# Morphology Characteristics of the Liquid-Vapour Interface in Porous Media
## 1 Introduction  
Under varying conditions of saturation, the liquid-vapour (l-v) interface ubiquitously manifests within porous media, inevitably engaging a multitude of natural and industrial systems, such as evaporation and transport in microporous membranes [1; 2], geological sequestration of carbon dioxide [3; 4], and playing pivotal roles in natural phenomena like plant transpiration and industrial processes such as desalination of seawater [5; 6]. Previous research has extensively investigated interface characteristics such as surface area, curvature, phase morphology, and phase connectivity during processes like CO\({}_{2}\) injection or oil/gas displacement in oil/water or CO\({}_{2}\)/salt interface [7; 8; 9]. [PERSON] et al. [10] utilized interface characteristics to describe the evaporation process of pore water in glass beads. [PERSON] et al. [11] employed Gaussian curvature to characterize the evaporation process, using curvature to delineate interface morphologies in oil-wet reservoir rocks, thereby providing pore-scale insights into the dynamics of two-phase fluid flow during oil and gas displacement. [PERSON] et al. [1] demonstrated using interface curvature analysis that negative Gaussian curvature is a prerequisite for the continuity of oil-water phase within pore spaces. The geometric and topological features such as interface surface and curvature necessitate further complex and detailed examination. Numerous experimental techniques have been employed to effectively characterize the pores and pore fluids within porous media. Techniques for studying interface characteristics include gamma-ray attenuation [12], time-domain reflectometry [13], nuclear magnetic resonance imaging [14], and X-ray computed tomography (CT) [15; 16; 17; 18]. Amongthese, the CT method has been successfully applied to provide non-destructive, three-dimensional, and high-resolution image observations, thus being widely adopted in the engineering field for studies including internal damage inspection of laboratory or in situ samples and characterization of pore-scale features in porous media [19; 20; 21]. This has led to the exploration of CT technology for microstructural characterization of porous media mechanics, percolation processes, and more. High-resolution X-ray imaging technology has revolutionized our understanding of multiphase flow within porous media, making the visualization of phase transitions at the pore scale a reality [22]. This work has been applied to address a wide range of issues, including drainage and wetting dynamics [23; 24; 25; 26; 27; 28], and multiphase flow displacement [29; 30; 31]. [PERSON] et al. [19; 20] documented the failure morphologies of sand columns under triaxial stress using micro-CT scanning technology and obtained curvature values of local curved liquid surfaces, calculating local capillary forces according to the Young-Laplace equation. This study applied CT scanning technology in the field of geomechanics to visually characterize the failure morphology of sand columns in triaxial tests. However, capillary forces calculated from curvature values of local curved liquid surfaces obtained from two-dimensional CT images lack representativeness compared to macroscopic capillary forces measured by tensiometers. [PERSON] et al. [21] obtained soil sample grain and pore-size distribution information through CT scanning and determined the area variation curves of water-air interface, soil particle-water interface, and soil particle-air interface with saturation during the soil water evaporation process. The study found that the area of water-air interface first increases and then decreases as saturation decreases, and the size of the water-air interface area is related to the grain size distribution. In the evaporation process, while the soil surface or pores are the final regions for water vapour exchange between soil pores and the atmosphere, the liquid-vapour interface of pore water is the actual region for phase transition (Figure 1).