Microscale modeling of water transport in fruit tissue

Mathematical Modelling of Conveyor-Belt Dryers with Tangential Flow for Food Drying up to Final Moisture Content below the Critical Value

This work presents the mathematical modeling of the conveyor-belt dryer with tangential flow operating in co-current, which has the advantage of improving the preservation of the organoleptic and nutritional qualities of the dried food. On the one hand, it is a more cumbersome dryer than the perforated cross flow belt dryer but, on the other hand, it has a low air temperature in the final section where the product has a low moisture content and, therefore, it is more heat sensitive. The results of the mathematical modeling allowed a series of guidelines to be developed for a rational design of the conveyor-belt dryer with tangential flow for the specific case of the moisture content of the final product XF lower than the critical one XC (XF < XC). In fact, this work follows a precedent in which a mathematical model was developed through the differentiation of the drying rate equation along the dryer belt with the hypothesis that the final moisture content XF of the product was higher than the critical one XC. The relationships between the extensive quantities (air flow rate and product flow rate), the intensive quantities (temperatures, moisture content and enthalpies) and the dimensional ones (length and width of the belt) were then obtained. Finally, based on these relationships, the rules for an optimized design for XF < XC were obtained.

Conveyor-Belt Dryers with Tangential Flow for Food Drying: Development of Drying ODEs Useful to Design and Process Adjustment

The mathematical investigation presented in this paper concerns the conveyor-belt dryer with tangential flow operating in co-current. This dryer is bigger than the continuous through-circulation conveyor dryer but has the advantage of better preserving the organoleptic and nutritional qualities of the dried product. In a previous work a mathematical modeling of the conveyor-belt dryer with tangential flow was carried out to offer guidelines for its optimized design. The last of those design guidelines indicated the need for an optimized adjustment of the dryer to ensure the constant maintenance of the final moisture content of the product. The fast and very precise measurement of the moisture content as the first step in the feedback chain was therefore necessary. Considering the difficulty of this type of measurement, two specific ordinary differential equations (ODEs) were obtained with the mathematical investigation of this work. Their solution became a relationship between the final moisture content of the product, the outlet air temperature, and other quantities that could be easily implemented in an automatic dryer control system. Therefore, the fast and accurate and much less expensive measurement of the temperature of the air leaving the dryer, owing to the relationship found, replaces the measurement of moisture content for the adjustment system. The experimental verification of the relationship highlighted the need to introduce a modification by which the relationship was finally validated.

Identifying in silico how microstructural changes in cellular fruit affect the drying kinetics

Convective drying of fruits leads to microstructural changes within the material as a result of moisture removal. In this study, an upscaling approach is developed to understand and identify the relation between the drying kinetics and the resulting microstructural changes of apple fruit, including shrinkage of cells without membrane breakage (free shrinkage) and with membrane breakage (lysis). First, the effective permeability is computed from a microscale model as a function of the water potential. Both temperature dependency and microstructural changes during drying are modeled. The microscale simulation shows that lysis, which can be induced using various pretreatment processes, enhances the tissue permeability up to four times compared to the free shrinkage of the cells. Second, via upscaling, macroscale modeling is used to quantify the impact of these microstructural changes in the fruit drying kinetics. We identify the formation of a barrier layer for water transport during drying, with much lower permeability, at the tissue surface. The permeability of this layer strongly depends on the dehydration mechanism. We also quantified how inducing lysis or modifying the drying conditions, such as airspeed and relative humidity, can accelerate the drying rate. We found that inducing lysis is more effective in increasing the drying rate (up to 26%) than increasing the airspeed from 1 to 5 m s^-1 or decreasing the relative humidity from 30% to 10%. This study quantified the need for including cellular dehydration mechanisms in understanding fruit drying processes and provided insight at a spatial resolution that experiments almost cannot reach.

Bio-chemo-electro-mechanical modelling of the rapid movement of Mimosa pudica

A remarkable feature of Mimosa pudica is its ability to deform in response to certain external stimuli. Here, a two-dimensional transient bio-chemo-electro-mechanical model of the rapid movement of the main pulvinus of Mimosa pudica is developed. Based on the laws of mass and momentum conservation, poroelasticity, and representative volume elements, a novel fluid pressure equation is proposed to characterize the cell elasticity. Experiments were conducted to measure the time and amplitude of the rapid movement. After examinations with the published experiments, it is confirmed that the model can predict well the ionic concentrations, petiole bending angle, and membrane potential. The simulation analysis of the biophysical properties provides insights to biomechanics: the hydrostatic pressure in the lowest extensor decreases from 0.35 to 0.05 MPa at t = 0.00 to 3.00 s; fluid pressure increases from 0.00 to 0.11 MPa at t = 0.00 to 0.14 s; and the peak bending angle increases from 57.0° to 70.9° when the reflection coefficient is assigned as 0.10 to 0.20 in the model. The results highlight the biochemical actuation mechanism of the Mimosa pudica movement, and they confirm the importance of ionic and water transports for causing changes in osmotic and hydrostatic pressures.

Effect of the moisture equilibrium process on the expansion behavior of instant controlled pressure drop (DIC) drying of dried apple cubes

BACKGROUND

Recently, consumers' demand on high quality dried fruit or vegetable products have increased dramatically. The instant controlled pressure drop (DIC) dried products have attracted consumers' attention due to its unique sensory characteristics. The product quality, especially the appearance quality of the DIC products, is influenced closely by water status and water distribution in the material, which is rarely reported in the literatures. In this study, a comparison system for the apple cubes with or without the moisture equilibrium process (MEP) was established to explain the effect of the MEP on the expansion behavior of the DIC dried apple cube.

RESULTS

The results showed that the MEP could induce a more homogenous spatial distribution of water in the semi-dried apple cube after pre-drying. Meanwhile, the MEP treated and DIC dried apple cubes showed better quality in terms of the appearance and texture properties including high porosity (71.77%), large pores (maximum pore size of 1.55 mm), and thin pore walls (pore wall thickness of 0.079 mm).

CONCLUSION

The MEP was approved to be a compulsory treatment to achieve the DIC dried apple cubes with good expansion behavior. © 2019 Society of Chemical Industry.

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.

Fundamental Understanding of Cellular Water Transport Process in Bio-Food Material during Drying

Bio-food materials are heterogeneous in structure with cellular diversity, where the majority of the water is located in the intracellular spaces. Understanding of the nature of the microscopic behaviour of water transport is crucial to enhance the energy efficiency in food processing and obtain the better quality of processed food. In this research, apoplastic and symplastic transport of cellular water in the bio-food material during drying was investigated using 1H-NMR-T2 relaxometry. We found that intracellular water (ICW) migrates from intracellular spaces to the intercellular spaces by progressive rupturing the cell membranes while drying at a higher temperatures (60 °C-70 °C). In this case, apoplastic process dominates the transport process. However, at lower temperature (45 °C), cell membranes do not rupture and therefore ICW migrates from cell to the neighbouring cell through micro-capillaries, where the symplastic process dominates the mass transfer at different stages of drying.

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.

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.

Spatial and temporal variations in mango colour, acidity, and sweetness in relation to temperature and ethylene gradients within the fruit

Managing fruit quality is complex because many different attributes have to be taken into account, which are themselves subjected to spatial and temporal variations. Heterogeneous fruit quality has been assumed to be partly related to temperature and maturity gradients within the fruit. To test this assumption, we measured the spatial variability of certain mango fruit quality traits: colour of the peel and of the flesh, and sourness and sweetness, at different stages of fruit maturity using destructive methods as well as vis-NIR reflectance. The spatial variability of mango quality traits was compared to internal variations in thermal time, simulated by a physical model, and to internal variations in maturity, using ethylene content as an indicator. All the fruit quality indicators analysed showed significant spatial and temporal variations, regardless of the measurement method used. The heterogeneity of internal fruit quality traits was not correlated with the marked internal temperature gradient we modelled. However, variations in ethylene content revealed a strong internal maturity gradient which was correlated with the spatial variations in measured mango quality traits. Nonetheless, alone, the internal maturity gradient did not explain the variability of fruit quality traits, suggesting that other factors, such as gas, abscisic acid and water gradients, are also involved.

Imaging of polysaccharides in the tomato cell wall with Raman microspectroscopy

BACKGROUND

The primary cell wall of fruits and vegetables is a structure mainly composed of polysaccharides (pectins, hemicelluloses, cellulose). Polysaccharides are assembled into a network and linked together. It is thought that the percentage of components and of plant cell wall has an important influence on mechanical properties of fruits and vegetables.

RESULTS

In this study the Raman microspectroscopy technique was introduced to the visualization of the distribution of polysaccharides in cell wall of fruit. The methodology of the sample preparation, the measurement using Raman microscope and multivariate image analysis are discussed. Single band imaging (for preliminary analysis) and multivariate image analysis methods (principal component analysis and multivariate curve resolution) were used for the identification and localization of the components in the primary cell wall.

CONCLUSIONS

Raman microspectroscopy supported by multivariate image analysis methods is useful in distinguishing cellulose and pectins in the cell wall in tomatoes. It presents how the localization of biopolymers was possible with minimally prepared samples.