Permeability is an indication of the ability to allow fluid (gases, liquids, and supercritical fluids) flow path through porous material, described by Darcy’s Law per
![Rendered by QuickLaTeX.com \vec{u}](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-ca3a44eb0b96414179bd51a4bd206b61_l3.png)
![Rendered by QuickLaTeX.com \nabla p](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-f0056ae3bedc3cc86f5eccfea8516315_l3.png)
![Rendered by QuickLaTeX.com {\mu}](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-961d8e14a684d1bcf1b2d5c89f658c0b_l3.png)
![](https://sites.tufts.edu/tplab/files/2023/03/Fig_MFP_vs_Lc.png)
![Rendered by QuickLaTeX.com u](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-43fe27dc3e528266a619764d90fce60b_l3.png)
![Rendered by QuickLaTeX.com u_\mathrm{wall}](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-337776e447694fe58b391ba530400a04_l3.png)
![Rendered by QuickLaTeX.com L_{c}](https://sites.tufts.edu/tplab/wp-content/ql-cache/quicklatex.com-1936c79e49012279c959edfa62eb74d7_l3.png)
We developed an experimental apparatus that can measure the permeability of aerogel at both ambient and supercritical conditions, using two redundant methods.
![](https://sites.tufts.edu/tplab/files/2022/10/Picture1-1-1024x768.jpg)
The permeability of aerogel is measured by two independent methods using the experimental apparatus shown above. First, it’s measured by a direct method where the fluid is pumped directly through the aerogel and the permeability of the aerogel can be extracted from the measured pressure drop across and the flow rate through it.
Secondly, it’s measured by an inverse method where the permeability is inferred from the relaxation time of the pressure reading for a step increase of pressure, inside a vessel with a sudden decreased volume.
![](https://sites.tufts.edu/tplab/files/2023/04/Fig_Setup_BOTH-1024x569.png)
Direct Method
compute permeability using Darcy’s law for 1-D steady flow per