Variable Effective Diffusivity Research Articles

Micro-CT images and variable effective diffusivity as tools in the analysis of Cariniana estrellensis (Raddi) Kuntze seeds hydration

Micro-CT images and variable effective diffusivity as tools in the analysis of Cariniana estrellensis (Raddi) Kuntze seeds hydration

Impact of ultrasound pretreatment on banana chip production by convective drying using hot air: Consideration of shrinkage and variable effective mass diffusivity in the process description

AbstractIn this study, we used experimental analysis and numerical simulation to describe and compare the convective drying (CD) of banana slices, without and with pretreatment with ultrasound (US) at 25 kHz. Banana slices, with an average initial thickness of about 6.60 × 10−3 m and an average diameter of about 3.01 × 10−2 m, were subjected to CD at temperatures of 60, 70, and 80°C, with air speed of 1.5 m s−1. Considering such dimensions, the one‐dimensional diffusion equation in Cartesian coordinates was numerically solved by the finite volume method, using a fully implicit formulation (direct problem). A solver with a numerical solution was developed for the direct problem. This solver was coupled to an optimizer to determine the parameters a and b of functions that relate the effective moisture diffusivity (D) with the local moisture ratio, and also to determine the convective mass transfer coefficient (h) (inverse problem), considering the shrinkage. The proposed model was used to describe the data obtained. The results revealed that the drying rate increased in samples that were subjected to pretreatment with US, for each drying temperature. The best‐simulated results were those that related D to the local moisture ratio by means of a bcosh (aMR2) function. It could be observed that pretreatment with US allowed saving of time (and consequently energy) of 28.3%, 16.0%, and 12.4% at drying temperatures of 60, 70, and 80°C, respectively.Practical applicationsThe main contribution of this paper is to present a solver and an optimizer to determine the mass transfer properties considering the shrinkage during convective drying of banana pieces pretreated with ultrasound by the inverse problem. With the information obtained for the mass transfer properties and the proposed numerical model with a hyperbolic cosine type function for the effective moisture diffusivity, it is possible to more accurately determine the time and, therefore, the energy savings of processing banana chips pre‐treated with ultrasound.

Physics informed neural networks reveal valid models for reactive diffusion of volatiles through paper

Predictive models for the transport of volatile organic compounds in paper need to consider the complex interplay of diffusion, adsorption, desorption, or chemical reactions. The relative importance of each of these processes is determined by the polarity of the volatile. Hence, it is challenging to pick a valid theoretical model that correctly predicts transport regardless of the polarity. Here, physics-informed neural networks (PINNs) assess which of five different models correctly describe transport of DMSO as polar and n-tetradecane as apolar model compound: (i) a pseudo first-order adsorption model for an irreversible sorption process, (ii) a first-order kinetics model allowing reversible sorption, (iii) a second-order model with a reversible process, and an effective diffusion model accounting for a constant (iv) and for a variable effective diffusivity (v). Each tested model is given as set of partial differential equations (PDE). Considering the model under testing and experimentally obtained spatially and temporally resolved concentration profiles through stacks of paper sheets, PINNs predict concentration of the volatiles and associated material constants such as sorption constants and effective diffusion coefficients by solving the inverse problem. Our PINNs revealed two models, pseudo first-order sorption and second-order reversible sorption, that correctly predict concentration profiles and polarity-driven differences in sorption times. While a PINN-based picking of valid transport models has important implications for the development of effective methods for controlling emission of volatiles from paper materials, PINNs represent a versatile mathematical tool to validate or refute the capability of PDE-based theoretical models to describe experimental data.

Modeling drying kinetics of Jacaranda mimosifolia seeds with variable effective diffusivity via diffusion model

Jacaranda mimosifolia D. Don, a tree widely used for afforestation, has been studied for different applications due to the composition of its extracts. The drying kinetics of J. mimosifolia seeds in a thin layer and its process were modelled using an analytical solution of diffusion model, first considering the parameter Effective Moisture Diffusivity (EMD) to be constant. For variable EMD, a sequential and partial adjustment technique using a classic analytical solution was proposed. Thin layer drying kinetics were conducted at temperatures of 40 °C and 50 °C. When EMD was treated as a constant parameter, adjustments showed values of R2 ≥ 0.976 and χ2 ≤ 1.60 × 10−3, but when it was treated as a variable parameter, values of R2 ≥ 0.998 and χ2 ≤ 1.49 × 10−4 were found showing it to be more accurate. The proposed sequential fitting method showed good results, improving the understanding of diffusive mass transfer mechanisms. The technique show promise for applications in process control and product quality, in addition to dryer sizing and design.

Extraction of Protodioscin from Tribulus terrestris-Optimisation of Kinetics and Modeling

The aim of the present study was to establish the optimal conditions for protodioscin extraction from Tribulus terrestris plant and to investigate the possibilities of mathematical modeling of the process and calculation of the diffusion coefficients essential for the industrial scale-up and management of the extraction process. The kinetics of protodioscin extraction from Tribulus terrestris was experimentally studied at varying the solvent type (70% and 96% ethanol) and temperature (20�C, 30�C, 40�C). The optimal process conditions for these parameters were determined. The experimental results were mathematically modelled. Numerical solutions of the propsed in the study empirical model with constant and variable effective diffusivity in the solid phase, Deff, were obtained. The empirical model was based on comparative analyses with the Regular regime model solutions. It was established that the experimental data complied satisfactorily with the the resulting numerical solutions.

Heat and mass transport analysis of the drying of freshwater fishes by a forced convective air‐dryer

AbstractThe drying behavior of different freshwater fishes (with/without scales) is investigated using a simple convective heated air dryer. Drying processes are analyzed to study the kinetics of drying, shrinkage dependent variable effective diffusivity, convective heat and mass transport, and the energy aspect of drying. Among the drying kinetic models, Hasibuan–Daud and Haghi–Angiz‐I models produce the best fit for fishes with scales and Hii model produces the best fit for fish without scales. Diffusion analysis performed based on simplified solution of Fick's diffusion equation shows higher effective diffusivity for fish without scales, proving additional barrier from scales (for fish with scales) that need to be considered during dryer design. Calculated instantaneous heat and mass transfer coefficients (different for fish with or without scales) also agree with this observation, accentuating the difference based on scales. Drying process for all fishes obeys the heat‐mass transfer correlation. Estimated parameters such as effective diffusivity (0.2–1 × 10−9 m2/s) and convective heat and mass transfer coefficients (7–14 W/m2/K and 2.8–4.5 × 10−6 m/s, respectively) can be utilized in designing different fish drying systems. Average and instantaneous total energy consumption, specific moisture extraction ratio, and specific energy consumption are evaluated in order to provide a comprehensive picture of the drying process.Practical ApplicationsFresh‐ and salt‐water fishes account for major sources of protein‐rich food for substantial parts of the population in underdeveloped and developing nations. To circumvent the wastage associated with microbial contaminations during prolific seasons, fish drying has been widely employed as a way of preserving this perishable food. Convective drying of agricultural products as well as marine foods is a commonly employed drying method for food preservation. This study investigates the drying behavior of three different freshwater fishes using an in‐house constructed forced convective air dryer. The experimental drying characteristics and estimated parameters by model fitting during fish drying will be particularly applicable in the wide field of fish drying. The outcome of this study can also be utilized for more effectively designing and evaluating low‐cost convective fish dryers.

Modeling of Effective Moisture Diffusivity in Corn Tortilla Baking.

The analytical solutions of the Fick's law of diffusion for the moisture content in products that can be represented as an infinite plate, considering variable diffusivity, can be useful in studies when accurate estimations of effective diffusivity and concentration are needed.

Setting up the drying regimes based on the theory of moisture migration during drying

Drying is energy intensive process which has important effect on the quality of the clay tiles that are dried commercially. Chamber and tunnel dryers are constantly improving. Better technical equipment and operational strategies have lead to higher quality of the dried clay products. The moisture migration during isothermal drying process can be visually traced on the curve that represents the relationship between variable effective moisture diffusivity (MR) with time (t). Proposed non isothermal drying regimes were consisted from several isothermal segments. For the first time, the choice of isothermal segments specification and its duration was not specified by experience or by trial-and-error method. It was detected from the isothermal curves Deff - MR in accordance with the theory of moisture migration during drying. Proposed drying regimes were tested. Clay roofing tiles were dried without cracks. Dried clay roofing tiles has satisfied all requirements defined in EN 1304 norm related to the shape regularity and mechanical properties.

Numerical approach to describe continuous and intermittent drying including the tempering period: Kinetics and spatial distribution of moisture

ABSTRACTContinuous and intermittent drying experiments were performed with whole bananas, using hot air at 70°C. The intermittent drying experiments were performed with intermittency ratio equal to 1/2 and tempering times of 0.5, 1.0, and 2.0 h. The conditions imposed to the experiments permitted to investigate the influence of these tempering times on the processes. A one-dimensional numerical solution of the diffusion equation coupled with an optimizer was used to determine the process parameters for four experiments. To describe the processes, a model was proposed. Model includes shrinkage, variable effective mass diffusivity, and two values for convective mass transfer coefficient (within and outside the dryer), enabling to consider moisture loss during the tempering period. For all experiments, the simulation of the drying kinetics has resulted in good statistical indicators. Proposed model also made it possible to predict moisture distributions during the entire processes, including the migration of moisture from the central part to the peripheral region of the cross section of the bananas, during the tempering period. The results indicated that, for the same effective operation time and intermittency ratio, increasing the tempering time implied moderate decrease in the final average moisture content.

Pulsed vacuum osmotic dehydration of tomatoes: Sodium incorporation reduction and kinetics modeling

Semi-dehydrated food is obtained via osmotic dehydration (OD). The influence of the osmotic agent (27.5% sucrose or maltodextrin combined with 10.0% of NaCl, 40 °C) with/without the application of a vacuum pulse (VP) (100 mbar, 20 min) on the NaCl incorporation and on the kinetics of water loss (WL), solid gain (SG), and water activity (aw) were studied in the OD of sliced tomatoes. The kinetics of the WL and SG were evaluated and fitted with diffusive and hydrodynamic models. The NaCl incorporation was 25% lower in the maltodextrin-NaCl solution (MN) compared to the sucrose-NaCl solution (SN). The MN reduced that incorporation compared to the SN. Moreover, the salt incorporation was significantly reduced (by approximately 50%) by using a VP in the osmotic process, which was independent of the ternary solution. The variable effective diffusivity improved the fitness of the OD kinetics with respect to the constant diffusivity or the modelling of the hydrodynamic mechanism. The large reduction of NaCl incorporation obtained in the present work, which was mainly due to the use of a VP, suggests that more attention is necessary in studies of OD with vacuum pulse involving the immersion of food in a ternary.

Model of a Chemical Looping Process for Hot Gas Desulfurization in Power Plants

A mathematical model of a transport reactor has been developed and implemented with the software Athena Visual Studio. The one-dimensional, steady state model takes into account kinetics and hydrodynamic effects. The reactor has been divided into three zones: the acceleration zone, the fully developed zone and the exit zone. Empirical correlations are used to describe the different regions, with particular reference to the axial voidage profile. The unreacted shrinking core model with variable effective diffusivity is applied to determine the sorbent conversion and the reaction rate. Two different sorbents were investigated: zinc titanate, considered as one of the most promising mixed metal oxide and calcium oxide as natural material. The differences, in terms of operating temperature and desulfurization efficiency, are discussed. Finally, to estimate the advantages of the described alternatives, they have been included in an Integrated Gasification Combined Cycle (IGCC) and simulated by the software package Thermoflex. The results show an interesting enhancement of the efficiency up to 3% accompanied by a simpler system configuration.

Non isothermal drying process optimisation - Drying of clay tiles

In our previous studies we have developed a model for determination of the variable effective diffusivity and identification of the exact transition points between possible drying mechanisms. The next goal was to develop a drying regime which could in advance characterize the real non isothermal process of drying clay tiles. In order to do this four isothermal experiments were recorded. Temperature and humidity were maintained at 350C / 75%; 450C / 70%; 450C / 60% and 500C / 60%; respectively in each experiment. All experimentally collected data were analyzed and the exact transition points between possible drying mechanisms were detected. Characteristic drying period (time) for each isothermal drying mechanism was also detected. The real, non-isothermal drying process was approximated by 5 segments. In each of these segments approximately isothermal drying condition were maintained. Temperature and humidity of the drying air, in the first four segments, was maintained on the same level as in recorded isothermal experiments while in the fifth segment, it were maintained at 700C / 40%. The duration of the first four segments were calculated from the diagrams Deff - t respectively for each experiment. The clay tile in experiment five was dried without cracking using the proposed non isothermal drying regime.

Drying of clay slabs: prediction by means of one-dimensional diffusion models

The main purpose of this article is to describe convective drying of clay slabs with initial moisture content of 0.11 (db) at temperatures of 50 and 90 °C. To describe the water diffusion process, was considered: a) constant effective mass diffusivity (Model 1); b) variable effective mass diffusivity (Model 2). A numerical solution of the one-dimensional diffusion equation with boundary condition of the third kind was proposed in order to describe the drying process. The solution was coupled with an optimizer in order to estimate the process parameters for each drying air temperature using experimental datasets and the inverse method. Comparative studies were performed between Models 1 and 2 in order to define the accuracy of description of the drying process. Comparative studies are also conducted on the proposed models and on diffusive models with two- and three-dimensional geometries. An analysis of statistical indicators shows that Model 2 is comparable to models with two- and three-dimensional geometries, being in perfect agreement with the experimental results. However, the computational processing time for the proposed model is much shorter than that obtained with the use of two- and three-dimensional geometries. However, it was observed that the one-dimensional model overestimates the process parameters.

Composite CaO-Based CO2 Sorbents Synthesized by Ultrasonic Spray Pyrolysis: Experimental Results and Modeling

We report the preparation of calcium oxide (CaO)-based sorbents by ultrasonic spray pyrolysis (USP) with both experimental results and modeling of the sorption process. To mitigate CaO deactivation during carbonation/regeneration cycles, metal oxides with high melting temperatures were dispersed into CaO particles in this bottom-up synthetic method (USP), and their performance was experimentally characterized and evaluated over 50 cycles. The performance of synthesized sorbents was then compared to those expected from an unreacted shrinking core model. The model was able to predict the experimental results and provide an explanation for the effect of sintering and agglomeration on the performance of the sorbents through a variable effective diffusivity. Moreover, it was used to extrapolate sorbent performance over large numbers of cycles.

A Numerical Approach to Determine Some Properties of Cylindrical Pieces of Bananas During Drying

Abstract This article uses several liquid diffusion models to describe convective drying of bananas cut into cylindrical pieces. A two-dimensional numerical solution of the diffusion equation with boundary condition of the third kind, obtained through the finite volume method, was used to describe the process. The cylindrical pieces were cut into the following dimensions: length of about 21 mm and average radius of 15 mm. Drying air temperatures were 40°C, 50°C, 60°C and 70°C. In order to determine the process parameters, an optimizer was coupled with the numerical solution. A model that considers the shrinkage and variable effective moisture diffusivity well describes drying for all the experimental conditions, and enables to predict the moisture distributions at any given time. For this model, the determination coefficient has varied from 0.99937 (70°C) to 0.99995 (40°C), while the chi-square ranged from 3.41 × 10−4 (40°C) to 4.15 × 10−3 (70°C).

Drying Kinetic Simulation of Clay Tiles Made from the Raw Material Having Less Clay Fraction

In order to describe the internal moisture rate and to take all different mechanisms of moisture movement into account, it is suitable to use effective diffusivity as a measure of moisture rate, irrespectively of the mechanisms really involved. This means that all different mechanisms and driving forces for internal moisture transport are lumped together and introduced into effective moisture diffusivity. Hence, diffusion equations are retained and reused with the effective diffusivity coefficient as a measuring parameter of internal moisture ratio. In our previous studies we have presented the calculation method which assumed constant diffusivity. The next goal was to estimate effective diffusivity at various moisture contents, in a real case of non-linear drying curves, and to predict drying kinetic. In our last study we have developed a model for determination of the variable effective diffusivity and identification of the exact transition points between possible drying mechanisms. In this paper we have tried to develop more accurate tool for determination of time dependent effective moisture diffusivity. An analytical model and computing procedure were developed to evaluate mass transfer properties and describe drying kinetic of clay tiles having less clay fraction. The proposed procedure was validated with experimental drying data. Presented results have demonstrated that the proposed dying model can be applied for the accurate description of experimental drying kinetics and a reliable estimation of effective diffusivity.

Comparison between two- and three-dimensional diffusion models to describe wood drying at low temperature

An experiment on convective drying of lumber was performed at a temperature of 40 °C. A two-dimensional numerical solution of the diffusion equation with boundary condition of the third kind and variable effective mass diffusivity (model 1) was proposed to describe drying. The solution was coupled with an optimizer to determine the process parameters. The results were compared with those obtained by a typical three-dimensional numerical solution (model 2). The analyses of the results indicated that the parameters (and the simulation) obtained using model 1 are very close to the results obtained with model 2. However, the optimization time for model 1 is about 20 times less than the optimization time for model 2.

Numerical description of guava osmotic dehydration including shrinkage and variable effective mass diffusivity

This article uses two diffusion models to describe osmotic dehydration of guavas cut into parallelepiped shaped pieces. A one-dimensional numerical solution of the diffusion equation with boundary condition of the first kind, obtained through the finite volume method, was proposed to describe the process. The slices were cut into the following average dimensions: 9.56 × 20.03 × 30.29 mm. Two experiments involving the dipping of the product in syrup of water and sucrose were carried out in the following conditions: (1) 40 °Brix and 30 °C, (2) 50 °Brix and 40 °C. In order to determine the process parameters, an optimizer was coupled with the proposed numerical solution. A model that considers the shrinkage and variable effective moisture diffusivity well describes osmotic dehydration for two experimental conditions, and makes it possible to predict the moisture and sucrose distributions at any stipulated time.

A Variable Diffusivity Model for the Drying of Spherical Food Particulates

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R2value greater than 98.6% for all temperatures.

A liquid diffusion model to describe drying of whole bananas using boundary-fitted coordinates

This article uses a liquid diffusion model to describe convective drying of whole bananas. The experiments were carried out with drying air temperatures at 40, 50, 60 and 70°C. A two-dimensional numerical solution in generalized coordinates of the diffusion equation with boundary condition of the third kind, obtained through the finite volume method, was used to describe the process. A structured non-orthogonal grid was obtained by digitization of the photography of the fruit. In order to determine the thermo-physical properties, an optimizer was coupled with the numerical solution. The model proposed in this article, which includes shrinkage and variable effective moisture diffusivity, well describes drying for all the experimental conditions, and makes it possible to predict the moisture distributions at any given time. The determination coefficients were greater than 0.99970 and the chi-squares were less than 8.33×10−4.