Mass Transfer

In ozone bleaching, the rate-determining step is governed by the mass transfer of

the oxidants to the active site in the fiber. This assumption is based on a model

accounting for the reaction between ozone and the pulp fiber. This model, originally

proposed by Osawa and Schuerch in 1963, involves low-consistency ozone

bleaching to demonstrate the single transport processes (Fig. 7.83) [17].

Mobile

water

Immobile

water

Ozone

(gas)

d

d

d

Fig. 7.83 Scheme of mass transfer in ozone bleaching according

to Osawa and Schuerch [17] “Film model” infinite rapid

transfer in the mobile water, and ‘kLa’ determines transfer in

immobile water.

In the first step, gaseous ozone, which is present in an oxygen/ozone gas mixture,

is dissolved in the bulk or mobile water layer (d1) where ozone is transported

by convection. The dissolved ozone (and its decomposition products) is further

transported through an immobile water layer (d2) by diffusion. The latter becomes

the rate-determining step as it is definitely slower than the convection transport in

d1. The amount of mobile water is gradually reduced by increasing the pulp consistency

from low to medium. It can be assumed that at medium consistency no

mobile water is present any more, and the thickness of the immobile water layer

(d2) is controlling the reaction rate. A relationship between the thickness of the

immobile layer and extent of the reaction has been recently established by Bouchard

et al. [18]. The thickness of the immobile water layer surrounding the fiber

as a function of pulp consistency can be easily calculated according to the concept

of Bouchard et al. [18]. Fig. 7.84 shows (a quadrant of) the cross-section through a

fiber considering both the dry and the swollen state.

798 7Pulp Bleaching

©2006 WILEY-VCHVerlag GmbH&Co.

Handbook of Pulp

Edited by Herbert Sixta

Lumen

r1

r2

r3

r4

Water

layer

Cell wall

swollen

dry

Fig. 7.84 Simplified scheme of a quadrant of the crosssection

through a pulp fiber in a medium-consistency pulp

suspension (according to Bouchard et al. [18]).

In order to calculate the thickness of the immobile water layer (r 4 – r 2), the following

assumptions are made:

_ Swelling occurs solely by shrinking the lumen.

_ Fiber length (L) remains constant during swelling.

_ Cell wall thickness of an unbleached kraft pulp with 50% yield is

1.4 lm (r 2 – r 1) [19].

_ r 2 is 19.6 lm [19].

_ Fiber saturation point (FSP) of an unbleached kraft pulp amounts

to 1.4 g water g–1 dry pulp [18].

_ Specific volume of dry cell wall (V DW) amounts to

1/1.53 = 0.654 mL g–1.

_ Volume of the swollen cell wall (V SW) amounts to

1/0.483 = 2.07 mL g–1.

Calculation of the radius of the lumen (r 3) in the swollen state to obtain the volume

of the water in the lumen (V L):

VSW

VDW _

p r 2

2 _ r 2

_ 3_ L

p r 2

2 _ r 2

_ 1_ L _100_

V L can be calculated according to Eq. (101) by using the value of r 3 = 14.7 lm:

VL

VDW _

p _ r 2

3 _ L

p _ r 2

2 _ r 2

_ 1__ L _101_

From Eq. (100), the value of V L calculates to 2.68 mL g–1. Considering this value,

the amount of external water (V EW ~ immobile water) can be calculated for any

7.5 Ozone Delignification 799

pulp consistency by subtracting the water in the cell wall (FSP = 1.4 mL g–1) and

the water in the lumen (V L = 2.68 mL g–1) from the total amount of water in a given

pulp suspension. The thickness of the external water layer (V EW) requires the

calculation of r 4 (see Fig. 7.84) according to Eq. (102):

VEW

VDW _

p r 2

4 _ r 2

_ 2_ L

p r 2

2 _ r 2

_ 1_ L _102_

The thickness of the adsorbed water layer can then be estimated by d = (r4 – r2).

The calculated values for d are summarized in Tab. 7.39.

Table 7.38 The thickness of the water layer surrounding the fiber

in the consistency range from 8 to 20% estimated according to

the assumptions made by Bouchard et al. [18].

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