Penetration

Penetration describes the flow of liquor into wood under the influence of a hydrostatic

pressure gradient which is the sum of external pressure, pE, and capillary

pressure, pC.

ptot _ pE pC _38_

The capillary pressure can be expressed by the Young–Laplace equation [Eq. (39)]:

pC _

2 _ c _ Cos h

r _39_

where c is the surface tension of the impregnation liquor [Nm–1], h is the contact

angle between the liquid and the solid phases, and r is the capillary radius [m].

From Eq. (39) it is clear that the penetration rate is sensitive to the diameter of

the individual capillaries. The total pressure, ptot, is opposed by the pressure drop

due to the liquid flow in the capillaries, pF, according to the Hagen–Poiseuille’s

law of laminar flow [Eq. (40)]:

D pF _

V _

_ 8 _ g _ l

r 4 _ p

_ Pa _40_

where g is the viscosity of the liquid (in Pa.s), V is the rate of volume flow (in

m3 s–1), and l is the capillary length or penetration distance (m).

4.2 Kraft Pulping Processes 133

Liquid flow through the capillaries occurs as near-perfect laminar flow. When N

identical capillary tubes of equal length are connected in parallel, the total flow

through them equals N times that of one single tube. For the penetration of a

liquid through a porous material with N parallel capillaries per unit surface area

A, the flow rate of volume flow can be expressed by Eq. (41), derived from

Eqs. (38–40):

V _

_

N p r 2 _ 2 _ r _ c _ Cos h PE _ r 2 _ _

8 _ l _ g

m 3

s _ _ _41_

Thus, the penetration rate will increase with any increase in applied external pressure,

increase in the capillary radius, with the surface tension of the impregnation

liquor, with reduction in liquor viscosity and with the contact angle between the

liquid and the solid phases. Since flow varies inversely as the fourth power of the

radius of the capillaries, the size of the pit-membrane openings will control the

rate of flow.

Acidic liquors penetrate faster than liquors which are sufficiently alkaline to

swell the cell walls beyond their water-swollen dimensions, as in the case of soda

and kraft liquors.

The ease of penetration of wood depends on the species and whether it is sapwood

or heartwood [24]. In contrast to diffusion, penetration is strongly affected

by the wood structure, and consequently structural differences between softwood

and hardwood must be clearly distinguished. The differences are due to the presence

of vessels in hardwoods, which run in the longitudinal direction and which,

when unplugged by tyloses, permit rapid penetration into the interior of the

wood. The number, diameter and distribution of vessels is highly dependent on

the hardwood species. In ring porous woods (e.g., oak) the vessels are concentrated

in the early wood, whereas in diffuse porous woods (e.g., beech) they are

more uniformly distributed over the annual ring. If the vessels are plugged by

tyloses (which frequently occurs), the penetration rate is exceedingly small in all

directions. Softwoods are not provided with vessels. There, the tracheids and their

interconnecting pit system take over the function of liquid transfer. Compared to

easily penetrated hardwoods, penetration through softwoods in a longitudinal

direction is less efficient, whereas transverse penetration is more rapid. This can

be explained by the fact that the pits in softwood tracheids are much larger and

more numerous than in hardwood fibers. The longitudinal flow of liquids is 50-

to 200-fold faster than flow in the other directions. Tangential flow in softwoods is

controlled by the bordered pits situated on the radial walls of tracheids, while the

flow in the radial direction is controlled by ray cells [25]. The permeability of softwoods

in the radial direction is considered to be more efficient than in the tangential

direction [26]. Thus, it can be concluded that water penetration into softwood

chips occurs through the longitudinal direction. Radial flow may contribute a

small part of the total penetration, whilst flow in a tangential direction can be

neglected. In hardwoods, no liquid flows in the transverse fiber direction [27]. It is

assumed that the hardwood fibers are totally enclosed cells, where no liquid trans-

134 4 Chemical Pulping Processes

fer occurs. In summarizing these observations, it can be concluded that the optimum

conditions for the impregnation of hardwoods is given when the fibers are

water-saturated (which is the case at the fiber saturation point) and the vessels are

empty, assuming that they are not plugged by tyloses. Liquor could then flow into

the interior of the wood via the vessels, and the pulping chemicals could diffuse

radially from the vessels into the surrounding fibers through the water present in

the cell walls. In case the vessels are plugged by tyloses, which prevents penetration,

the wood should be water-saturated in order to provide optimum conditions

for diffusion.

A semiquantitative method to determine the penetrability of a wood has been

proposed by Stone [24]. The rate of air permeability is measured using an apparatus

consisting of two flowmeters in series, the restrictions in one being a glass

capillary of known dimensions and the restrictions in the other being a dowel of

known dimensions of the wood being tested. By applying the Poiseuille equation,

the following relationship is obtained:

Penetration Factor _ r 4

wood _

r 4

glass

N _ A _

pglass

pwood _

lwood

lglass _ const

pglass

pwood _42_

where r is the radius of capillary, p the pressure drops, l the length of capillary, N

the number of capillaries and A the cross-sectional area of wood.

The porosity of the wood is then defined as the fourth power of the radius of a

glass capillary, which would permit the same flow of air as 1 cm2 of the wood in

question. At this stage, neither rwood nor N – the number of capillaries per unit

cross-section – is known. To overcome this problem, all the capillaries in 1 cm2 of

wood are considered to be gathered together into a single capillary which gives the

same rate of flow. For any given glass capillary and length of wood dowel, the

penetration factor = r4

wood = const. pglass/pwood. Many different wood species have

been characterized according to this penetration factor, and average values for a

number of wood species are summarized in Tab. 4.9 [24].

Typically, the ratio of the penetration factor in sapwood to heartwood lies between

10 and greater than 1000. Aspen, beech, Douglas-fir and white oak show

poor penetrability. The reason for poor penetrability is the occurrence of tyloses in

the vessels which cause blockade of these passages.

Penetration of water into the chips of three selected softwood species, Picea

abies, Larix sibrica and Pinus silvestris, was studied using a specially designed

impregnator [28]. In agreement with the data listed in Tab. 4.9, penetration into

heartwood chips proved to be less efficient than into sapwood chips. In the case of

spruce, the degrees of penetration were 65% and 92% into heartwood and sapwood,

respectively. The results were similar for the other wood species. Thickness

(between 4 and 8 mm) and width do not influence the efficiency of impregnation

significantly. The chip length, however, has a much more pronounced effect on

the efficiency of penetration, since the longitudinal flow in softwoods is 50- to

200-fold faster than the tangential or radial flows. Impregnation of water can be

controlled by adjusting the process conditions. An increase in temperature (e.g.,

4.2 Kraft Pulping Processes 135

Tab. 4.9 Penetrability of a selection of wood species by means of

a semiquantitative method [24].

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