Wetting in porous media

随机无序材料的表征和真实建模，如土壤，沉积岩，木材，骨头，纸张，聚合物复合材料，催化剂，涂料，陶瓷，多年来一直是物理学家，地球科学家和工程师的主要问题。然而，从形貌和拓扑结构的测量来预测材料的机械和光学性质，以及预测流体在多孔结构中的输运和相行为仍然是一个未解决的问题。从一个微观密度泛函的多孔介质中的非均匀流体，我们的目标是在这个项目中，以确定热力学量的依赖关系，如自由能和润湿行为的流体上的基板的几何形状。多孔基板是由重叠的晶粒（布尔晶粒模型）建模，其特征在于结构功能和形态的措施，如体积，表面积，积分平均曲率，和孔的连通性。这些措施被称为闵可夫斯基泛函在积分几何提供了强大的定理，使微积分方便。特别是，平行表面的概念允许一个确定的物理现象，如润湿，毛细冷凝和两相流取决于随机结构和孔隙的形态。不均匀尺寸和形状的毛细管通道的互连三维网络的复杂孔结构将多孔介质与任何其它固体或平面基底区分开。该项目试图连接两个主要因素，形态和界面效应，如表面能和润湿性，以预测相行为和多孔介质中流体的传输。

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.