Wetting in porous media

多年来，对土壤、沉积岩、木材、骨、纸、聚合物复合材料、催化剂、涂层、陶瓷等随机无序材料的表征和真实模拟一直是物理学家、地球科学家和工程师面临的主要问题。然而，如何预测材料的力学和光学性质，以及从微观形态和拓扑结构来预测流体在多孔结构中的输运和相行为，仍然是一个悬而未决的问题。从多孔介质中非均匀流体的微观密度泛函出发，我们的目标是确定热力学量，如自由能和流体的润湿行为与衬底的几何形状的关系。多孔衬底由重叠的颗粒(布尔颗粒模型)建模，并以结构函数和形态指标(如体积、表面积、积分平均曲率和孔的连通性)为特征。这些度量在积分几何中被称为Minkowski泛函，它提供了强大的定理使微积分变得方便。特别是，平行表面的概念使人们能够确定润湿、毛细冷凝和两相流等物理现象如何依赖于随机结构和孔隙的形态。由大小和形状不均匀的毛细管通道组成的相互连接的三维网络的复杂的孔结构使多孔介质有别于任何其他固体或平面衬底。该项目试图将形态和界面效应(如表面能和润湿性)这两个主要因素联系起来，以预测流体在多孔介质中的相行为和输运。

The characterization and realistic modelling of random disordered materials as diverse as soils, sedimentary rocks, wood, bone, paper, polymer composites, catalysts, coatings, ceramics has been a major problem for physicists, earth scientists and engineers for many years. Nevertheless, the prediction of mechanical and optical properties of the material, as well as the prediction of transport and phase behavior of fluids in porous structures from measures of the morphology and topology is still an unsolved problem. Starting from a microscopic density functional for inhomogeneous fluids in porous media, we aim in this project to determine the dependence of thermodynamic quantities such as the free energy and the wetting behavior of a fluid on the geometry of the substrate. The porous substrate is modelled by overlapping grains (Boolean grain model) and is characterized by structure functions and morphological measures such as volume, surface area, integral mean curvature, and the connectivity of the pores. These measures are known as Minkowski functionals in integral geometry which provides powerful theorems to make the calculus convenient. In particular, the concept of parallel surfaces allows one to determine how physical phenomena such as wetting, capillary condensation and two-phase flow depend on the random structure and the morphology of the pores. The complicated pore structure of an interconnected three-dimensional network of capillary channels of nonuniform sizes and shapes distinguishes a porous medium from any other solid or planar substrate. The project attempts to connect the two main factors, morphology and interfacial effects such as surface energies and wettability, in order to predict phase behavior and transport of fluids in porous media.