9.4. EQUILIBRIUM MOISTURE CONTENT OF MATERIALS

9.4A. Introduction

As in other transfer processes, such as mass transfer, the process of drying of materials must be approached from the viewpoint of the equilibrium relationships together with the rate relationships. In most of the drying apparatus discussed in Section 9.2, material is dried in contact with an air–water vapor mixture. The equilibrium relationships between the air–water vapor and the solid material will be discussed in this section.

An important variable in the drying of materials is the humidity of the air in contact with a solid of given moisture content. Suppose that a wet solid containing moisture is brought into contact with a stream of air having a constant humidity H and temperature. A large excess of air is used, so its conditions remain constant. Eventually, after exposure of the solid sufficiently long for equilibrium to be reached, the solid will attain a definite moisture content. This is known as the equilibrium moisture content of the material under the specified humidity and temperature of the air. The moisture content is usually expressed on a dry basis as kg of water per kg of moisture-free (bone-dry) solid or kg H2O/100 kg dry solid; in English units as lb H2O/100 lb dry solid.

For some solids the value of the equilibrium moisture content depends on the direction from which equilibrium is approached. A different value for the equilibrium moisture content is obtained according to whether a wet sample is allowed to dry by desorption or a dry sample adsorbs moisture by adsorption. For drying calculations it is the desorption equilibrium that is the larger value and is of particular interest.

9.4B. Experimental Data of Equilibrium Moisture Content for Inorganic and Biological Materials

1. Typical data for various materials

If the material contains more moisture than its equilibrium value in contact with a gas of a given humidity and temperature, it will dry until it reaches its equilibrium value. If the material contains less moisture than its equilibrium value, it will adsorb water until it reaches its equilibrium value. For air having 0% humidity, the equilibrium moisture value of all materials is zero.

The equilibrium moisture content varies greatly with the type of material for any given percent relative humidity, as shown in Fig. 9.4-1 for some typical materials at room temperature. Nonporous insoluble solids tend to have equilibrium moisture contents which are quite low, as shown for glass wool and kaolin. Certain spongy, cellular materials of organic and biological origin generally show large equilibrium moisture contents. Examples of these in Fig. 9.4-1 are wool, leather, and wood.

Figure 9.4-1. Typical equilibrium moisture contents of some solids at approximately 298 K (25°C). [From National Research Council, International Critical Tables, Vol. II. New York: McGraw-Hill Book Company, 1929. Reproduced with permission of the National Academy of Sciences.]


2. Typical food materials

In Fig. 9-4.2 the equilibrium moisture contents for some typical food materials are plotted versus percent relative humidity. These biological materials also show large values for equilibrium moisture content. Data in this figure and in Fig. 9.4-1 for biological materials show that at high percent relative humidities of about 60 to 80%, the equilibrium moisture content increases very rapidly with increases in relative humidity.

Figure 9.4-2. Typical equilibrium moisture contents of some food materials at approximately 298 K (25°C): (1) macaroni, (2) flour, (3) bread, (4) crackers, (5) egg albumin. [Curve (5) from ref. (E1). Curves (1) to (4) from National Research Council, International Critical Tables, Vol. II. New York: McGraw-Hill Book Company, 1929. Reproduced with permission of the National Academy of Sciences.]


In general, at low relative humidities the equilibrium moisture content is greatest for food materials high in protein, starch, or other high-molecular-weight polymers and lower for food materials high in soluble solids. Crystalline salts and sugars as well as fats generally adsorb small amounts of water.

3. Effect of temperature

The equilibrium moisture content of a solid decreases somewhat with an increase in temperature. For example, for raw cotton at a relative humidity of 50%, the equilibrium moisture content decreased from 7.3 kg H2O/100 kg dry solid at 37.8°C (311 K) to about 5.3 at 93.3°C (366.5 K), a decrease of about 25%. Often, for moderate temperature ranges, the equilibrium moisture content will be assumed constant when experimental data are not available at different temperatures.

At present, theoretical understanding of the structure of solids and surface phenomena does not enable us to predict the variation of equilibrium moisture content of various materials from first principles. However, by using models such as those used for adsorption isotherms of multilayers of molecules and others, attempts have been made to correlate experimental data. Henderson (H2) gives an empirical relationship between equilibrium moisture content and percent relative humidity for some agricultural materials. In general, empirical relationships are not available for most materials, and equilibrium moisture contents must be determined experimentally. Also, equilibrium moisture relationships often vary from sample to sample of the same kind of material.

9.4C. Bound and Unbound Water in Solids

In Fig. 9.4-1, if the equilibrium moisture content of a given material is continued to its intersection with the 100% humidity line, the moisture is called bound water. This water in the solid exerts a vapor pressure less than that of liquid water at the same temperature. If such a material contains more water than indicated by intersection with the 100% humidity line, it can still exert a vapor pressure only as high as that of ordinary water at the same temperature. This excess moisture content is called unbound water, and it is held primarily in the voids of the solid. Substances containing bound water are often called hygroscopic materials.

As an example, consider curve 10 for wood in Fig. 9.4-1. This intersects the curve for 100% humidity at about 30 kg H2O/100 kg dry solid. Any sample of wood containing less than 30 kg H2O/100 kg dry solid contains only bound water. If the wood sample contained 34 kg H2O/100 kg dry solid, 4 kg H2O would be unbound and 30 kg H2O bound per 100 kg dry solid.

The bound water in a substance may exist under several different conditions. Moisture in cell or fiber walls may have solids dissolved in it and have a lower vapor pressure. Liquid water in capillaries of very small diameter will exert a lowered vapor pressure because of the concave curvature of the surface. Water in natural organic materials is in chemical and physical–chemical combination.

9.4D. Free and Equilibrium Moisture of a Substance

Free moisture content in a sample is the moisture above the equilibrium moisture content. This free moisture is the moisture that can be removed by drying under the given percent relative humidity. For example, in Fig. 9.4-1 silk has an equilibrium moisture content of 8.5 kg H2O/100 kg dry material in contact with air of 50% relative humidity and 25°C. If a sample contains 10 kg H2O/100 kg dry material, only 10.0 − 8.5, or 1.5, kg H2O/100 kg dry material is removable by drying; this is the free moisture of the sample under these drying conditions.

In many texts and references, the moisture content is given as percent moisture on a dry basis. This is exactly the same as the kg H2O/100 kg dry material multiplied by 100.

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