# The Significance of the Sorption Isotherm on the Simulated Performance of Grain Driers
## 2 Mechanisms of Drying Hyroscopic Porous Media  
Beds of moist hygroscopic materials, such as canola, are dried by ventilating them with warm air that has a low relative humidity. Grains in proximity to the air inlet attain the temperature of the incoming air, referred to as state A shown in Figure 1.  
Grains distant from the entrance of the bed are at their initial temperature, state B. Two heat and mass transfer fronts propagate through the bed, namely a slow-moving drying front and a relatively rapidly moving heating front. The two  
Figure 1: Velocities of the drying, AP, and temperature, PB, fronts through a bed of canola. State A represents the system in equilibrium with the incoming air, and B is the system at its initial state prior to the initiation of drying. The drying fronts are separated by the plateau state, P.  
plateau state, P. The moisture in the canola in state A is deemed to be in thermodynamic equilibrium with the moisture in the incoming air, whilst canola in state B retains its initial moisture content, as shown in Figure 1. It is observed that the moisture content of the grain in the plateau state, P, is higher than its initial value, i.e., this region of grain has adsorbed moisture. Figure 1 shows the values of the humidity of the interstitial air that correspond to the initial temperature and moisture content of the grain. The states of the air used in this example are depicted on the psychrometric chart shown in Figure 2.  
Figure 1 suggests that the heating and drying waves are sharp. In practice, dispersive effects such as the resistance to mass transfer between the solid phase and the surrounding intergranular air cause the formation of waves that have finite widths. The dispersive effects result in some of the moisture in the air not being adsorbed instantaneously; hence, the moisture content profiles of the grains and air become smeared along the drier. However, neglecting dispersive effects has a significant advantage, namely it permits a simple mathematical expression for the speed of the heating and drying fronts to be calculated. This provides a direct and powerful method of comparing the influence of the sorption isotherm on the degree and rate of cooling beds of hygroscopic porous media, such as food grains. In this work, we do not consider dispersive effects, although [PERSON] [15] and [PERSON] [16] show that the analysis provides the correct average speed of the transfer waves. The analysis also provides the correct value of temperature and grain moisture content at the plateau state. Furthermore, dispersive effects may be accounted for by superimposing spreads of moisture, temperature, and humidity on the drying and temperature fronts. Figure 1 shows the velocities of the drying and wetting waves traversing a bed of canola when the specific mass flow rate of the dry component of the moist air is 1 kg/s per square metre cross-section of the bed. This is an order of magnitude greater than air flow rates typical encountered in grain drying systems; hence, in practice, the velocity of a drying front, AP, is likely to be on the order of \(10^{-5}\) m/s. This low speed occurs because the bulk density of canola is three orders of magnitude greater than that of the intergranular air, i.e., \(10^{3}\). Furthermore, it is observed in Figure 1 that the change in the moisture content of the solid is on the order of \(10^{-1}\) and the change in humidity of the air is on the order of \(10^{-2}\). By considering mass transfer, we therefore anticipate that a large volume of air must flow to remove the moisture from the solids. This reasoning is confirmed in Figure 1,  
Figure 2: The states of the air and grain in the system portrayed on a psychrometric chart. As indicated in Figure 1, states A and B are, respectively, those of the air at the entrance to the drier and at the initial conditions. The plateau state is denoted by P. The dotted lines between AP and PB indicate the discontinuities across the drying and heating fronts, respectively.