## 2 Materials and Methods
### Experimental Procedures  
Either 233 g of air-dried coarse-grained silica sand (grain size: 1.2-2.4 mm) or 221 g of air-dried relatively fine-grained silica sand (grain size: 0.074-0.35 mm) was first homogeneously packed into the column, as shown by the vertical X-ray computed tomography slice images in Figure 2. The images were captured at an X-ray tube voltage of 120 kV, X-ray tube current of 150 \(\upmu\)A, and voxel size of 40 \(\times\) 40 \(\times\) 40 \(\upmu\)m using a microfocus X-ray computed tomography system (ScanXmate-D225 RSS270, Comscentenco Co., Ltd., Kanagawa, Japan), where a lighter color corresponds to a higher density in the image. Although the shape of each grain of the finer-grained silica sand is difficult to identify in the figure because of the voxel size employed, the homogeneity of the packing can be confirmed by the homogenous color displayed in the figure. Both silica sands are natural silica sands produced in Japan, where the courser and finer ones are Keisha No. 3 (Takeori Mineral Mining Co., Ltd., Tokyo, Japan) and Toyoura silica sand (Toyoura Keiseki Kogyo Co., Ltd., Yamaguchi, Japan), respectively. As these sands have been utilized widely in Japan for various purposes, their chemical characteristics are well documented [25; 26; 27]. Typically, these sands contain \(\geq\)90% silica and rarely contain organic impurities [27; 28; 29; 30]. Figure 1: Experimental system for vertical vapor-phase diffusive transport of VOC through soil sample. During wet soil sample preparation, the prescribed amount of water (described in Section 2.3) was added to the top face of the soil sample using a syringe, and the column was left to rest overnight. As no water dropped from the soil sample to the bottom space, we expected that all added water was naturally distributed in the soil sample. The amount of water may decrease gradually from the top to the bottom owing to the addition of water from the top and matric potential/capillary forces, and the water retention behavior may be different between the coarser- and finer-grained silica sands. This type of vertical variation in water content simulates conditions for a depth of up to 3 m in near-surface soils, under which an inverse correlation between temperature and VOC flux changes was observed by [PERSON] et al. (2014) [8]. However, measurements on the distributions of water, which should be addressed in future studies, were not conducted in this study. After the bottom and top space temperatures reached 25 \({}^{\circ}\)C, approximately 3 mL of benzene gas was injected into the bottom space of the column through a gas detector circulation tube connected to a syringe. A preliminary experiment confirmed that no detectable pressure changes (<0.1 kPa) were produced during the injection. Benzene gas was extracted from the headspace of a sealed 10 mL vial, which contained 0.5 mL of liquid benzene (99.7% purity, Wako Pure Chemical Industry, Ltd., Osaka, Japan) and was heated to 60 \({}^{\circ}\)C. Benzene was chosen for this study, because it is a typical VOC that poses hazards to human health. The boiling point and solubility in water at 25 \({}^{\circ}\)C for benzene are 80.1 \({}^{\circ}\)C and 22.8 mmol/L, respectively [31; 32]. The benzene concentration and temperature changes--for both the bottom and top spaces--and RH changes within the column were measured for 100 min, either without changes in temperature (constant at 25 \({}^{\circ}\)C) or under sinusoidal changes in temperature between 20 and 30 \({}^{\circ}\)C, that is, 25 \(\pm\) 5 \({}^{\circ}\)C (Figure 3). During the measurement, the benzene concentrations in the bottom and top spaces, respectively, decreased and increased with time owing to the upward diffusive transport of benzene. The RH measured at the top space changed in response to changes in the amount of saturated water vapor resulting from temperature changes, and changes in the amount of existing water vapor owing to evaporation and condensation within the column.