Characterization of Porous Media Using a Geometric Depiction of Fibrous Materials

Sumanth Swaminathan, W. L. Gore.

• Final Report

Characterization of porous media is fundamentally important in a variety of industrial applications. In porous filtration, for example, filter performance (contaminant retention and flux efficiency) is heavily dependent on material properties such as porosity, pore size, and toruosity. A refined understanding of microscopic structural features and how they relate to membrane permeability and particle retention efficiency can aid in design and performance optimization. In this workshop, we will hypothesize, execute, and evaluate methods for pore size characterization.

A variety of experimental tools currently aid in understanding pore size distribution in porous media. Porometry, for example, is a test in which inert gas flow is used to displace fluid in a liquid filled structure at increasing pressure. Pore size is then established by relating the pressure required to evacuate a pore to the pressure necessary to evacuate a cylindrical capillary. The test is widely used in filtration applications to evaluate the largest, smallest, and mean pore sizes in addition to the cumulative pore size distribution. The major flaw with this test, however, is that pore geometry is assumed to be cylindrical. Similar evaluation tools including porosimetry and capillary condensation experiments rely on an assumed input geometry to establish a pore size distribution.

The goal of this workshop is to mathematically characterize a porous fiber structure and geometrically evaluate microscopic properties (pore size, porosity, tortuosity, etc). Our hope is that direct numerical evaluation of pore size and shape will provide a more effective characterization and subsequent understanding of performance than the prevailing experimental methods. Some of the key modeling challenges and goals are shown below. We hope that this problem stimulates further discussion on mathematical characterization techniques related to porous media.

Modeling Goals:

1. Generate a 3D structure that characterizes a fibrous porous membrane.
   1. Create lines in space with inputted thickness.
   2. Create curves into space with inputted thickness.
   3. Grow lines/curves from nodes.
2. Define a pore.
   1. Polygonal area enclosed by intersecting/overlapping fibrils.
   2. Largest inscribed/circumscribed sphere related to a polygon.
3. Write a program that sweeps out pore areas, identifies intersecting fibers (or overlapping/nearly intersecting fibers), and generates a pore size distribution.
4. Identify the ways in which a spherical particle can move from the top of a structure to the bottom.
5. Calculate mean flow paths.
6. Calculate other relevant physical properties such as largest/smallest pore size, porosity, permeability, etc.