# Exploring Convective Drying Behavior of Hydroxide Sludges Through Micro-Drying Systems
## 2 Materials and Methods
### Drying Tests  
In this study, a full factorial design with two factors, each at three levels, was employed to evaluate the effects of temperature and air speed on the drying process. The key responses evaluated included the time required to reach 90% solid content, the average drying rate (or evaporation rate), the volume change (or shrinkage), and the critical moisture content. Detailed information regarding the factor levels, units, and response measurements is provided in Table 1. The experimental design results were analyzed using the Design Expert 13 software.  
The sludge samples were extruded and covered with a paraffin jacket (as shown in Figure 2) to make the drying and handling easier.  
The drying experiments were performed using a convective \"micro-dryer\" (Figure 3), specifically designed to process small, extruded sludge samples ranging in mass from 0.5 to 5 g. The micro-dryer operates under conventional convective drying conditions, controlled by key parameters such as relative humidity, temperature, and air velocity. Further technical details of the micro-dryer setup have been thoroughly described in a previous study [7]. The absolute humidity of the air was maintained at a constant value of 0.005 kg of water per kg of dry air.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{4}{c}{**Factors**} \\ \hline
**Variable** & **Abbreviation** & **Units** & \(-\) & **0** & **+** \\ \hline Temperature & T & \({}^{\circ}\)C & 70 & 90 & 110 \\ \hline Air speed & V\({}_{\text{a}}\) & m/s & 1 & 2 & 3 \\ \hline Diameter & D & mm & & 12 & \\ \hline Height & H & mm & & 15 & \\ \hline \multicolumn{5}{c}{Responses} \\ \hline Drying time & Dt & Min & & \\ \hline Evaporation rate & Mv & kgwater/min & & \\ \hline Critical moisture & Xc & kgwater/KgDS & & \\ \hline Total shrinkage & \%Sh & \%Voloss & & \\ \hline \end{tabular}
\end{table}
Table 1: Experimental design factors and responses.  
Figure 2: Sample geometry (**a**) and covering (**b**) [10].  
During the experiments, the drying exchange surface and volume of sludge samples were measured through the drying (i.e., samples' shrinkage) using the methodology created by [PERSON] (2002) [7]. During the drying test, the sludge samples were removed from the dryer chamber and placed in the X-ray microtomographic device in order to obtain images of several cross-sections, then the samples were replaced in the micro-drier. The sequence was repeated about 10 times during the drying process. It has been verified that the drying interruptions do not exert any influence on the drying kinetics [12; 13; 14].  
The X-ray microtomographic equipment employed in this study was a \"Skyscan-1074 X-ray scanner\". Operating at 40 kV and 1 mA, the X-ray source is accompanied by a 2D detector comprising a 768 \(\times\) 576-pixel, 8-bit X-ray camera that generates images with a pixel size of 41 \(\upmu\)m.  
The supplied software (Skyscan/NRecon) accompanying the machine was utilized for the image reconstruction processing. The quality of the resulting image is influenced by the quantity of acquired data, and its improvement is directly proportional to the number of projections captured. Subsequently, MATLAB software was employed for the analysis of the microtomography-derived images and their conversion into mathematical data suitable for generating the Krischer representation. Figure 4 shows, from left to right, the raw images obtained from tomography, a transverse cut obtained from Nrecon.  
During each interruption of the drying process, the average equivalent diameter (d\({}_{\text{eq}}\), mm) and average height (h, mm) were determined and utilized to calculate the surface area of the sample. In this study, the sludge samples were assumed to be perfect cylinders  
Figure 4: Images before and after processing.  
Figure 3: Micro-dryer tool [11].  
with their entire surfaces in contact with the drying air. The obtained equations for each sample were used for the calculation of water flux and the plotting of the Krischer's curve.