# The Significance of the Sorption Isotherm on the Simulated Performance of Grain Driers
## 6 Anomalies  
### EMC as a Function of Temperature and Humidity  
A key feature of sorption isotherms is that they encapsulate the relationship between the equilibrium moisture content of hygroscopic solids and the temperature and humidity of their surrounding atmosphere. In this work, it is found that in the range of relative humidity, \(0.2\lesssim r\lesssim 0.8\), all of the isotherms are defined above yield moisture contents \begin{table}
\begin{tabular}{l l l} \hline \(\beta_{1}\) & \(1.8334\) & \(\gamma_{1}\) & \(1.0775\) \\ \(\beta_{2}\) & \(-42.684\) & \(\gamma_{2}\) & \(-0.75002\) \\ \(\beta_{3}\) & \(1098.1\) & \(\gamma_{3}\) & \(3.1343\) \\ \(\beta_{4}\) & \(-16873\) & \(\gamma_{4}\) & \(-6.7330\) \\ \(\beta_{5}\) & \(1.5600\times 10^{5}\) & \(\gamma_{5}\) & \(7.3033\) \\ \(\beta_{6}\) & \(-8.4449\) & \(\gamma_{6}\) & \(-3.1724\) \\ \(\beta_{7}\) & \(2.4564\times 10^{6}\) & \\ \(\beta_{8}\) & \(-2.9579\times 10^{6}\) & \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters used in Equations (58) and (59) to calculate the heat of wetting of canola by means of [PERSON]’s [19] isostere equation. of canola within 0.01 of each other. However, there are considerable differences between the predicted moisture contents at low and high extremes of relative humidity. Figure 4 shows the behaviour of the six isotherms in the range \(0\leq r\leq 0.15\) at 30 \({}^{\circ}\)C. It can be seen that there are discrepancies between all of the isotherms, and this inevitably leads to erroneous predictions of the moisture contents of canola that is being dried. Significantly, it is observed that the ubiquitous modified Chung-Pfost isotherm yields negative values of moisture content when the relative humidity is less than about 0.025. This is a physical impossibility, but it is inherent in the form of the Chung-Pfost isotherm. It is found that the modified Halsey isotherm predicts that the moisture content of canola exceeds 0.01 when the relative humidity of the air exceeds \(8\times 10^{-5}\). However, in the extreme, as the relative humidity approaches zero, the Halsey equation predicts that the moisture content approaches zero. Compared with other isotherms considered in this work, this result is distinctly anomalous. As the relative humidity approaches unity, the moisture contents predicted by the modified Chung-Pfost and Henderson isotherms are similar. Hence, for the sake of clarity, Figure 5 shows only the Henderson isotherm fitted to [PERSON] et al. 's [18] data However, as the relative humidity of air approaches unity, the moisture contents predicted by the modified Halsey, Oswin, and Hunter isotherms are markedly higher and different from each other. This is important from a practical point of view, because if an isotherm predicts that the relative humidity of air is too high, it follows that water vapour will be expelled from the drier at a higher rate. This may result in a drier being under-sized. Figure 4: The Chung–Pfost (C-P), Henderson (HEN-GAZ), Hunter, Halsey, and Oswin isotherms are fitted to the experimental data presented by [PERSON] [8], whilst the remaining Henderson isotherm (HEN-SOK) is fitted to data presented by [PERSON] et al. [18]. The Hunter and Oswin isotherms are almost coincident in the range of relative humidities depicted in the figure. Note that relative humidity is expressed on a fractional basis, hence \(r=0.1\) is equivalent to \(\dot{m}=10\%\) on a percentage basis. The rapid increase in the moisture content with increasing humidity is consistent with the [PERSON], [PERSON], and [PERSON] [21] isotherm, which assumes that the water molecules form multilayers. However, it should be noted that [PERSON]'s [19] isotherm is purely empirical, although it apparently captures a multi-layering effect. Recall that the isotherms were fitted to the same experimental data, hence the forms of the isotherms play a key role in their accuracy. However, it is important to note that the isotherms are extrapolated beyond the data on which they are based, and this may contribute to the divergence in results.