Comparative Evaluation of Diffusion Coefficients

Table 4.13 provides a selected overview of published D-values for sodium ions

from both NaOH and NaCl in radial and tangential directions of a variety of wood

species. For reasons of comparison, the D-values were calculated or directly determined

at 25 °C.

The measured diffusion coefficients for the important radial direction were in

rather good agreement. This was very surprising, because quite different experimental

set-ups (from saturated wood to dilute solution versus from high concentration

in the bulk liquid to low concentration in the wood void system), analytical

methods to determine the sodium ions, wood species and modes of calculation

(Fick’s first versus second laws of diffusion) were applied. The diffusion coefficient

in the radial direction out of cooked chips, as determined by McKibbins,

appeared to be comparatively low, though this may have been caused by diffusion

combined with chemical reaction (deacetylation), as was noted by Constanza et al.

[41]. On the other hand, their objection was quite doubtful because cooked chips

no longer contain acetyl groups. Very remarkable, however, was the very low activation

energy determined by Kazi and colleagues [55,56]which was almost one

magnitude lower as compared to values obtained by others (see Tab. 4.13). Two

150 4 Chemical Pulping Processes

Tab. 4.13 Comparison of published diffusion coefficients (D)

of sodium ions at various conditions and wood substrates,

T = 25 °C = const.

Publication Species Yield

[% o.d.]

CNaOH

[mol L–1]

Dlong *1010

[m2 s–1]

Drad *1010

[m2 s–1]

Along * 107

[m2·s–1·K–0.5]

EA, long

[kJ mol–1]

Arad * 107

[m2 s–1·K–0.5]

EA, rad

[kJ mol–1]

McKibbins, 1960 Spruce x50 neutral 4.7 2.6 7.97 25.5 0.53 20.2

Christensen,

Pine 100 neutral 5.7 0.5 0.57 18.5 0.02 16.6

Talon & Cornell,

Lobolly

pine

99 pH > 12.9 2.9 1.36 22.3

Talon & Cornell,

Lobolly

pine

67 pH > 12.9 10.5 4.90 22.3

Robertsen &

Lonnberg, 1991

Spruce °99 > 0.5 3.7 3.02 23.7

Constanza, 2001 Poplar °99 0.05 1.4

Constanza, 2001 Poplar °99 1.00 7.3

Kazi, 1997 Spruce °99 2.27 54.0 1.5 0.01130 3.2 0.00027 2.8

x Estimation based on permanganate number.

° Assumed after NaOH treatrment.

reasons have been quoted as being responsible for the low activation energy –

namely, the application of Fick’s second law of diffusion, which does not consider

surface area, and the special experimental set-up used (impregnator) where no

NaOH-desorption step from the wood block (which also needs activation) was considered.

Nevertheless, the numerical values of D in radial directions were quite

comparable, such that any of these values can be used for modeling the impregnation

process by diffusion.

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