Lotion Distribution in Wet Wipes Investigated by Pore Network Simulation and X-ray Micro Tomography

Dynamic Pore-Scale Model of Drainage in Granular Porous Media: The Pore-Unit Assembly Method

Dynamics of drainage is analyzed for packings of spheres, using numerical experiments. For this purpose, a dynamic pore-scale model was developed to simulate water flow during drainage. The pore space inside a packing of spheres was extracted using regular triangulation, resulting in an assembly of grain-based tetrahedra. Then, pore units were constructed by identifying and merging tetrahedra that belong to the same pore, resulting in an assembly of pore units. Each pore unit was approximated by a volume-equivalent regular shape (e.g., cube and octahedron), for which a local capillary pressure-saturation relationship was obtained. To simulate unsaturated flow, a pore-scale version of IMPES (implicit pressure solver and explicit saturation update) was employed in order to calculate pressure and saturation distributions as a function of time for the assembly of pore units. To test the dynamic model, it was used on a packing of spheres to reproduce the corresponding measured quasi-static capillary pressure-saturation curve for a sand packing. Calculations were done for a packing of spheres with the same grain size distribution and porosity as the sand. We obtained good agreement, which confirmed the ability of the dynamic code to accurately describe drainage under low flow rates. Simulations of dynamic drainage revealed that drainage occurred in the form of finger-like infiltration of air into the pore space, caused by heterogeneities in the pore structure. During the finger-like infiltration, the pressure difference between air and water was found to be significantly higher than the capillary pressure. Furthermore, we tested the effects of the averaging, boundary conditions, domain size, and viscosity on the dynamic flow behavior. Finally, the dynamic coefficient was determined and compared to experimental data.

The Effects of Swelling and Porosity Change on Capillarity: DEM Coupled with a Pore-Unit Assembly Method

In this study, a grain-scale modelling technique has been developed to generate the capillary pressure–saturation curves for swelling granular materials. This model employs only basic granular properties such as particles size distribution, porosity, and the amount of absorbed water for swelling materials. Using this model, both drainage and imbibition curves are directly obtained by pore-scale simulations of fluid invasion. This allows us to produce capillary pressure–saturation curves for a large number of different packings of granular materials with varying porosity and/or amount of absorbed water. The algorithm is based on combining the Discrete Element Method for generating different particle packings with a pore-unit assembly approach. The pore space is extracted using a regular triangulation, with the centres of four neighbouring particles forming a tetrahedron. The pore space within each tetrahedron is referred to as a pore unit. Thus, the pore space of a particle packing is represented by an assembly of pore units for which we construct drainage and imbibition capillary pressure–saturation curves. A case study on Hostun sand is conducted to test the model against experimental data from literature and to investigate the required minimum number of particles to have a Representative Elementary Volume. Then, the capillary pressure–saturation curves are constructed for Absorbent Gelling Material particles, for different combinations of porosity values and amounts of absorbed water. Each combination yields a different configuration of pore units, and thus distinctly different capillary pressure–saturation curves. All these curves are shown to collapse into one curve for drainage and one curve for imbibition when we normalize capillary pressure and saturation values. We have developed a formula for the Van Genuchten parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}α (which is related to the inverse of the entry pressure) as a function of porosity and the amount of absorbed water.