) and particular features such as stone cells were also accounted for by our model. The algorithm was shown to produce cell architectures that are very similar to measured tissue structures of the pear and cortex tissue with intercellular air spaces. The resulting geometric models can be used in finite element simulations to study exchange processes within the fruit tissue and between the tissue and the surrounding environment. The geometric models can also be used to study coupled phenomena of moisture migration and tissue shrinkage in a multiscale approach. These approaches were demonstrated to be useful using our 2D version of the algorithm. The 3D version of the algorithm avoids many of the limitations of the 2D algorithm such as lack of intercellular air space connectivity in the 2D geometric models and hence, will help to better understand the exchange mechanisms.status: accepte

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.status: publishe

Probing inside fruit slices during convective drying by quantitative neutron imaging

Quantitative neutron imaging was applied for the dynamic monitoring of the internal moisture distribution of fruit slices during convective drying in a drying tunnel. The impact of several process conditions was evaluated, including airflow temperature, air speed and incident radiation. This technique also unveiled that anisotropic shrinkage was caused, in part, by spatially heterogeneous dehydration, as induced by the presence of the peel. Neutron imaging provided unique graphical and quantitative in-sights on how the internal water distribution evolved. Thereby, this imaging technique has large potential to complement conventional techniques for monitoring, controlling and optimising drying processes of complex biomaterials, or to generate high-resolution validation data for numerical simulations. (C) 2016 Elsevier Ltd. All rights reserved.publisher: Elsevier articletitle: Probing inside fruit slices during convective drying by quantitative neutron imaging journaltitle: Journal of Food Engineering articlelink: http://dx.doi.org/10.1016/j.jfoodeng.2016.01.023 content_type: article copyright: Copyright © 2016 Elsevier Ltd. All rights reserved.status: publishe

Modelling of coupled water transport and large deformation during dehydration of apple tissue

Water loss of fruit during storage has a large impact on fruit quality and shelf life and is essential to fruit drying. Dehydration of fruit tissues is often accompanied by large deformations. One-dimensional water transport and large deformation of cylindrical samples of apple tissue during dehydration were modeled by coupled mass transfer and mechanics and validated by calibrated X-ray CT measurements. Uni-axial compression-relaxation tests were carried out to determine the nonlinear viscoelastic properties of apple tissue. The Mooney-Rivlin and Yeoh hyperelastic potentials with three parameters were effective to reproduce the nonlinear behavior during the loading region. Maxwell model was successful to quantify the viscoelastic behavior of the tissue during stress relaxation. The nonlinear models were superior to linear elastic and viscoelastic models to predict deformation and water loss. The sensitivity of different model parameters using the nonlinear viscoelastic model using Yeoh hyperelastic potentials was studied. The model predictions proved to be more sensitive to water transport parameters than to the mechanical parameters. The large effect of relative humidity and temperature on the deformation of apple tissue was confirmed by this study. The validated model can be employed to better understand postharvest storage and drying processes of apple fruit and thus improve product quality in the cold chain. © 2012 Springer Science+Business Media, LLC.status: publishe

Model-based design and validation of food texture of 3D printed pectin-based food simulants

A prime interest in 3D food printing consists of controlling the texture of food products by means of structure design. Analytical and finite element models were used to predict the texture properties of printed honeycomb structures. Structures with varying cell size were 3D printed using food-inks composed of three different pectin concentrations and characterized with micro-CT and compression analysis. Porosity and average wall thickness of the samples appeared independent of food-ink composition but structure deviations could be distinguished between actual printed structures and CAD designs. The comparison between the texture properties of printed structures and those predicted by analytical and FE modelling in function of porosity showed that both predicted and actual texture properties matched to the same decreasing trend with increasing porosity. Finally, a good fit of the analytical model to the measured Young's modulus was obtained by using the actual porosity of the printed structures, while the validated finite element model provides a means to design more complex structures. The results emphasize the importance of structure correspondence for reliable design of texture properties of printed food structures.status: Published onlin

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

Water loss of fruit typically results in fruit tissue deformation and consequent quality loss. To better understand the mechanism of water loss, a model of water transport between cells and intercellular spaces coupled with cell deformation was developed. Pear (Pyrus communis L. cv. Conference) was chosen as a model system as this fruit suffers from shriveling with excessive water loss. A 2D geometric model of cortex tissue was obtained by a virtual fruit tissue generator that is based on cell growth modeling. The transport of water in the intercellular space, the cell wall network and cytoplasm was predicted using transport laws using the chemical potential as the driving force for water exchange between different microstructural compartments. The different water transport properties of the microstructural components were obtained experimentally or from literature. An equivalent microscale model that incorporates the dynamics of mechanical deformation of the cellular structure was implemented. The model predicted the apparent tissue conductivity of pear cortex tissue to be 9.42±0.40×10−15kgm−1s−1Pa−1, in the same range as those measured experimentally. The largest gradients in water content were observed across the cell walls and cell membranes. A sensitivity analysis of membrane permeability and elastic modulus of the wall on the water transport properties and deformation showed that the membrane permeability has the largest influence. The model can be improved further by taking into account 3-D connectivity of cells and intercellular pore spaces. It will then become feasible to evaluate measures to reduce water loss of fruit during storage and distribution using the microscale model in a multiscale modeling framework.publisher: Elsevier articletitle: Microscale modeling of coupled water transport and mechanical deformation of fruit tissue during dehydration journaltitle: Journal of Food Engineering articlelink: http://dx.doi.org/10.1016/j.jfoodeng.2013.10.007 content_type: article copyright: Copyright © 2013 Elsevier Ltd. All rights reserved.status: publishe

Study of water distribution and shrinkage of apple tissue during dehydration with neutron tomography and finite element modeling

Dehydration of fruit during postharvest storage decreases its commercial value and the consumer acceptance. Understanding this process requires knowledge on both water transport and mechanical deformation. In this study, a comparison was made between different methods to study water distribution and shrinkage of apple tissue during dehydration: experimentally with quantitative neutron tomography, and numerically with finite element modeling using a nonlinear viscoelastic model coupled with water transport. Both techniques provided three-dimensional information of the transient water distribution and shrinkage of the cylindrical apple tissue during dehydration. The neutron experiments were found to accurately predict the water loss from the samples, when compared to gravimetric measurements, indicating this technique is successful in directly quantifying water content for this type of experiments. The total water loss and local water content of experiments and simulations also compared well, indicating the numerical model is a viable alternative to neutron experiments. This is a particular advantage since access to facilities which produce neutrons is limited.status: accepte

Novel application of neutron radiography to forced convective drying of fruit tissue

status: publishe

Quantitative neutron imaging of water distribution, venation network and sap flow in leaves

MAIN CONCLUSION: Quantitative neutron imaging is a promising technique to investigate leaf water flow and transpiration in real time and has perspectives towards studies of plant response to environmental conditions and plant water stress. The leaf hydraulic architecture is a key determinant of plant sap transport and plant-atmosphere exchange processes. Non-destructive imaging with neutrons shows large potential for unveiling the complex internal features of the venation network and the transport therein. However, it was only used for two-dimensional imaging without addressing flow dynamics and was still unsuccessful in accurate quantification of the amount of water. Quantitative neutron imaging was used to investigate, for the first time, the water distribution in veins and lamina, the three-dimensional venation architecture and sap flow dynamics in leaves. The latter was visualised using D2O as a contrast liquid. A high dynamic resolution was obtained by using cold neutrons and imaging relied on radiography (2D) as well as tomography (3D). The principle of the technique was shown for detached leaves, but can be applied to in vivo leaves as well. The venation network architecture and the water distribution in the veins and lamina unveiled clear differences between plant species. The leaf water content could be successfully quantified, though still included the contribution of the leaf dry matter. The flow measurements exposed the hierarchical structure of the water transport pathways, and an accurate quantification of the absolute amount of water uptake in the leaf was possible. Particular advantages of neutron imaging, as compared to X-ray imaging, were identified. Quantitative neutron imaging is a promising technique to investigate leaf water flow and transpiration in real time and has perspectives towards studies of plant response to environmental conditions and plant water stress.status: publishe