Directions Pine

[m2]

Birch

[m2]

Spruce

[m2]

Tangential 0.042 0.023 0.032

Longitudinal 0.736 0.532 0.787

The values presented in Tab. 4.12 are slightly higher in the longitudinal and

lower in the tangential directions as compared to the ECCSA values published by

Hartler for spruce [50]and Stone for aspen [44]. In relation to the values for spruce

and pine, the calculated value for A_ for birch is obviously too low considering the

very high diffusion coefficient (see Chapter 4.2.3.5.1).

An overall diffusion coefficient for white liquor DWL(T) has been developed by

using the Stones–Einstein relationship [see Eq. (62)]to the following expression

[51]:

DWL _ T __1_6 _ 10_9 1_083

2_0 _ g w _ T _

T

290 _64_

148 4 Chemical Pulping Processes

where the coefficients are related to the value of DWL(T) at 17 °C as a reference.

The kinematic viscosity of the white liquor is approximated by doubling the value

for water, gw, which is 1.0 m2 s–1 at 20 °C and 0.28 m2 s–1 at 100 °C.

The combined dependence of the diffusivity of sodium ions on temperature, hydroxide

ion concentration and the residual lignin fraction was taken into account

by one single expression [52]:

D _ 9_5 10_8 _ __ T _

_ Exp _

2452_4

T _ __ _2_0 _ a L 0_13 __ OH _ 0_550_58 _ __65_

where aL is the mass fraction of lignin.

This expression for the diffusion coefficient of sodium ions is integral part of

the kinetic model for kraft pulping introduced in Chapter 4.2.5 (Reaction

kinetics).