Modeling at Pore-Scale Isothermal Drying of Porous Materials: Liquid and Vapor Diffusivity

Numerical simulations of isothermal drying of non-hygroscopic liquid-wet rigid porous media are performed. Two- and three-dimensional pore networks represent pore spaces. Two types of mechanisms are considered: evaporation and hydraulic flow. The drying is considered to be a modified form of invasion percolation. Liquid in pore corners allows for a hydraulic connection throughout the network at all times. As drying progresses, liquid is replaced by vapor by two fundamental mechanisms: evaporation and pressure gradient-driven liquid flow. Using a Monte Carlo simulation, evaporation and drainage times are computed. The controlling mechanism is indicated by the shorter calculated time. Initially, the drying is governed by liquid flow, then by a combination of liquid flow and evaporation and finally by local evaporation. Reported here are the distributions of liquid and vapor with drying time, capillary pressure curves, liquid film saturation curves, and liquid diffusivity and vapor diffusivity as a function of liquid saturation.     

Pore-Scale Simulation of Drying of a Porous Media Saturated with a Sucrose Solution

This work presents results of Monte Carlo simulations of isothermal drying of a nonhygroscopic porous media initially saturated with a sugar solution. The porous media is represented by a two-dimensional network of cubic pores connected by throats with a given radius distribution. The considered network had just one open side (the three other sides were sealed) from which water evaporation occurred. Water evaporation, hydraulic flow, and diffusivity of sucrose in water are considered in the physical model. It was considered that drying occurred under isothermal conditions (low drying rates) and that the capillary forces surpass the viscous forces, as in invasion percolation. It was also considered that water evaporation inside the network of pores and throats causes solution concentration, which remains at the corners, allowing hydraulic connection throughout the whole network. At each simulation step, a single meniscus moves through a particular pore segment with the higher displacing force. As drying progresses, air replaces the solution. Determination of the mechanism prevailing at any given drying stage requires calculation of evaporation. In other words, each step of the simulation involves finding the solution to three systems of equations: the vapor pressure field in the vapor phase, the pressure field in the liquid phase, and the solutes' concentration in the liquid phase. Herein, we report results of drying curves calculated as a function of the sucrose and water saturation and of the distribution of liquid, sucrose, and vapor as drying advances. The results presented in this work showed that network models are a powerful tool for investigating the influence of the main mechanisms controlling drying at its different stages; that is, from liquid saturation condition to very low saturation (end of drying). Despite the applied simplifications, the model can capture the main aspects of drying of liquids and solutions present in porous media.     

Drying of Turnip Seeds with Microwaves in Fixed and Pulsed Fluidized Beds

This article presents experimental and modeled drying kinetics of turnip seeds as a function of the type of air-particle contact (fixed bed, pulsed fluidized bed), humidity of the air, and three levels of microwave irradiation. The effects of those factors on the drying time required to reach a moisture content of 0.1 kg/kg d.b. were determined with an experimental design of 12 experiments by using the software Statgraphics. It was found that in drying, a significant factor was the application of microwaves to a pulsed fluidized bed. The effect of the humidity of the air only became noticed when the moisture contents of the seeds was below 0.2 kg/kg d.b. The simplified variable diffusivity model (SVDM) gave the least deviations for the experimental data. The effective diffusivity values determined in this work are similar to those informed in the literature for experiments without microwave application. The application of microwaves in combination with pulsed fluidization of the turnip seeds resulted in a fourfold increase of the effective diffusivity.     

Drying of Turnip Seeds with Microwaves in Fixed and Pulsed Fluidized Beds

This article presents experimental and modeled drying kinetics of turnip seeds as a function of the type of air-particle contact (fixed bed, pulsed fluidized bed), humidity of the air, and three levels of microwave irradiation. The effects of those factors on the drying time required to reach a moisture content of 0.1 kg/kg d.b. were determined with an experimental design of 12 experiments by using the software Statgraphics. It was found that in drying, a significant factor was the application of microwaves to a pulsed fluidized bed. The effect of the humidity of the air only became noticed when the moisture contents of the seeds was below 0.2 kg/kg d.b. The simplified variable diffusivity model (SVDM) gave the least deviations for the experimental data. The effective diffusivity values determined in this work are similar to those informed in the literature for experiments without microwave application. The application of microwaves in combination with pulsed fluidization of the turnip seeds resulted in a fourfold increase of the effective diffusivity.     

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10^?10 to 6.73 × 10^?10 m²/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.     

Mathematical Modeling of the Fluidized Bed Drying of Cubic Materials

The unsteady‐state simultaneous heat and mass transfer between gas and potato cubes during the drying process in a batch fluidized bed was described by a mathematical model. Mass transfer was considered to occur in three dimensions whereas heat transfer between the gas and dried material was assumed to be lumped. It was found that the model could describe the drying process with acceptable accuracy. The moisture profile inside the material at any cross‐section and at any time can be predicted by the model.     

Pore-Level Modeling of Isothermal Drying of Pore Networks Accounting for Evaporation,Viscous Flow,and Shrinking

Abstract

Simulation results of pore-level drying of non-hygroscopic, non-rigid, liquid-wet porous media are presented. Two- and three-dimensional pore networks represent pore spaces. Two kinds of mechanisms are considered: evaporation and hydraulic flow. The process is considered under isothermal conditions. Capillary forces thus dominate over viscous forces and the drying is considered as a modified form of invasion percolation. Liquid in pore corners allows for hydraulic connection throughout the network. During drying, liquid is replaced by vapor by two fundamental mechanisms: evaporation and pressure gradient–driven liquid flow. The development of capillary pressure as menisci turn concave induces shrinkage of the matrix, which contributes to the pressure gradient that drives liquid toward the surface of the network. Using Monte Carlo simulation, we find evaporation and drainage times; the shortest calculated indicates the controlling mechanism. Here we report distributions of liquid and vapor as drying time advances. For the calculation of transport properties, details of pore space and displacement are subsumed in pore conductances. Solving for the pressure field in each phase, vapor and liquid, we find a single effective conductance for each phase as a function of liquid saturation. Along with the effective conductance for the liquid-saturated network, the relative permeability of liquid and diffusivity of vapor are calculated.     

Pore-Level Modeling of Isothermal Drying of Pore Networks Accounting for Evaporation, Viscous Flow, and Shrinking

Simulation results of pore-level drying of non-hygroscopic, non-rigid, liquid-wet porous media are presented. Two- and three-dimensional pore networks represent pore spaces. Two kinds of mechanisms are considered: evaporation and hydraulic flow. The process is considered under isothermal conditions. Capillary forces thus dominate over viscous forces and the drying is considered as a modified form of invasion percolation. Liquid in pore corners allows for hydraulic connection throughout the network. During drying, liquid is replaced by vapor by two fundamental mechanisms: evaporation and pressure gradient-driven liquid flow. The development of capillary pressure as menisci turn concave induces shrinkage of the matrix, which contributes to the pressure gradient that drives liquid toward the surface of the network. Using Monte Carlo simulation, we find evaporation and drainage times; the shortest calculated indicates the controlling mechanism. Here we report distributions of liquid and vapor as drying time advances. For the calculation of transport properties, details of pore space and displacement are subsumed in pore conductances. Solving for the pressure field in each phase, vapor and liquid, we find a single effective conductance for each phase as a function of liquid saturation. Along with the effective conductance for the liquid-saturated network, the relative permeability of liquid and diffusivity of vapor are calculated.     

Drying of Potato Slices in a Pulsed Fluidized Bed

This article presents experimental and modeled drying kinetics of potato slices of the Desiree variety (9 × 9 × 3 mm³) in a pulsed fluid bed as a function of the air velocity, air temperature, and rotating disk velocity of the pulse generator. A statistical multifactor experimental design (2³) was applied to analyze the drying process with two levels each of drying temperature, air velocity, and rotating disk velocity. The results showed that the significant factors were air temperature, air velocity, rotating disk velocity, and the binary interactions of air velocity with both the temperature and the rotating disk velocity. The simplified variable diffusivity model (SVDM) gave the least deviation for the experimental data. The effective diffusivity values determined in this work are similar to those reported in the literature.     

Drying of Potato Slices in a Pulsed Fluidized Bed

This article presents experimental and modeled drying kinetics of potato slices of the Desiree variety (9 × 9 × 3 mm³) in a pulsed fluid bed as a function of the air velocity, air temperature, and rotating disk velocity of the pulse generator. A statistical multifactor experimental design (2³) was applied to analyze the drying process with two levels each of drying temperature, air velocity, and rotating disk velocity. The results showed that the significant factors were air temperature, air velocity, rotating disk velocity, and the binary interactions of air velocity with both the temperature and the rotating disk velocity. The simplified variable diffusivity model (SVDM) gave the least deviation for the experimental data. The effective diffusivity values determined in this work are similar to those reported in the literature.     

Water Vapor Emission From Rigid Mesoporous Materials during the Constant Drying Rate Period

It has long been thought that the evaporation rate from mesoporous materials during the constant drying rate period (CDRP) is equal to that of a free-water surface, due to the presence of a liquid film covering the surface of the material. In this article we review several early articles and demonstrate that the experimental scrutiny this hypothesis has received is insufficient. Further, we report a set of evaporative drying experiments on eight building materials whose results also do not confirm such hypothesis. Indeed, the drying rate during the CDRP is not equal either among the tested materials or between these and the free-water surfaces. To explain the differences in drying rate, we have looked at the influence of surface texture and porosity. We have concluded that surface texture, which could increase the effective surface area of the materials, did not have a relevant effect on the CDRP drying rate. However, we have found a good correlation between the CDRP drying rate and capillary porosity. This is consistent with the hypothesis that drying occurs at the pore level during the CDRP. Further, it contradicts the suggestion that there is a film of water covering the surface of the materials during this period.     

Modeling Moisture Loss during Vacuum Belt Drying of Low-Fat Tortilla Chips

A continuous vacuum drying method was used to develop low-fat tortilla chips with good sensory properties. To better understand the process, drying models were developed to determine the effects of drying thickness and temperature on drying rate. Drying rates were determined at three conduction plate temperatures (80, 90, and 100°C) and three product thicknesses (0.8, 1.5, and 2.3 mm). An effective diffusion model and semi-empirical models were used to fit the data. In addition, a model was developed from the drying rate curves that incorporated a drying coefficient [k(t)] that varied with time and could be described by a two-term Lorentzian model. All models had good agreement between experimental data and predicted data, with R ² > 0.98. With consideration of other goodness-of-fit indicators (sum of squared errors [SSE] and χ²), the Page and variable coefficient models provided the best fit. The average effective moisture diffusivity was calculated using nonlinear regression and ranged from D _eff = 1.19 to 1.54 × 10^?9 m²/s. D _eff increased with temperature and was described by an Arrhenius equation with E _a  = 14.1 kJ/mol.

Continuous vacuum drying of a presteamed corn dough can be used to produce low-fat tortilla chips with high crispness and acceptable sensory properties. The drying rate models presented in this study will help predict appropriate drying times, optimize process conditions, and better understand the mechanisms of drying.     

多孔介质干燥孔道网络模型的研究进展

建立在物质微观传输基础上的孔道网络干燥理论，通过完全离散化的方法在孔道等级上对干燥过程进行研究，描述了多孔介质内部结构参数对干燥过程的影响。介绍了建立孔道网络模型的原理和方法，阐述了基于单元体上孔道网络研究的内容及目的，综述了基于产品等级上孔道网络研究的最新进展，阐明了孔道网络模型方法对干燥理论研究的重要意义。指出，进一步提高网络模型中孔道的拓扑等价性、形状的不规则性及尺寸的相关性，探索网络构建新方法以及增加孔道网络信息量，是孔道网络干燥理论的主要发展方向，并应加强同分形、渗流理论的进一步结合。     

Thin-Layer Drying of Flax Fiber: II. Modeling Drying Process Using Semi-Theoretical and Empirical Models

Thin-layer drying experiments were performed for drying flax fiber under four different drying conditions. In all drying treatments the absolute humidity of drying air was 0.0065 kg of water per kg of dry air, but the drying temperature were 30, 50, 70, and 100°C. The drying process was modeled using the drying data and five semi?theoretical and empirical models cited in different literatures. From the five tested models, the Page model gave the best fitting for experimental data with R ² equal to 0.99, for all treatments. The estimated drying constants at different drying temperatures were highly correlated with drying air temperature. The drying constants were also highly correlated with the calculated coefficient of diffusions.     

Thin-Layer Drying of Flax Fiber: II. Modeling Drying Process Using Semi-Theoretical and Empirical Models

Thin-layer drying experiments were performed for drying flax fiber under four different drying conditions. In all drying treatments the absolute humidity of drying air was 0.0065 kg of water per kg of dry air, but the drying temperature were 30, 50, 70, and 100°C. The drying process was modeled using the drying data and five semi-theoretical and empirical models cited in different literatures. From the five tested models, the Page model gave the best fitting for experimental data with R² equal to 0.99, for all treatments. The estimated drying constants at different drying temperatures were highly correlated with drying air temperature. The drying constants were also highly correlated with the calculated coefficient of diffusions.     

Modeling of the Seedless Grape Drying Process using the Generalized Differential Quadrature Method

Mathematical modeling of the grape drying process is important in understanding the transport phenomena involved in the production and processing of dried grapes. Drying models proposed in the literature have simplifying assumptions, and thus ignore important phenomena such as shrinkage and changes in transport properties which occur during the drying process. Consequently, a mathematical model is developed for the seedless grape drying process, which considers the effects neglected in previous models. Since an analytic solution to this nonlinear model is impossible, the generalized differential quadrature method is used to solve the models' equations. The model is validated with experimental data obtained from a laboratory scale convective tray dryer operating at 50–70 °C and an air velocity of 1.5 m/s. Model predictions are in close agreement with experimental data due to the inclusion in the model of shrinkage and variation in moisture diffusivity. Model results can serve as a framework to improve the performance of existing and novel dryers, and also in the design of process simulators for dryers.