Differential spontaneous capillary flow through heterogeneous porous media

Engineered heterogeneous porous materials with aeolotropic liquid transport properties can have many applications. In this work, spontaneous flow of liquids through layered heterogeneous porous materials is analyzed based on fractal theory. Both capillary pressure and hydraulic resistance are expressed in terms of microscopic variables such as minimum and maximum pore sizes and fractal dimensions. The transplanar liquid flow in terms of the mass absorbed by the different layers against time is computed. The effect of layer configuration and pore size, fractal dimension and porosity in each layer are numerically investigated. It is found that different combinations of porous layers of different porosity and pore size distribution create different absorption patterns, and differential liquid transport properties can be achieved by having a gradient of porosity and pore size across the thickness.