The validity of Darcy's law in the axial penetration of wood

Summary

Longitudinal air permeability measurements were made on specimens of British Columbia Interior and Coastal types of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco) sapwood and heartwood, kiln dried and solvent dried, which were successively reduced in length from 3.5 to 0.5 cm. Most sapwood, which was quite permeable, was found to obey Darcy's law with respect to length. Heartwood and kiln-dried Interior sapwood specimens were less permeable, and were found to deviate from Darcy's law. A physical model was proposed in which, due to random blockage of tracheids by aspirated pits, the number of conducting tracheids was reduced exponentially with depth of penetration. This was expressed as a linear relationship between the logarithm of permeability and specimen length at lengths exceeding one tracheid. This model conformed with the experimental data. A new mathematical equation was proposed:

$$\frac{{dQ}}{{dt}} = \frac{{KA e^{ - bl} \Delta P}}{{\eta ^l }}$$

which differs from the Darcy equation only by the insertion of e^-bt, where e = base of natural logarithms andb is a positive constant determined by experiment. Whereb=0, e^-bl=1, and the equation reduces to the Darcy equation.