Equilibrium-moisture curves

Latent heat of vaporization is the energy required to evaporate per kg of liquid (in this case water) and latent heat of sublimation is the energy required for 1 kg of solid to evaporate. These values can be obtained from the steam tables. In carrying out heat calculations for dryer, the enthalpy of drying can be calculated using the following equation 

The study of the relationship between air and water is called psychrometry. Psychrometric charts show properties of mixture of air and water as shown in Figiu-e 11.4. Any point on this chart represents specific mixture of water and air. The curved line represents saturation curve for 100 % humidity of air saturated with water as a function of dry bulb temperature. 

The dry bulb temperature (DBT) is the temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture. The wet-bulb temperature (0w) is the temperature a parcel of air would have if it were cooled to saturation (100% relative humidity) by the evaporation of water into it, with the latent heat being supplied by the parcel. In other words, wet bulb temperature is the temperature reached by water surface if the air is passed over it. Wet bulb temperature is a function of dry bulb temperature and humidity. The chart shows dry bulb temperature on the x-axis and moisture content on the y-axis. Any point below the saturation line represents air that is unsaturated, therefore, the chart has relative humidity cxirves going up to 100% relative humidity. Wet bulb temperature lines are constant enthalpy or adiabatic cooling lines. The change in composition of 

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FIGURE 23.3 Equilibrium moisture curves for different types of solids. 

The surface humidity 7, is found in the manner previously described, and X is given by the equilibrium-moisture curve for the appropriate Y. 

Equilibrium moisture content curves vary greatly with the type of material examined. Insoluble, non-porous materials, such as talc or zinc oxide, have equilibrium moisture contents of almost zero over a wide humidity range. A moisture content between 10 and 15% may be expected for cotton fabrics under normal atmospheric conditions. Drying below the equilibrium moisture content for room conditions may be deliberately undertaken, particularly if the material is unstable in the presence of moisture subsequent storage becomes important. 

The effects of storage after drying also may be assessed from the equilibrium moisture content curves. Storage conditions are not critical for the lactose granulation.f If the antacid formulation is stored at a relative humidity of only 65% it would, given sufficient time, absorb moisture until the content was 91%. This could be associated with poor flow characteristics and its attendant difficulties during compression. 

The relationship between water activity and moisture content for most foods at a particular temperature is a sigmoidal-shaped curve called the sorption isotherm (Figure 3.10). The term equilibrium moisture content curve is also used. Sorption... 

Consider, for instance, curve 2 for worsted yarns. This intersects the curve for 100 percent humidity at 26 percent moisture consequently, any sample of wool that contains less than 26 percent water contains only bound water. Any moisture that a sample may contain above 26 percent is unbound water. If the sample contains 30 percent water, for example, 4 percent of this water is unbound and 26 percent bound. Assume, now, that this sample is to be dried with air of 30 percent relative humidity. Curve 2 shows that the lowest moisture content that can be reached under these conditions is 9 percent. This, then, is the equilibrium-moisture content for this particular set of conditions. If a sample containing 30 percent total moisture is to be dried with air at 30 percent relative humidity, it contains 21 percent free water and 9 percent equilibrium moisture. Any amount up to a concentration of 26 percent is still bound water, but most of this can be evaporated into the air and hence is free water. Thus water can be both bound and free at the same time—partially bound to the solid but free to be evaporated. The distinction between bound and unbound water depends on the material itself, while the distinction between free and equilibrium moisture depends on the drying conditions. 

Figure 9.9, finally, shows the Tan fi/T curve of the aged DMA sample with an equilibrium moisture saturation of 0,74 %wt. and the same curve after drying due to heating to 150°C. The Y-relaxation, clearly present in the wet sample, is strongly reduced in intensity in the dried sample. Hence, absorped moisture is for an important part responsible for the intensity of the y-relaxation of polyketone (such an effect of moisture absorption was described before, see 5.2.2). This might also be the reason for the nearly identical transition effects as shown in Figure 9.6. 

The equilibrium moisture of a material can be attained either by adsorption or by desorption, as expressed by the respective isotherms of Figure 4.11. The usually observed deviation of the two curves is due to the phenomenon of hysteresis, which has not yet been quantitatively described. Many explanations for the phenomenon have been put forth that converge in that there are more active sites during the desorption than during adsorption. It is clear from Figure 4.11 that the desorption isotherm is the curve to use for the process of drying. 

Moisture sorption in wood is complex and the final equilibrium moisture content is affected by temperature and humidity. The equilibrium moisture content can also vary by up to 3-4% (although usually less), depending on whether it is approached from a higher or lower humidity (i.e., wood exhibits a moisture sorption hysteresis). Table 15.3 shows approximate equilibrium moisture contents for wood at different temperatures and humidities at a midpoint between the hysteresis curves. 

Typical equilibrium moisture contents of some food materials at approximately 298 K (2j C) (/) macaroni, (2) flow, (J) bread, (4) crackers, (5) egg albundn. [Curoe (5) from ref (El). Curves (/) to (4) from National Research Council, International Critical Tables, Vol. ll. New York McGraw-Hill Book Company, 1929. Reproduced with permission of the N ational Academy of Sciences. ... 

Figure 1.8 shows the shape of the sorption isotherm characteristic of many dry food products. If the partial pressure of the external atmosphere Pw is nearly zero, then the equilibrium moisture inside the dry product will also be almost zero. Section A of the curve represents a region in which the monomolecular layers are formed, although there may be multimole-cular layers in some places toward the end of A. 

A few typical equilibrium-moisture relationships are shown in Fig. 12.1, where the moisture in each case is water. Here the equilibrium partial pressure p of the water vapor in the gas stream has been divided by the vapor pressure of pure water p to give the relative saturation, or relative humidity (see Chap. 7), of the gas, since the curves are then applicable over a modest range of temperatures instead of being useful for one temperature only. Consider the curve for wood. If the wood contained initially a very high moisture content, say 0.35 kg water/kg dry solid, and were exposed to a continuous supply of air of 0.6 relative humidity, the wood would lose moisture by evaporation until its equilibrium concentration corresponding to point A on the curve was eventually reached. Further exposure to this air, for even indefinitely long periods, would not bring about additional loss of moisture from the solid. The moisture content could be reduced further, however, by exposure of the solid to air of lower... 

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