An Experimental Evaluation of the Governing MoistureMovement Phenomena in the Paper Coating ProcessPart I: Theoretical Aspects & Part II:Experimental

Carl-Gustav Berg, Johan Åkerholm, Ville Kirstilä and Markku KarlssonProcess Design Laboratory, Åbo Akademi University

BACKGROUND

As the coating of paper and paperboard is becoming more and more common, tougher demands on the coating and on the following drying process occurs. The most important issue, is the modelling of the moisture movement in the coating process. The occuring phenomena, as a wet coating colour comes to contact with a dry base paper, can only be considered superficially known. But an in-depth knowledge of the phenomena are essential as basic knowledge when developing future coating sections. The basic knowledge can also be considered central when running existing coating sections optimally.

COATING APPLICATION ASPECTS

The most common coating method is the blade coater with an applicator roll. Jet application will probably be more common in the coating industry, especially for coated board, while it provides good runnability at high speeds and a wide coat weight interval. Another surface treatment method, which is common for base paper, in the paper industry is symsizing. So far there is no coating application and metering process that would produce good quality for all the paper and board products being produced today. The demand for exellent quality at ever higher speed, raises the need to further develop the coating section. In the coating process, the aim is to make an outstanding printing surface. This requires an even surface of the coated paper as well as an even distribution of the binders in the dryed coating colour. However, the task of modelling the moisture movement is ambiguous, whilst every base and coating colour combination acts differently; as well as taking into account the wide variation in the use of the coated paper product.

Figure 1. The coating process in a blade coater with an application roll (shown left). The important zones are the application area, the metering area and the following drying lay-out. A convection dryer is shown right.

EXPERIMENTAL APPARATUS

The experimental apparatus is a laboratory coater, with which a sheet of paper is coated. The apparatus coats the base paper with a bar, which moves over the paper sheet. The coating color is put in front of the bar and is evenly spread on the paper surface by the bar. The bar moves over the paper sheet with the help of a pneumatic apparatus and the speed of the coating bar is adjustable. The laboratory apparatus is shown in figure 5 with extra devices. The measurements are obtained by measuring the dry content of the scraped off material and comparing it with the initial dryness of the coating color. The distance between the point at which the coating is scraped off and applied can be adjusted, as can the speed of the application. This means that almost any desired time delay between application and scrape-off can be achieved. The shortest time interval is however 0.05 s.

Figure 4. The experimental apparatus with its extra devices is illustrated to the left. The function of the new laboratory application is illustrated on the right.

EXPERIMENTAL RESULTS

The following figures shows the extent to which some properties of the coating color and the base paper influence the liquid drainage from the coating color into the base paper. The aim of this poster presentation is to give a picture of the complex drainage phenomena and to give a clue about the governing moisture movement phenomenon.

CONCLUSIONS

We find that the temperature and the moisture content of the base paper have major influence on the drainage rate of liquid. We believe we have shown that neither the moisture content of the coating colour nor the external bar pressure has a significant effect on the liquid drainage rate. Based on these measurements we have not found any evidence that the liquid drainage when coating paper could be described using Darcy's law.This concludes that the water loss from the coating colour into a hygroscopic material can be much more accurately explained by applying vapour diffusion as the governing mass transfer mechanism (i.e. resistance) rather than solely using the capillary suction theory.

Figure 5. On the left is the influence of base paper and coating color moisture content on the drainage rate. LP = Liquid Package paper board, z = ( ) kg H2O/kgbd, CC = Coating color, Y = ( ) kgbd/kg tot. The measurements for LP are made at 40°C and the CC moisture dependency series are made at 23°C. The right hand figure illustrates laboratory measurements at different temperatures. The base paper is a fine paper grade and the coating color is lattice-based with, the pigments CaCO kaolin and plastic pigment at 23°C for each series.3,

MATHEMATICAL MODELLING

The aim is to create a relatively simple mathematical model that desribes the actual events of the moisture movement in both the coating and the drying process. Basic thermodynamic equations are used in the modelling process. From the first and the second thermodynamic laws one can derive the following equation for the inner energy of a substance;

This equation can be extended to include the effect of chemically bound water. While the water in the paper web tends to be in this state during both the coating section and the drying section;

While the binding of water in the paper is an exotermic process, we will have a contribution of heat to the energy balance, which is implemented in the equations. The released heat is referred to as the heat of sorption. The chemical potential for water in a porous media can be calculated, as (Lampinen 1998) suggested, with the following equation;

The equations above show that it is possible to model the coating process with relatively simple equations related to thermodynamics. Of course we have to take into account the properties of the coating colour, to be able to determine the chemical nature of the drained liquid. Additionally, the mechanical forces affecting both the paperweb and the coating colour at the coating station are only partially analysed.

As (Heikkilä 1993) shows in his academic dissertation, a simulation model can be developed from mass and energy balances. The paper or the paperboard is divided into layers. The mass balance and the energy balance is deduced for each layer individually. In the following we give the reader an example of how this can be done. The paper web is divided into layers as shown in figure 3.

Figure 3. The coated paper web, which is divided into mathematical layers and an illustration of the different boundary conditions that contribute to the model.

The moisture content of each layer can be calculated with a mass balance and the boundary conditions which belong. In the following model the water that drains from the coating colour drains only into the uppermost layer of the paperweb. From there on the water movement is assumed to take place as vapour transport. This gives the following set of equations;

To determine the temperature of the layers, an energy balance for each layer, with its boundary conditions, is deduced. This means that it is possible to calculate how the temperature and the moisture content of each layer develops through the coating and the subsequent drying process. The energy balances are, for example, written in the following way;

The movement of the water in the coating colour is one of the most critical issues in the coating process. Many of the final product quality aspects are determined by the water movement. When the relatively dry fibres in the paperweb come into contact with the liquid in the coating colour they start to swell and this might affect the end quality. An important definition is the point of immobilisation, this is the point where the coating colour particles stop moving with respect to the base paper. Therefore, the drying intensity at the point of immobilisation can cause quality problems, e.g. mottling. The water movement in the coating section is illustrated in figure 2.

Figure 2. A schematic diagram of the moisture movement in a coated web during drying.

NOMENCLATURE

Figure 6. shown left

An illustration of measurements made in the laboratory and in a pilot coating plant is . The measurements are made with the same base paper and coating color. The differences can be explained by the fact that the base paper was at 40°C - 45°C during the pilot measurements and at 30°C in the laboratory. The graph to the right illustrates how the pressure under the coating bar influences the drainage rate. There is no significant change in the drainage rate at different pressures. The divergence at the last points (at 1.4 s) is due to lower specific coat weight at higher pressure.

REFERENCES! Berg C-G., "Heat and Mass Transfer in Turbulent Moist Air Drying

Processes - Experimental and Theoretical Work", Academic dissertation to be held at Åbo Akademi during autumn 1999

! Heikkilä P., "A Study on the Drying Process of Pigment Coated Paper Webs", Academic dissertation, Åbo Akademi 1993

! Lampinen M., Kotiaho W. and Leskelä M., "Huokoisen materiaalin kuivauksen termodynaamiset perusteet", TKK 1998

APPLICATION AREA

Coating colour

METERING AREA

Coated paper

DRYING SECTION

Paper web

In Cooperation with Valmet Air Systems and Raisio Chemicals

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Greek Letters A m2 area a W/m²K heat transfer coefficient m kg mass b,b¢ W/m²K mass transfer coefficient B m web width l W/mK thermal conductivity c,cp kJ/kgK specific heat q º contact angle

C, Ck - constant j - relative humidity m& kg/s mass flow rate m J/kg chemical potential n mol moles h kg/ms dynamic viscosity l m length r kg/m3 density

p, DpE kPa pressure, ext. pressure diff. t s time q& kW heat flow g N/m surface potential r m radius Subscripts and superscripts Sm J/molK molar entrophy a air T, t K, °C temperature b base paper Um J/mol molar inner energy c coating x kgH2O/kgda air humidity e evaporation X kgH2O/kgbd moisture content dry basis n,k running index, last line number Y kgbd/kgtot consistency, dry content v vapour y, Dy m length property, distance w water w m/s velocity l liquid Vm m3/mol molar volume tot total v m3/kg specific volume ¢, ¢¢ physical property in vicinity of evaporating surface R J/molK Gas constant Unit shortenings others than SI ls J/kg latent heat of sorption da, bd dry air, bone dry h0, Dhv kJ/kg specific enthalpy, latent

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