Structure of drying fronts in three-dimensional porous media

Abstract

Evaporation in a three-dimensional (3D) porous medium, a sand column saturated by water, was studied using synchrotron x-ray tomography. Three-dimensional images of the medium with a resolution of 7 µm were obtained during the evaporation. The entire column was scanned seven times, resulting in nearly 10 4 2D cross sections and illustrating the spatial distribution of air, liquid and solid phases at the pore scale. The results were analyzed in order to gain new insights and better understanding of the characteristics of the drying front that was formed when the liquid-filled pores were invaded by air, as well as the structure of the liquid phase as it was dried. The analysis indicates that the liquid phase has a self-similar fractal structure, with its fractal dimension D f in all the cross sections being a function of the water content or saturation. In addition, D f for the 3D liquid structure, as well as its density correlation function, were computed using the 3D images. A crossover length scale ξ was identified that separates the fractal regime from the compact geometry. For length scales r > ξ, the density correlation function approaches asymptotically the water content of the porous medium. The drying front is shown to be rough and multi-affine, rather than self-affine. Its properties were also computed using the 3D images. The rougness characteristics agree with those for imbibition in porous media, but not with those of fracture surfaces and crack lines. PACS number(s):

Roughness Control on Multiphase Flow in Rock Fractures

“…Here, D f is calculated by the box‐counting method (Figure S7), and S nwb is defined as the ratio of the volume of invading fluid to the pore volume of a fracture. From Figure c, we see that the fractal dimension D f correlates with saturation S nwb by D f ∝log 10 S nwb , which is in excellent agreement with the theoretical model (Yu & Li, ) and the experimental and numerical results (Bakhshian et al, ; Shokri & Sahimi, ). This relation has important implications for analyzing the hydraulic properties of multiphase flow by fractal theory (Yu & Li, ).…”

Transport of a water-soluble polymer during drying of a model porous media

“…Some 2D model porous systems consisting of glass beads exist, allowing imaging the drying process using a camera. [13][14][15] To measure fluid distributions inside 3D porous materials, techniques like synchrotron X-ray tomography [16] and nuclear magnetic resonance (NMR) imaging [17][18][19] allow noninvasive probing of moisture with a sufficiently high spatial and time resolution. For this study, NMR imaging was used to monitor the moisture distribution during drying process.…”

Patterns of Desiccation Cracks in Saline Bentonite Layers

“…In order to fully establish this, the fractal dimension, D f , of the crack patterns was calculated using the 'box-counting method.' As explained by several researchers (e.g., Sahimi 1993Sahimi , 2003Shokri and Sahimi 2012), in the box-counting method, the fractal object is covered by boxes of side length, r. The number of such boxes, denoted as N (r ), which are required to cover the entire object is counted and then plotted versus r. An example of this method is presented in the inset of Fig. 7a which corresponds to the desiccating bentonite with 4 % salt concentration.…”