A STUDY ON THE SEPARATION OF DIFFUSION AND SURFACE EMISSION COEFFICIENTS IN WOOD

ABSTRACT

For a more accurate simulation of the moisture sorption process in wood, the precise separation of surface emission and diffusion coefficients is essential. In this paper, a non-linear simplex technique that was developed to obtain the optimum pair of the surface emission coefficient he, and the diffusion coefficient D from a single sorption curve is presented and tested with experimental data. An easy to use computer program was employed to carry out the evaluation. Data analysis showed that the new method resulted in a more statistically accurate calculation of b_c and D than currently existing methods.     

Isothermal Vapour and Liquid Transport Inside Clay During Drying

ABSTRACT

A model is presented to describe the moisture transport inside a partially saturated porous material. The transport is caused by vapour diffusion and liquid diffusion. The evaporation inside the porous material is described with a mass transfer coefficient and a specific evaporating surface. Predictions of the model for moisture profiles are compared to experimentally oblained profiles found in the literature. The model needs further extension in the form of incorporating sorption isotherms.     

Mathematical Relationship Between Surface Emission and Diffusion Coefficients

This naver analvzes the surface emission coefficient corresponding to anv diffusion coefficient expressed as an exponential function of the concentration diffusing substance in capillary porous solids. Theoretical equations for surface emission coefficient for both sorption and desorption are presented. Procedures to derive the diffusion coefficient and to verify the corresponding surface emission coefficient are made using experimental sorption data of aspen (Populur sp.) wood. It is of interest to note that the theoretical models for diffusion and surface emission coefficients can be established and/or evaluated using the same set of experimental dara.     

Isothermal Vapour and Liquid Transport Inside Clay During Drying

ABSTRACT

A model is presented to describe the moisture transport inside a partially saturated porous material. The transport is caused by vapour diffusion and liquid diffusion. The evaporation inside the porous material is described with a mass transfer coefficient and a specific evaporating surface. Predictions of the model for moisture profiles are compared to experimentally obtained profiles found in the literature. The model needs further extension in the form of incorporating sorption isotherms.     

MATHEMATICAL RELATIONSHIP BETWEEN DESORPTION AND SORPTION SOLUTIONS

ABSTRACT

This paper presents a theoretical equation relating the dimensionless times of Newman's solutions of the diffusion equation for desorption and sorption. The derived equation provides a theoretical proof of the linear relationship between dimensionless time and the inverse of transport ratio for a given fraction of diffusing substance as observed numerically in the literature. Following the same approach proposed earlier by the writer, a theoretical expression for the diffusion coefficient is derived as a function of time and the inverse of desorption rate when the fraction of diffusing substance is 0.5. Evaluation of the diffusion coefficient from an experimental desorption curve is discussed.     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

ABSTRACT

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

SOLUTIONS OF DIFFUSION EQUATION WITH CONSTANT DIFFUSION AND SURFACE EMISSION COEFFICIENTS

ABSTRACT

Closed-form solutions of the non-steady state diffusion equation with constant transport coefficients are presented. The diffusion coefficient is assumed to be finite, but the surface emission coefficient can be either finite or infinite. Mathematical conditions are established for the transport coefficients to be constant. When these conditions are met, the transport coefficients can then be easily evaluated. Diffusion test data can be compared against these conditions to determine whether or not the transport coefficients are constant. Desorption test data of northern red oak indicate that initial moisture content in wood and equilibrium moisture content in the environment are closely related to the constancy of the transport coefficients.     

Water diffusion into transcrystalline layers on polypropylene

The diffusion constant of water through transcrystalline surface layers on isotactic polypropylene (i‐PP) is reported. A suitable experimental technique was developed, based on sorption or desorption measurements. The accompanying change in sample weight is detected by the corresponding change in mechanical resonance frequency. The facility allows investigation of the diffusion current parallel to as well as perpendicular to the sample surface. Tests with commercial polyethylene films revealed that reproducibility and reliability are better than 6%. The samples were prepared as thin films in which the transcrystallinity was controlled by use of several substrate materials and different thermal conditions during solidification of the melt. The water diffusion constant of finely spherulitic i‐PP turned out to be 15.9 μm²/s; whereas the values for transcrystalline material amounted to 19.6 μm²/s parallel and between 12 and 10 μm²/s perpendicular to the film surface, depending on the actual supermolecular structure. These results are discussed with respect to the underlying transcrystalline texture and the texture of the amorphous percolation network. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 3275–3285, 1999     

Diffusion coefficient and equilibrium solubility of water molecules in biodegradable polymers

The diffusion coefficient and solubility of water molecules were measured in polyglycolide (PGA), poly(L ‐lactide) (PLLA), poly[(R)‐3‐hydroxybutyrate] (PHB), poly(ϵ‐caprolactone) (PCL), and Skygreen^R (SG). The diffusion coefficient and equilibrium solubility decreased in the order SG > PCL > PLLA > PHB > PGA and PGA > SG > PLLA > PHB > PCL, respectively. The diffusion coefficient and solubility of water at low sorption temperature in PHB varied according to the initial crystallinity of the matrix polymer even though crystallization of PHB molecules took place during the sorption experiment. In contrast, the amorphous PLLA and the crystalline PLLA showed an almost identical diffusion coefficient and solubility of water, in spite of the fact that the amorphous PLLA remained practically amorphous during the whole sorption procedure. A strong correlation existed between the water solubility and the surface tension or contact angle of the polymer matrix. The water diffusivity in PGA was almost 2 orders of magnitude lower while water was more soluble in PGA with a lower heat of sorption than that corresponding to the other more hydrophobic polymers, indicating that the transport of water molecules in PGA followed the solution–diffusion model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1716–1722, 2000     

Water sorption behaviors of the BPDA‐based polyimide films depending upon the structural isomers of diamine

For the biphenyltetracarboxylic dianhydride (BPDA)‐based polyimide thin films, the water sorption behaviors were gravimetrically investigated by using a thin film diffusion analyzer. The water sorption behaviors of the polyimide thin films are quite different and strongly dependent upon the sort of polyimide. The diffusion coefficients of the polyimide thin films vary in the range of 1.6 × 10⁻¹⁰ to 12.4 × 10⁻¹⁰cm²/s and the water uptakes vary from 1.52 to 5.25 wt %. Both the diffusion coefficient and water uptake of the polyimide thin films are in the increasing order: BPDA‐pPDA < BPDA‐p,p′ODA < BPDA‐p,m′ODA < BPDA‐mPDA ∼ BPDA‐p,p′DDS < BPDA‐m,m′DDS. Specifically, the polyimide films with para‐oriented linkages in backbone structure showed relatively lower diffusion coefficient and water uptake than the corresponding polyimide films with meta‐oriented linkages because of the well‐developed crystalline structure and good intermolecular chain ordering. In addition, the polyimide thin films having higher chain order showed relatively lower diffusion coefficient and water uptake. The crystallinity and intermolecular chain ordering in the morphological structure are critical parameters in controlling the water sorption behaviors of the polyimide thin films. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2121–2127, 2001     

EFFECTIVE DIFFUSION COEFFICIENT OF ACTIVE SOLVENTS IN COMPOSITE POLYMERIC MATERIALS

ABSTRACT

A method and a device for determination of the effective diffusion coefficient of active solvents in composite polymeric materials (CPM) based on cellulose derivatives are proposed and examined. This method accounts for anomalous mass transfer phenomena, considerable shrinkage and changes of sorption capacity of the CPM specimen allowing selection of the rational technological regime. Results of experimental studies on diffusion of acetone and ethanol in cellulose nitrate with various degrees of substitution are given as examples.     

MODELING OF ROUGH RICE DRYING IN THIN VERTICAL COLUMNS

ABSTRACT

The solution of classical diffusion equation based on the assumption of average moisture diffusion coefficient did not adequately represent natural convection drying of rough rice in thin vertical columns exposed on both sides to hot air. Instantaneous moisture diffusivity coefficients determined from experimental drying curves decreased continuously with an increase in exposure duration and were linearly related to moisture ratio. The proponionality constant which was called apparent moisture diffusion coefficient was distinctly related to air temperature, relative humidity, and initial moisture content of rough rice. The modified moisture diffusion model using the instantaneous moisture diffusion coefficient was found to best represent the moisture removal from bulk rough rice.     

Sorption and desorption parameters of water or ethanol in light‐cured dental dimethacrylate resins

Two cycles of sorption/desorption of water or ethanol by light‐cured dental resins of bisphenol A glycol dimethacrylate (Bis‐GMA), bisphenol A ethoxylated dimethacrylate (Bis‐EMA) urethane dimethacrylate (UDMA) triethylene glycol dimethacrylate and decanediol dimethacrylate (D₃MA) were studied. The experimental curves m_t = f(t) taken for the first water sorption by poly‐Bis‐GMA, poly‐Bis‐EMA and poly‐UDMA showed a maximum. A maximum was also observed in the curve obtained for first sorption of ethanol by poly‐Bis‐GMA. In all other cases, the curves for sorption or desorption of water or ethanol showed Fickian behavior. The experimental data obtained for first sorption of water or ethanol were perfectly fitted to a new proposed equation, which predicts water or ethanol sorption with simultaneous extraction of unreacted the monomer. This equation gave us the possibility for the determination of the diffusion coefficient of the extraction of the unreacted Bis‐GMA during the water and ethanol sorption, as well as the diffusion coefficient of the extraction of the unreacted Bis‐EMA and UDMA during the water sorption. The maximum water or ethanol absorbed at equilibrium and the diffusion coefficient are determined from the second sorption/desorption cycle during which the extraction of the monomer is negligible. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Isothermal Vapour and Liquid Transport Inside Clay During Drying

A model is presented to describe the moisture transport inside a partially saturated porous material. The transport is caused by vapour diffusion and liquid diffusion. The evaporation inside the porous material is described with a mass transfer coefficient and a specific evaporating surface. Predictions of the model for moisture profiles are compared to experimentally oblained profiles found in the literature. The model needs further extension in the form of incorporating sorption isotherms.     

Isothermal Vapour and Liquid Transport Inside Clay During Drying

A model is presented to describe the moisture transport inside a partially saturated porous material. The transport is caused by vapour diffusion and liquid diffusion. The evaporation inside the porous material is described with a mass transfer coefficient and a specific evaporating surface. Predictions of the model for moisture profiles are compared to experimentally obtained profiles found in the literature. The model needs further extension in the form of incorporating sorption isotherms.     

Cellulose nanofibres and cellulose nanowhiskers based natural rubber composites: Diffusion,sorption, and permeation of aromatic organic solvents

This article investigates the transport behavior of three aromatic organic solvents, viz. benzene, toluene, and p‐xylene in natural rubber nanocomposite membranes containing cellulose nanofibres (CNFs) and cellulose nanowhiskers (CNWs) isolated from bamboo pulp. The solvent molecules act as molecular probes to study the diffusion, sorption, and permeation through the nanocomposites, and provide information on the nanocomposite structure and matrix–filler interactions. Both the nanocelluloses were found to decrease the uptake of aromatic solvents in nanocomposite membranes, but the effect was more significant in the case on nanofibers compared to nanowhiskers. Furthermore, the uptake decreased with increased penetrant size; being the highest for benzene and the lowest for p‐xylene. Transport parameters such as diffusion coefficient, sorption coefficient, and permeation coefficient have been calculated. Comparison of the experimental values of equilibrium solvent uptake with the predicted values indicated that both the nanocelluloses have restricted the molecular mobility at the interphase and thereby decreased the transport of solvents through the materials; being more significant for nanofibers. The results showed that both the used cellulosic nanomaterials act as functional additives capable of manipulating and tailoring the transport of organic solvents through elastomeric membranes, even at concentrations as low as 2.5 wt %. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Water sorption kinetics in light‐cured poly‐HEMA and poly(HEMA‐co‐TEGDMA); determination of the self‐diffusion coefficient by new iterative methods

The present investigation is concerned with the determination of self‐diffusion coefficient (D) of water in methacrylate‐based biomaterials following Fickian sorption by two new methods: the Iterative and the Graphical methods. The D value is traditionally determined by means of the initial slope of the corresponding sorption curve and the so‐called Stefan's approximation. The proposed methods using equations without approximations and data resulting from the whole sorption range reach to accurate values of D, even when the sorption curve does not present an initial linear portion. In addition to D, the Graphical method allows the extrapolation of the mass of the sorbed water at equilibrium (M_∞), even when the equilibrium specimen's mass fluctuates around its limited value (m_∞). The test of the proposed procedures by means of ideal and Monte Carlo simulated data revealed that these methods are fairly applicable. The obtained D values compared with those determined by means of the Stephan's method revealed that the proposed methods provide more accurate results. Finally, the proposed methods were successfully applied to the experimental determination of the diffusion coefficient of water (50°C) in the homopolymer of 2‐hydroxyethyl methacrylate (HEMA) and in the copolymer of HEMA with triethylene glycol dimethacrylate (98/2 mol/mol). These polymers were prepared by light curing (λ = 470 nm) at room temperature in presence of camphorquinone and N,N‐dimethylaminoethyl methacrylate as initiator. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

TWO-STAGE MOISTURE DIFFUSION IN WOOD WITH CONSTANT TRANSPORT COEFFICIENTS

To determine whether transport coefficients in desorption curves for northern red oak are constant, four sets of desorption data were compared against previously established mathematical conditions for infinite-series solution of the non-steady-state diffusion equation. For each data set, when moisture fraction in wood is above a certain value, designated as the first stage, these conditions are satisfied, with the diffusion and surface emission coefficients being positive and finite; below that value, designated as the second stage, these conditions are still satisfied, with the diffusion coefficient taking a smaller positive value but the surface emission coefficient becoming negative and finite. Mathematically, these two pairs of transport coefficients can be used to predict the whole diffusion curve that describes the variation of moisture fraction with time. However, the negative surface emission coefficient in the second stage of the desorption process implies that the moisture gradient has cut the surface at a point below the equilibrium moisture content, which is physically impossible. Alternatively, the second stage can be considered as a new stage with moisture fraction values normalized with respect to the lowest value in the first stage, which is also the starting point of the second stage. The transport coefficents are obtained in the same manner as in the first stage and are found to be positive and finite. The two pairs of transport coefficients can describe the diffusion curve with high accuracy. However, the assumption used in the second stage is that the initial moisture content in wood is uniform, which again is physically impossible. We therefore conclude that the transport coefficients for northern red oak are not constant. Although the two-stage approaches presented in this study can predict the diffusion curves accurately, their physical interaction is difficult to justify.     

DIFFUSION COEFFICIENTS OF CARBON DIOXIDE WITHIN TYPE 13X ZEOLITE PARTICLES

The self-diffusion processes of CO₂ in a single particle of commercial type 13X zeolite have been studied by a new sorption rate method using a constant volume, variable pressure system. Experiments were carried out at 303.2 and 343.2 K. An inverse analysis of experimental uptake curves based on a macropore and micropore series diffusion model was performed to determine effective diffusion coefficients for both macropore and micropore diffusion simultaneously. Knudsen diffusion occurs within the macropore and the micropore diffusion coefficients having values of the order 10^?15–10^?14 m²/s, which are slightly greater than the previously reported micropore diffusion coefficients of type 5A zeolite crystals.     

MATHEMATICAL RELATIONSHIP BETWEEN DESORPTION AND SORPTION SOLUTIONS

This paper presents a theoretical equation relating the dimensionless times of Newman's solutions of the diffusion equation for desorption and sorption. The derived equation provides a theoretical proof of the linear relationship between dimensionless time and the inverse of transport ratio for a given fraction of diffusing substance as observed numerically in the literature. Following the same approach proposed earlier by the writer, a theoretical expression for the diffusion coefficient is derived as a function of time and the inverse of desorption rate when the fraction of diffusing substance is 0.5. Evaluation of the diffusion coefficient from an experimental desorption curve is discussed.