Academic Open Internet Journal

Volume 11, 2004

Experimental determination of the diffusion coefficients of wood in isothermal conditions

Joseph Albert Mukam Fotsing

Senior Lecturer

Email: mukam_fotsing_j_a@fulbrightweb.org

And

Claude Wanko Tchagang

Graduate Student

University of Yaounde I

Ecole Normale Supérieure

P. O. Box 3482

Yaounde CAMEROON

ABSTRACT

The diffusion coefficients of frake (Terminalia superba) was determined in the radial, tangential, and longitudinal directions at tree different temperatures: 30°C, 35°C an 40°C.

The longitudinal diffusion coefficient is larger than the transverse diffusion coefficient. In addition the radial coefficient is larger than the tangential coefficient.

Keywords: diffusion coefficient, frake, isothermal diffusion, wood water relationships.

INTRODUCTION

The goal of this paper is to bring some elements of comprehension on the process of experimental determination of the diffusion coefficients of wood in isothermal conditions. These coefficients are of capital importance as well for drying, as for the modelling of the

hygroscopic behavior of wood. We will make a study of the diffusion of wood, that will enable us to try to understand the process of water transfer in wood, as well as the characteristics allowing to quantify it. We will make an experimental study with the aim to obtain the radial, tangential and longitudinal diffusion coefficients of frake (terminalia superba), a tropical wood species from Cameroon, at several temperatures.

MATERIALS ET METHODS

Diffusion is the process by which a fluid migrates and spreads itself through capillaries, vessels and cellular walls of wood.

Water is present in wood in two forms: interstitial water and bound water. The interstitial water is contained in the cellular cavities, and dependent water is retained in the cellular walls. The force which retains the interstitial water molecules is relatively weaker than that exerted on the bound water molecules. During the diffusion process, a difference in concentration between the various cellular layers is established. Water migrates then from the more concentrated medium towards the less concentrated one. The longitudinal diffusion results in the transport of the water molecules through fibres. Water is conveyed in fibres in the same way as a transport is made by pipe. As for the transverse diffusion, it results in the progressive crossing of several cellular cavities.

The gradient of steam pressures of water (Bramhall 1976) and the gradient of water concentration are supposed to play an important part in the forces responsible of the transport of water through wood. Researchers who studied this diffusion phenomena think in their great majority that, the diffusion is prevailed by the gradient of water concentration (Skaar 1954; Stamm 1960; Comstock 1963 Choong 1965).

Water diffuses in the form of vapor, of bound water and interstitial water. Each one of these cases obeys the Fick’s law.

(1)

The first Fick’s law stipulates that flow is proportional to the concentration gradient

(2)

On the other hand the second law of Fick takes into account the temporal dependence

) ou (3)

J is the flow of the considered parameter through wood. C is the concentration, Ñ is the gradient operator, D is the diffusion coefficient. The knowledge of the flux and the gradient makes it possible to deduce the diffusion coefficient .

The diffusion depends on the environmental hygrometric conditions and the temperature to which the studied sample is subjected. This phenomenon is very sensitive to the moisture content and the temperature. These parameters must be taken into account for the measurement of the diffusion coefficients of wood. Indeed, the variation of the moisture

content modifies the conductibility of wood. From measurements of the conductance of wood at a given moisture content, one can deduce the diffusion coefficient from it.

In order to undertake our study, we had the following material:

- Samples of fraké of 1 mm thickness, cut in a manner to obtain two large surfaces in the radial, tangent or axial plans,

- Cylindrical boxes of diffusion used as diffusion cups

- A water solution saturated with sodium chloride,

- A METLER PM15 electronic balance,

- A dry oven

- Wood adhesive and aluminium paper.

Les échantillons de bois, préalablement taillés pour s’adapter aux boîtes, ont été fixés sur les coupes contenant de l’eau salée, jusqu’à 5 mm du bord. L’ensemble, maintenu par la colle à bois et les bords fermés par du papier aluminium a servi de coupe de diffusion.

Le schéma de principe est le suivant :

Wood the samples, cut to adapt to the boxes openings, were fixed on the boxes containing the salted water, up to 5 mm of the edge. The unit, maintained by a woodworking glue and the edge closed by aluminium foil, was used as diffusion cup. Here are the picture of the cup (vaporimeter) and its chematic diagram :

Figure 1 : Picture of the vaporimeter (diffusion cup).

Echantillon de bois

Boîte de diffusion

Figure 2 : Schematic diagram of the vaporimeter (diffusion cup).

The diffusion cups are placed in the dry oven, at temperatures of 30° C, 35°C or 40°C. the device is then periodically weighed. The aim here is to be able to quantify the transfers of water moisture through wood. On the basis of numerical data obtained in stationary conditions, we calculate the flux of water moisture through the sample. These stationary conditions are established when the variation of mass is a linear function of time.

Knowing the transfer surface of the vaporimeter, the flux is calculated by the formula:

(4)

In addition, according to the first Fick’s law, we can write

(5)

from where

(6)

DC is the difference in water concentration between the solution and the wood sample.

Dz is the distance the specimen the solution (fig 2).

We deduce that

(7)

where DC is obtained by taking into account the water concentration in the wood sample at the end of the experiment.

At the end of the experiment, the sample is weighed (m) and desiccated with the oven, at 103°C. It is once more weighed (m_a). The water concentration is obtained by the relation

(8)

One can thus have the knowledge of the diffusion coefficient from the formula (7). This work is made for measures in the radial, tangential and longitudinal directions.

During our work, we used samples of thickness e=1mm, with Dz =5mm and cups of interior diameter d=12cm. We have hereafter the results obtained.

RESULTS AND DISCUSSION

The graphs of figures 3, 4 and 5 present the evolutions of the mass of the vaporimeter as a function of time, for the radial, tangential and longitudinal specimens at various temperatures.

Figure 3: Evolution of the weight of the vaporimeter according to time at 30°C.

Figure 4 : Evolution of the weight of the vaporimeter according to time at 35°C

Figure 5: Evolution of the weight of the vaporimeter according to time at 40°C

For each sample the transfer surface is s=113cm². On the basis of the graphic exploitation and using formula (7), we calculated the diffusion coefficients that are summarized in the following table:

Temperature	30°C	35°C	40°C
D_R(m²s^-1)	1,35 x 10^-11	3,70 x 10^-11	5.37 x 10^-11
D_L(m²s^-1)	3,23 x 10^-11	5,38 x 10^-11	6,73 x 10^-11
D_T(m²s^-1)	1,16 x 10^-11	2,65 x 10^-11	3,05 x 10^-11

Table 1: Diffusion coefficients of fraké at 30°C, 35°C and 40°C and a zero relative humidity.

We note that these coefficients are all of the order of 10^-11. Generally, the coefficients grow with the temperature. This is in agreement with the predictions of Choong (1963) and Stamm (1964) who obtained a variation of the diffusion coefficient according to Arrhenius law.

(9)

where E_b is the activation energy of wood.

Moreover, the longitudinal diffusion coefficient is the largest of all. Then, the radial coefficient is always higher than the tangential coefficient, probably because of the contribution of fibres in the transport of water. These results are in agreement with the theoretical predictions.

We deduced that the temperature causes the increase of the diffusion coefficient of wood. In addition we showed that the longitudinal diffusion is more important than the radial diffusion, more important than the tangential diffusion. In fact, the cellular cavities constitute obstacles difficult to cross for the water molecules or any other aqueous solution diffusing in wood.

Consequently, the longitudinal diffusion is 10 to 15 times faster than the transverse diffusion (radial and tangential). On tha other hand, the radial diffusion accross the rings is faster than the tangential diffusion, parallel with the rings. This is probably due to the contribution of fibres in the transport of water.

In 1959, Stamm made measurements of the coefficient of the longitudinal diffusion while following the evolution of an alloy lead-tin-bismuth introduced into the wood. He found that the layouts of moisture content according to the square root of the time of diffusion was linear. The coefficient of longitudinal diffusion results by the formula:

(10)

where E_L is the fraction of moisture at equilibrium according to time.

In 1963, Comstock formulated a relation giving the average diffusion coefficient by the relation :

(11)

is the coefficient of transverse diffusion at the moisture content (resp.M).

CONCLUSION

These results are likely to be useful in a modeling of the industrial wood seasoning of frake. Their consideration would be useful for the prediction of the hygroscopic behavior of frake in a given environment.

REFERENCES

Bramhall G. 1979. Mathematical model for lumber drying , Wood Sci. (12) 14-21.

Chen Y. , Choong E.T. 1994. Wetzel D. M. , optimum average diffusion coefficient: an objective index in description of wood drying data , Wood Fiber Sci. (26) 412-420.

Choong E.T. 1963. Movement of water through a softwood in the hygroscopic range , For. Prod. J. (13) 489-498.

Choong E.T. 1965. Diffusion coefficients of softwood by steady state and theoretical methods, For. Prod. J. (15) 21-27.

Comstock G. L. 1963. Moisture diffusion coefficients in wood calculated from adsorption , desorption and steady state data , For. Prod. J. (13) 97-103.

Siau J. F. 1965. Wood influence of water on physical properties , Virginia Tech. 227p.

Skaar, C. 1954. Analysis of methods for determining the coefficient of moisture diffusion in wood. For. Prod. J. 4:403-410.

Simpson W.T. 1993. Determination and use of moisture diffusion coefficient to characterize drying of northern red oak , Wood Sci. Technol. (27) 409-420.

Stamm, A. J. 1959. Bound-water diffusion into wood in the fiber direction. For. Prod. J. 9:27-32.

Zoulalian A. , Mouchot N. 2000. Détermination indirecte des coefficients de diffusion de la vapeur d’eau dans les directions tangentielle et radiale du hêtre , Ann. For. Sci.( 57) 793-801.

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