Moisture and fluid transport
The transport of fluids (liquids or gases) through paper takes places primarily in the thickness direction. As a first approximation, one might envision the fibre network as an inert system. In this system, fluids would be transported through the open space between the fibres. Transport phenomena in paper are often more complex than that, because the fibre network does not remain inert and transport is often complicated by the presence of coating layers. For example, many fluids — water and water vapour in particular — interact with the fibres. Absorption of water into fibres leads to swelling that changes the porous network structure. Because of such interactions, the transport of inert fluids and that of water through paper differ significantly. In addition to this, the internal friction of liquids makes their flow properties quite different from those of gases. The role of the fibre network as a flow resistor is correspondingly different.
As a first approximation, one might envision the fibre network as an inert system. In that system, fluids would be transported through the open space between the fibres. Unfortunately, transport phenomena in paper are often more complex than that, because the fibre network does not remain inert.
For example, many fluids — water and water vapour in particular — interact with the fibres. Absorption of water in fibres leads to swelling that changes the porous network structure. Because of such interactions, the transport of inert fluids and that of water through paper differ significantly. In addition to this, the internal friction of liquids makes their flow properties quite different from those of gases. The role of the fibre network as a flow resistor is correspondingly different.
It is necessary to discuss the following factors in order to understand fluid transport phenomena in paper:
- Interaction of water with fibres /LINK:03090701/
- Fluid transport in pores /LINK:03090702/
- Transport of inert gases /LINK:03090703/
- Diffusion of water vapour /LINK:03090704/
- Describing liquid penetration into paper with Lucas-Washburn equation /LINK:03090705/
- Wetting and swelling in liquid penetration /LINK:03090706/
Moisture in paper
In equilibrium conditions, the moisture content of paper depends on the ambient relative humidity and temperature of the surrounding air. The moisture content is highest in humid and cold conditions. It is also history-dependent, affected by the preceding states of moisture content. Time-dependent or rate-dependent moisture sorption phenomena are important in some applications.
The pulp furnish used in papermaking affects the moisture content of paper. This relates in part to the chemical interactions of water with the cellulosic fibre wall structure, and in part to the internal and external fibrillation and fines content of the pulp. The fibre wall structure changes when water is removed. Depending on the type of pulp, these changes may be partially irreversible during paper drying.
Relative humidity and moisture content
The relative humidity, RH, of air refers to the amount of water vapour in air relative to the amount in saturation. The saturation moisture content increases with increasing temperature. Thus, relative humidity alone does not give the concentration of water in air; also temperature is important. This is helpful to remember when one considers the moisture content of paper in different conditions.
Other useful quantities are the water vapour pressure, pw, and its saturation value, pw,s. The saturation vapour pressure occurs in a closed vessel that contains some liquid water in equilibrium with the vapour. In that case, the rate of evaporation is equal to the rate of condensation — dynamic equilibrium. Evaporation requires that water molecules have sufficient thermal energy to escape from the liquid phase. Since the available kinetic energy increases with increasing temperature, the saturation vapour pressure also increases.
By definition, relative humidity is the ratio of the ambient vapour pressure to the saturation vapour pressure:
Figure 1 shows the relationship between temperature, relative humidity, and water vapour pressure in air.
Figure 1. Relation between temperature, relative humidity, and vapour pressure of water 1.
The climatic system is never in thermodynamic equilibrium. In summer, sunshine evaporates water from the sea, lakes and other bodies of water. Relative humidity can be almost 100 %. In winter, water condenses and freezes on cold surfaces, making the ambient vapour pressure and saturation vapour pressure low.
Wood fibres are hygroscopic — they absorb water readily. The moisture content of paper is the ratio of absorbed water divided by the total mass of paper. When in equilibrium with the surrounding air, the moisture content of paper depends on the relative humidity of air and the equilibrium temperature. Prahl has studied relevant thermodynamic relationships 2.
The moisture content of paper decreases with increasing temperature or with decreasing relative humidity, as shown in Figure 2. There is a slight difference in the moisture content, depending on whether one starts from humid or dry conditions. We return to this hysteresis effect in the next section.
Figure 2. Moisture content vs. relative humidity in a pine pulp at T = 22 °C, 35 °C, 50 °C, and 80 °C. The isotherms are different in absorption, when coming from dry conditions (a), and in desorption, when coming from humid conditions (b) 2.
At the saturation conditions of T = 23 °C and RH = 100 %, the moisture content of paper is typically 25–30 %.
At a constant RH, the moisture content is insensitive to temperature. Except in humid conditions, a temperature change of more than ±10 °C is necessary before the moisture content of paper changes significantly.
The moisture content of paper is sensitive to the properties of papermaking pulp. Throughout the relative humidity range RH < 100 %, mechanical pulps often contain more moisture than chemical pulps, as shown in Figure 3. The fines of mechanical pulps make a strong contribution to this 3,4. In chemical pulps, the proportions of amorphous cellulose and hemicellulose are more important factors.
Figure 3. Moisture content vs. relative humidity in a chemical pulp and a groundwood at T = 50 °C 2.
Hysteresis and dynamic phenomena
Hysteresis means that the moisture content of paper at a certain relative humidity of air is different in absorption, when coming from dry conditions (a), and in desorption, when coming from humid conditions. This difference is evident in Figures 2 and 3. A pair of boundary curves shown in Figure 4 determine the lowest and highest moisture contents that paper can have at a given RH level 5. Depending on the humidity history, the moisture content can be anywhere between the boundary curves. For example, Figure 4 shows two desorption paths.
Figure 4. Boundary curves of moisture content of a bleached kraft paperboard vs. relative humidity at T = 23 °C (solid lines) and the desorption paths of the same material starting from RH = 90 % and 75 % (dashed lines) 5.
The boundary curves result when one starts from zero moisture content and goes to saturation and vice versa. The difference in moisture content at fixed RH and T becomes large at high humidity or low temperature.
Hysteresis is connected to the hygroscopic nature of wood fibres. Thus, thermal energy, heat of desorption, is necessary to remove water from fibres. Likewise, heat of adsorption releases when water absorbs to fibres. The heat of sorption translates into a difference in vapour pressure or RH between absorption and desorption. Hysteresis is not a dynamic effect or somehow caused by a lack of time for fibres to reach equilibrium. The hysteresis loop does not collapse even if moisture content changes very slowly.
Various mechanisms have explained the hysteresis curve. In the domain theory, hysteresis arises from independent microscopic domains that can be in two states 6,
“sorbing” or “nonsorbing”. The domain state switches upon absorption or desorption of water. Crossing an energy barrier is necessary for this to happen. Some research workers argue that the shape of the microscopic domains — bottleneck theory —
controls the hysteresis. The domains may have different sizes. Capillary pressure causes small domains to absorb water more readily than large domains 7.
Urquhart and Williams 8 provided an explanation that the availability of hydroxyl groups changes. The cellulose molecules form groups — micelles — that weakly bond to each other. Upon absorption of water, some of the bonding hydroxyl groups become free to associate with more water. In desorption, the opposite occurs.
Barkas 9 explained hysteresis through swelling stresses and the irreversible plastic deformations they cause. Swelling stresses arise in the fibre wall because crystalline cellulose does not swell. At small amounts of absorbed water the deformations are reversible, and elastic. With larger amounts of water, the swelling stress may exceed a yield limit and cause plastic deformations. For example, weakly bonded micelles may slip and free more OH groups to absorb water.
If the external conditions suddenly change, the moisture content of paper or board cannot change immediately to reflect the new situation. In ordinary diffusion, the moisture content would change proportionally to the square root of time. Diffusion times should therefore generally be proportional to grammage squared. This holds at relatively high grammages 10,11.
At low grammages, the diffusion time of moisture into paper relates linearly to grammage 10,11. This is characteristic of a boundary layer formed at the sheet surface. In the boundary layer the local humidity and temperature differ from the ambient conditions. The solution of the ordinary diffusion equation would require that the boundary condition of the sheet were constant. With the boundary layer this is not the case and therefore the ordinary solution does not apply.
Heat of sorption governs the conditions in the boundary layer. With moisture absorption, temperature increases and RH decreases in the boundary layer. This retards the diffusion process because the relative humidity seen by the sheet surface is lower than the ambient RH. The opposite happens during desorption. As a result, changes in the moisture content are slower than they would be if the diffusivity of water vapour alone determined the sorption rate.
The sorption rate of paper increases if heat is exchanged effectively between paper and its surroundings. This occurs if air blows against the sheet surface 10.
Sometimes dimensional stability problems in paper or board occur when opening a moisture-sealed package where the vapour pressure differs from that of the surrounding air. Water vapour then moves to or from the paper. For example, cold or dry paper absorbs moisture. To prevent moisture changes, one should open a sealed package only when the vapour pressure inside it equals that of the surrounding air. One can achieve this by adjusting temperature. One cannot change the ambient relative humidity because it is controlled by climatic conditions. A pedagogical discussion is available 1.
The penetration of liquid water in operations such as coating and printing differs greatly from the diffusion of water vapour considered above. Several mechanisms affect the liquid water penetration, including the wetting of fibre surfaces, transport along fibre walls, and capillary penetration of inter-fibre and intra-fibre pores (lumens), which are discussed later in this chapter.