Moisture Diffusion Model Research Articles

Internal Heating Effect and Enhancement of Drying of Ceramics by Microwave Heating with Dynamic Control

The effectiveness of internal heating for enhancing the drying of molded ceramics is evaluated by both modeling and experiments. In the theoretical analysis, three dimensional drying-induced strain-stress are modeled, and the numerical solutions show that the internal heating generates lower internal stress than continuous convective heating or intermittent convective heating. Microwave drying is examined experimentally to study the effect of internal heating on the drying behavior of a wet sample of a kaolin slab. The drying behavior is compared among three modes: microwave heating, hot air heating and radiation heating. The transient behavior of temperatures in microwave drying is quite different from conventional drying by external heating. In particular, the temperature of the slab drops once in the progress of drying. This phenomenon cannot be predicted adequately by a simple model of one-dimensional heat conduction and moisture diffusion accompanied with an internal heat generation rate given as a linear function of the moisture content. It should be noted that the temperature behavior takes place due to the combined interactions with internal evaporation of moisture by rise in internal vapor pressure and shift of impedance or interference in the applicator. Microwave heating with a constant power above 100 W results in sample breakage due to the internal vapor pressure. However, if the power is dynamically controlled so as to maintain the temperature less than the boiling point of water, the drying succeeds without any crack generation until completion with a significantly faster drying rate than drying in convective heating or in the oven.

Two-Dimensional Moisture Flow–Soil Deformation Model for Application to Pavement Design

Seasonal cycles of wetting and drying in highway subgrade soils induce corresponding cycles of soil swelling and shrinkage that contribute to roughness and loss of serviceability of pavements. The design of defensive measures to mitigate the effects of this process requires a realistic model of moisture diffusion and associated swelling and shrinkage of soil. A Windows-based two-dimensional finite element program, FLODEF, is presented; it performs a sequentially coupled flow-displacement analysis for the prediction of vertical movement in highway subgrade soils. The theoretical formulations of moisture flow and stress–deformation components of the model are introduced first. Parametric studies illustrate capabilities of the model to evaluate the effectiveness of vertical moisture barriers, horizontal barriers, soil replacement or improvement, and paved medians in reducing swell–shrink deformations beneath highway pavements.

Two-Dimensional Moisture Flow-Soil Deformation Model for Application to Pavement Design

Seasonal cycles of wetting and drying in highway subgrade soils induce corresponding cycles of soil swelling and shrinkage that contribute to roughness and loss of serviceability of pavements. The design of defensive measures to mitigate the effects of this process requires a realistic model of moisture diffusion and associated swelling and shrinkage of soil. A Windows-based two-dimensional finite element program, FLODEF, is presented; it performs a sequentially coupled flow-displacement analysis for the prediction of vertical movement in highway subgrade soils. The theoretical formulations of moisture flow and stress-deformation components of the model are introduced first. Parametric studies illustrate capabilities of the model to evaluate the effectiveness of vertical moisture barriers, horizontal barriers, soil replacement or improvement, and paved medians in reducing swell-shrink deformations beneath highway pavements.

Modeling of Moisture Diffusion in Crushed Basaltic Rock Stabilized with Cementitious Binders

The prediction of moisture diffusion within the cementitiously stabilized materials is essential for assessing their shrinkage and associated cracking potential. A theoretical approach was presented for modeling of moisture loss during drying of cementitiously stabilized pavement materials. The moisture loss process was characterized by isotropic nonlinear diffusion theory. Laboratory experiments were undertaken to measure the material properties and characteristics that included the coefficient of moisture diffusivity and the humidity isotherm. Independent laboratory tests were undertaken to validate the theoretical approach adopted, and the experimental and predicted results displayed close agreement. The laboratory results indicated that as the drying progressed, the rate of moisture loss became slower, which can be explained by the reduction in the coefficient of moisture diffusivity with the decrease of moisture content. The humidity isotherms measured also indicated that the stabilized pavement materials appear not to dry significantly further after they reach a pore relative humidity of about 65%.

A comparison of three models of 1-h time lag fuel moisture in Hawaii

The U.S. National Fire Danger Rating System currently uses a moisture diffusion model developed by Fosberg to predict fine fuel moisture in woody fuels. Nelson recently developed a fuel moisture model that includes functions for both heat and moisture transfer. Fuel moisture samples were collected in Hawaii hourly for up to 96 h for three litter, one herbaceous, and eight grass fuels at sites ranging from near sea level to 2200 m. Weather data were collected every 5 min. Observed fuel moistures were compared to predictions from three models—a simplified form of Fosberg's equation (Simple), the Nelson physical model, and a Markov model fit to the observed data. Mean difference, average deviation, and percentage of predictions closer to the observed data than the Simple model were used to evaluate model performance. Performance of the Markov model was best and of the Simple model was poorest. All models underestimated fuel moisture with the Simple model having the greatest errors and the Markov model having the smallest. The Markov model and the Nelson model predictions were closer to the observed fuel moistures than the Simple model for more than 75% of the observations. Further testing and application of the Nelson physical model is recommended.

Research on the effect of microwave pretreatment on moisture diffusion coefficient of wood

Based on the pathway of moisture diffusion in wood below FSP, an improved moisture diffusion model has been proposed. The theoretical solution of the mathematic model shows that the diffusion coefficient for microwave pretreated wood was increased no more than 3% compared with that of wood without being treated even under extreme condition. Experiments indicate that the pit membrane structure can be effectively destroyed during microwave pretreatment, but the moisture diffusion coefficient can not be significantly improved. In practice, the effect of microwave pretreatment on moisture diffusion coefficient can be ignored. The drying rate of wood during the sequent conventional drying can not be significantly improved by microwave pretreatment.

Modeling of moisture migration in an FRP reinforced masonry structure

The study of moisture migration in a layered structure made of distinct building materials is of great importance for the understanding of its hygrothermomechanical response and for the design consideration of long-term structural integrity and durability. Modeling of moisture migration in an fiber reinforced polymer (FRP) composite upgraded masonry structure is particularly necessary, since the interfacial adhesive between the reinforcing FRP laminate and the host masonry can be susceptible to moisture damages. In this study, a generic theoretical formulation based on the framework of the Fourier moisture diffusion model was developed for a layered structure. The resulting governing equation was expressed in terms of humidity potential state variable whose relation with the moisture content state variable of the constituent material was defined in the sorption isotherm material property. Finite element implementation of the humidity potential formulation was also carried out. The finite element humidity migration modeling scheme was then utilized to perform two case studies. It was shown that the moisture migration processes in a concrete slab with a reinforcing FRP laminate partially covering one surface as well as in an FRP reinforced URM unit with air cavity can be captured in details when these structures are subjected to outdoor/indoor isothermal humidity gradients.

Three-Dimensional Model for Moisture and Volume Changes Prediction in Expansive Soils

A three-dimensional moisture diffusion and volume change model Suction heave ~SUCH! is described. The model SUCH is capable of predicting soil moisture changes in terms of soil suction and the resulting volume changes ~shrink/heave! in expansive soils under a covered area ~e.g., flexible slab model ! with respect to time when the supporting soil mass is subjected to different edge conditions that commonly cause moisture changes ~e.g., climate, trees, ponded water!. The moisture movement in unsaturated soils model was based on Mitchell's diffusion equation for soil suction and the volume changes ~shrink/heave! calculation was based on Wray's model. The model SUCH was validated against field data from four test sites in three countries ~i.e., United States, Saudi Arabia, and Australia! with widely varying climatic and soil conditions. In each of these widely diverse sites, the moisture diffusion and volume change model SUCH was shown to be valid.

Method for Calculating the Edge Moisture Variation Distance

A three-dimensional moisture diffusion and volume change model was developed for determining the distribution of soil suction and the associated volume changes in an expansive soil mass under a covered area (e.g., slab foundations or pavements) with respect to time. The model was used to determine a relationship among the edge moisture variation distance, em, the amplitude of surface suction change, U0, and the diffusion coefficient of the soil, α. The edge moisture variation distance calculation is based on the change in soil suction beneath the covered area as a result of climate changes. The edge moisture variation distance is considered to be the distance between the edge of the covered area and the point beneath the covered area where suction change is no more than 0.12 kPa (0.1 pF). Comparison between the predicted values of edge moisture variation distance by using the proposed relationship to that measured in the field or predicted by other methods is also presented.

Shallow Slides in Compacted High Plasticity Clay Slopes

Shallow slide failures in embankments constructed of high plasticity clays create costly maintenance problems on highway projects and can threaten the integrity of water-retaining earth structures. This paper investigates the mechanisms of stability degradation that lead to these slope failures. The failure mechanism involves moisture infiltration into the slope surface that leads to decreases in suction and soil shear strength. Both the degree and time rate of strength loss are investigated based on stability and moisture diffusion analyses, respectively. Stability analyses indicate that the failures are associated with destabilizing hydraulic gradients in the pore water, and the suction level at the surface of the slope declines to a limiting suction of about u = 2 pF when exposed to moisture. Moisture diffusion analyses indicate that the time rate of strength degradation is controlled by the depth and spacing of desiccation cracks that form in the soil mass and the moisture diffusion properties of the soil. The stability and moisture diffusion models described above were evaluated in light of 34 documented shallow slides in Texas high plasticity clays.

Reducing spatial dimensionality in a model of moisture diffusion in a solid material

A model of the moisture movement in solid wood under isothermal conditions taking into consideration coating (insulation) of the surface of the material, is presented in a 2-D-in-space formulation. The validity of using a corresponding 1-D model on a 2-D problem is investigated. A measure of reliability of the 1-D model is introduced. This paper presents a new technique, which adjusts the width of a material as well as the degree of coating of the edges, to ensure the relative error of the problem solution is less than the required, resulting from reducing the model from 2-D to 1-D-in-space. This technique is based on the computer simulation of 2-D diffusion to estimate the reliability of the corresponding 1-D diffusion model.

Reliability assessment and hygroswelling modeling of FCBGA with no-flow underfill

In the flip-chip ball grid array (FCBGA) assembly process, no-flow underfill has the advantage over traditional capillary-flow underfill on shorter cycle time. Reliability tests are performed on both unmolded and molded FCBGA with three different types of no-flow underfill materials. The JEDEC Level-3 (JL3) moisture preconditioning, followed by reflow and pressure cooker test (PCT) is found to be a critical test for failures of underbump metallization (UBM) opening and underfill/die delamination. In this paper, various types of modeling techniques are applied to analyze the FCBGA-8×8 mm on moisture distribution, hygroswelling behavior, and thermomechanical stress. For moisture diffusion modeling, thermal-moisture analogy is used to calculate the degree of moisture saturation in the multi-material system of FCBGA. The local moisture concentration along the critical interface, e.g. die/underfill, is critical for delamination, because the moisture weakens the interfacial adhesion strength, generates internal vapor pressure during reflow, and induces tensile hygroswelling stress on UBM during PCT. The results of moisture distribution can be used as loading input for the subsequent hygroswelling modeling. The magnitude of hygroswelling stress acting on UBM is found to be greater than the thermal stress induced during reflow, both in tensile mode which may cause the UBM-opening failure. Underfill with lower saturated moisture concentration ( C sat) and coefficient of moisture expansion (CME) are found to induce lower UBM stress and has better reliability results. Molded package generally has higher stress level than unmolded package. Parametric studies are performed to study the effects of no-flow underfill materials, package type (molded vs. unmolded), die thickness, and substrate size on the stresses of UBM during reflow and PCT.

Moisture Damage Evaluation of Asphalt Mixtures by Considering Both Moisture Diffusion and Repeated-Load Conditions

Two moisture damage models based on major moisture failure mechanisms are proposed. The adhesion failure model was developed to analyze the adhesive fracture between asphalt and aggregate in the presence of water. Cohesive and adhesive fractures in an asphalt-aggregate system are directly related to the surface energy characteristics of asphalt and aggregate. The surface energy of adhesion with or without the presence of water can be calculated from the surface energies of asphalt and aggregate. A moisture diffusion model was developed based on the one-dimensional consolidation of soil and a gas adsorption model. The moisture diffusion model was used to obtain the moisture diffusion characteristics of asphalt binders, including the amount of moisture that can permeate a binder and the diffusivity of the binder. The amount of moisture that permeates a binder is identified as a key factor in the moisture damage. Finally, mechanics-based experiments conducted on asphalt mixtures validated the results from the adhesion failure and diffusion models.

Test of Four Different Experimental Methods to Determine Sorption Isotherms

One important property of materials is their moisture fixation capacity, i.e., their ability to hold moisture at different relative humidities. The sorption isotherm is one of the main input data in moisture diffusion models, and it can also be used to evaluate properties of the microstructure. We have used four different methods to measure the sorption isotherm of sandstone and porous glass. The first method was to equilibrate samples over saturated salt solutions. The second was a sorption balance in which small material samples were weighed as they were exposed to different relative humidities. The third method was the pressure plate extractor, in which a totally wet sample was equilibrated at various overpressures, corresponding to certain relative humidities. The fourth method was a newly developed microcalorimetric technique to measure sorption isotherms. Despite the different natures of the methods, a satisfying agreement was found.

Reliability of One Dimensional Model of Moisture Diffusion in Wood

A model of the moisture diffusion in wood under isothermal conditions taking into con- sideration coating of the surface of a specimen is presented in a 2-D-in-space formulation. A re- liability of a corresponding 1-D model is investigated for a simulation of moisture movement in 2-D medium. This paper presents a technique to determine the width as well as the degree of edges coating of the specimen making the 1-D model relevant for 2-D medium. This technique bases on the computer simulation of 2-D moisture diffusion to estimate the reliability of the corresponding 1-D model. In the technique, approximate coefficients of the diffusion and surface emission may be employed if accurate values of these coefficients are unknown. Wood drying is a highly energy intensive process of some industrial significance. It is a process whereby the moisture moves from an area of higher moisture content to an area of lower moisture content within the medium. When the surface moisture evaporates from the sides or ends, moisture moves from interior toward these locations. This process continues until the wood reaches its equilibrium moisture content with the ambient air climate (Skaar, 1988; Siau, 1984). Mathematical modelling is gaining an increasing acceptance within the timber dry- ing industry and the use of mathematical simulators, which describe the complex heat and mass transfer phenomena at a fundamental level, can provide important information which could be used in both the design and optimisation of the kiln (Rosen, 1987; Siau, 1984; Turner and Mujumdar, 1997). From a mathematical point of view, the moisture transport process can be treated as a diffusion problem based on the Fick's second law. A model of the wood drying, under ∗ This research was partially supported by Lithuanian State Science and Studies Foundation Grant

Modeling of moisture diffusion in the presence of bi-axial damage in polymer matrix composite laminates

It is now well known that Fick’s Law is frequently inadequate for describing moisture diffusion in polymers and polymer composites. Non-Fickian or anomalous diffusion is likely to occur when a polymer composite laminate is subjected to external stresses that could give rise to internal damage in the form of matrix cracks. As a result, it is necessary to take into account the combined effects of temperature, stress (or strain), and damage in the construction of such a model. In this paper, a modeling methodology based on irreversible thermodynamics applied within the framework of composite macro-mechanics is extended to the case of a bi-axially damaged laminate. The model allows characterization of non-Fickian diffusion coefficients as well as moisture saturation level from moisture weight gain data for laminates with pre-existing and non-evolving damage. A symmetric damage tensor based on continuum damage mechanics is incorporated in this model by invoking the principle of invariance with respect to coordinate transformations. For tractability, the diffusion governing equations are simplified for the special case of a laminate with bi-axially oriented matrix cracks that is subjected to a uniaxial tensile stress. The final equations obtained from this derivation indicate that both effective diffusivity and maximum saturation level for this particular case can be expressed as quadratic functions of crack density. Comparisons with test data for a bi-axially damaged AS4/PR500 graphite/epoxy woven composite are provided for model verifications.

Tests of sequential data assimilation for retrieving profile soil moisture and temperature from observed L-band radiobrightness

Sequential data assimilation (Kalman filter optimal estimation) techniques are applied to the problem of retrieving near-surface soil moisture and temperature state from periodic terrestrial radiobrightness observations that update soil heat and moisture diffusion models. The retrieval procedure uses a time-explicit numerical model to continuously propagate the soil state profile, its error of estimation, and its interdepth covariances through time. The model's coupled soil moisture and heat fluxes are constrained by micrometeorology boundary conditions drawn from observations or atmospheric modeling. When radiometer data are available, the Kalman filter updates the state profile estimate by weighing the propagated state, error, and covariance estimates against an a priori estimate of radiometric measurement error. The Kalman filter compares predicted and observed radiobrightnesses directly, so no inverse algorithm relating brightness to physical parameters is required. The authors demonstrate Kalman filter model effectiveness using field observations and a simulation study. An observed 1 m soil state profile is recovered over an eight-day period from daily L-band observations following an intentionally poor initial state estimate. In a four-month simulation study, they gauge the longer term behavior of the soil state retrieval and Kalman gain through multiple rain events, soil dry-downs, and updates from radiobrightnesses.

MOISTURE DIFFUSION MODELING OF WHEAT KERNELS DURING SOAKING

A finite element moisture diffusion model was refined for the purpose of examining the distribution of moisturewithin single mature kernels of wheat. Among the gross kernel components (endosperm, pericarp, and germ), moisturediffusion coefficients of the endosperm and pericarp were determined from soaking experiments and optimized with afinite element model. Nine commercial varieties of wheat, representing six U.S. market classes or subclasses, wereexamined. Through separate soaking experiments of pearled wheat, which represented the endosperm alone, and intactwheat, which represented the pericarp by mathematical subtraction (neglecting the contribution from the germ), theranges in diffusion coefficients across the nine varieties were as follows: 0.46 10 10 1.4 10 10 m2/s for endosperm,0.042 1010 0.42 10 10 m2/s for pericarp. During finite element modeling, spherical and ellipsoidal geometrieswere assumed for pearled and intact kernels, respectively. With the kernel moisture ratio defined as the overall moisturecontent normalized with respect to the level of moisture at equilibrium, the soft varieties (Rely, Penawawa, andVanna) demonstrated a higher ratio than the hard variety TAM107. Agreement between modeled and measured valuesfor overall moisture content was very good, as seen by the ranges in the standard deviation of differences which were0.014-0.041 and 0.008-0.029% d.b. for pearled and intact kernels, respectively. Knowledge gained from this study will beuseful in understanding how the tempering process affects the milling of hard and soft wheats.

Analysis of the drying shrinkage behaviour of concrete using a micromechanical model based on the micropore structure of concrete

A micromechanical model for moisture diffusion within concrete and the associated shrinkage of concrete is presented in this paper. The model is based on the micropore structure of the concrete and the thermodynamic behaviour of the water in the pores. The drying shrinkage behaviour, both time-dependent moisture loss and volumetric change, of mortar and concrete specimens is analysed under various conditions. The suitability and applicability ofthe proposed model are discussed on the basis ofthe results.

Effect of Particle Structure on Quality Retention of Bio-Products During Thermal Drying

ABSTRACT To study the influence of particle structure on quality retention of hioproducts during thermal drying, the porous particles formed of albumin and solid carriers were dried in a vibm-fluidized bed dryn at different inlet air temperatures and different initial bulk porosities. Equations to predict temperature and moishrre content of panicles as well as the kinetics of biomass degradation were developed. The particle bulk porosity was incorporated into concentration-dependent moisture diffusivity model to estimate the erect of particle structure on product quality. The analysis of both calculated and experimental results indicates that the more porous structure promotes moisture diffusion, increases drying rate and finally improves the quality retention of bio-products. An extensive literature survey on quality retention issues during thermal drylng has been done.