36 Drying of Wood

FIGURE 36.14 Relative permeability curves calculated using equations (36.10) and (36.11).10.8TransverseLongitudinalRelative permeability0.60.40.200 0.2 0.4 0.6 0.8Saturation1model of the tracheid shape proposed by Comstock(1970). Although it may be simplistic toassume that all tracheids have exactly the sameshape,theyobtainedagoodtrendforthecapillarypressure function by this means.. Because the longitudinal direction of wood isvery marked, it is quite simple to obtain thethree-dimensional structure of the materialfrom a cross section. Figure 36.15 depicts theexamples of capillary pressure curves calculatedfrom microscopic images of cross sections ofwood. In this case, the pore-size distributionhas been calculated using image processing(Perré , 1997; Perré and Turner, 2002).36.2.2 .4 Bound -Water Diffusio nMacroscopic bound-water diffusion results fromtransport mechanisms that take place at the microscopicscale, i.e., diffusion of the bound waterthrough the cell walls and vapor diffusion due toFick’s law. At the microscopic scale, these two fluxescan be expressed as follows:f b ¼ r s D b rX b (Bound-water flux) (36 :12)f v ¼ r g D v rv v (Vapor flux) (36 :13)In Equation 36.12 and Equation 36.13, D b and D vrepresent the microscopic bound-liquid and vapordiffusivities, respectively having units m 2 s 1 and v vis the mass fraction of vapor in the gaseous phase.By using the bound-liquid diffusivity data ofStamm (1963), it is possible to obtain the followingleast-squares, best-fit correlation for D b :4300D b ¼ exp 12 :82 þ 10 :90 X b (36:14)Twhere T is the temperature in Kelvin.On assuming isothermal conditions and constanttotal pressure, the microscopic vapor flux can be expressedwith the gradient of the bound-water contentas the driving force by Equation 36.13. M vf v ¼RT D @P vv rX b (36:15)@X bWithin the anatomical structure of wood, anycombination in series or parallel of vapor diffusion(in lumen and pits) and bound-water diffusion (in thecell walls) is a possible pathway to drive water fromhigh to low moisture content regions (Figure 36.16).Because Equation 36.12 and Equation 36.15 use thesame driving force, the expressions for the macroscopicbound-water diffusivity in the radial and tangentialdirectionscanbecalculatedevenusinghomogenizationtechniques according to these microscopic properties,together with the pore morphology (Perré and Turner,2002). Equation 36.14, derived from specific experimentalmeasurements, exhibits a dramatic increase ofß 2006 by Taylor & Francis Group, LLC.