## 2 Materials and Methods
### Mass Transfer  
Mass transfer was measured using silica gel as bed material and moisturized air as fluidizing gas. Similar experiments have previously been made by e.g., [PERSON] et al. [18], who concluded that the adsorption rate of water onto the silica gel particles is mass transfer controlled for a relatively long time period. The air moisturization device used in these experiments was constructed using industry grade PVC piping. The main pipe outer diameter was 16 cm and it was 2 m tall. The pipe was capped in both ends, and in the top cap two holes were drilled as inlets for dry air and one as outlet for moisturized air. On the inside of the pipe the inlets were connected to tubing of approximately the same length as the pipe; perforated at the bottom. This caused the dry air to bubble up through a water column of 1.5 m height and become moisturized. The moisture content varied between 75-95% relative humidity depending the temperature of the room and the dry air.  
The cold flow model was placed upon a scale which logged the total system weight over the duration of each experiment, and weight increase logged then corresponded to the mass of water adsorbed on the particles. Using this data together with the recorded moisture content of the air, a mass transfer rate coefficient, k, was calculated according to Equations (1)-(4). The water vapor concentration in the bulk of the gas was calculated assuming a logarithmic mean of the in- and outgoing concentrations, Equation (2). The concentration of water on the particle surface was calculated by performing a calibration experiment. In the experiment the fluidizing solids were completely saturated with water. Knowing that the concentrations on the particle surface and in the bulk gas were equal at this point, a material dependent coefficient, \(\alpha\), was obtained (Equation (4)). For the material used here \(\alpha\) = 0.0241 kg/m\({}^{3}\). Assuming linearity, this corresponds to a Henry's law constant \(\left[K=\frac{m_{ads,sat,cal}}{m_{0}}/\frac{pH_{2O}}{pH_{2O,sat}}\right]\) of 0.36 g/g, to be compared to e.g., [19] who report a value of ca. 0.44 g/g for Davidson Bead Gel.  
\[k=\frac{dm_{H_{2}O}}{dt}\frac{1}{A_{p}\big{(}C_{H_{2}O,\infty}-C_{H_{2}O,s} \big{)}} \tag{1}\]  
\[C_{H_{2}O,\infty}=\frac{C_{H_{2}O,in}-C_{H_{2}O,out}}{\ln\big{(}C_{H_{2}O,in} \big{)}-\ln\big{(}C_{H_{2}O,out}\big{)}} \tag{2}\]  
\[C_{H_{2}O,s}=\alpha*m_{ads}(t)/m_{fs} \tag{3}\]  
\[\alpha=\frac{C_{p,sat}}{m_{ads,sat,\ cal}}*m_{fs,cal} \tag{4}\]  
Five different cases were tested: One for each type of packing solids and a comparative experiment using the same bed mass as in the other cases, but without packing. For all cases the superficial gas velocity was u\({}_{0}\) = 29.5 cm/s. The experiments are summarized in Table 1.  
Due to excessive noise the signals acquired from the scale required conditioning before the mass transfer coefficients could be calculated. They were filtered with a Lowess-type smoothing filter and then fitted to an exponential expression of the type \(f(x)=a*e^{-b*x}+c\). The signals were also down sampled from 10 Hz to 1 Hz, matching the native sampling frequency of the relative humidity meter. An example of raw and conditioned logged weight can be seen in Figure 2. In addition to this, only the first 10 minutes of the sampled data was used. This ensured that the adsorption was mass-transfer limited (i.e., the mass transfer coefficient was constant).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Packing Type** & **Bed Height 1 (cm)** & **Bed Mass (g)** & **Packing Mass (g)** & **Notes** \\ \hline
6.35 mm ASB & 13.5 & 464 & 2297 & \\
12.7 mm ASB & 13.5 & 467 & 2134 & \\
25.4 mm ASB & 13.5 & 467 & 1990 & \\
12 mm ECA & 13.5 & 475 & 410 & \\ No packing & 6 & 475 & - & Equal bed \\ \hline \end{tabular} \({}^{1}\)Unfluidized  
\end{table}
Table 1: Description of experiments with silica gel.