  In the study of packed granular materials, the performance of a sample (e.g.,
the detonation of a high-energy explosive) often correlates to measurements of
a fluid flowing through it. The "effective surface area," the surface area
accessible to the airflow, is typically measured using a permeametry apparatus
that relates the flow conductance to the permeable surface area via the
Carman-Kozeny equation. This equation allows calculating the flow rate of a
fluid flowing through the granules packed in the sample for a given pressure
drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and
flow paths that may not accurately hold in situations where the particles
possess a wide distribution in shapes, sizes, and aspect ratios, as is true
with many powdered systems of technological and commercial interest. To address
this challenge, we replicate these measurements virtually on micro-CT images of
the powdered material, introducing a new Pore Network Model based on the
skeleton of the Morse-Smale complex. Pores are identified as basins of the
complex, their incidence encodes adjacency, and the conductivity of the
capillary between them is computed from the cross-section at their interface.
We build and solve a resistive network to compute an approximate laminar fluid
flow through the pore structure. We provide two means of estimating
flow-permeable surface area: (i) by direct computation of conductivity, and
(ii) by identifying dead-ends in the flow coupled with isosurface extraction
and the application of the Carman-Kozeny equation, with the aim of establishing
consistency over a range of particle shapes, sizes, porosity levels, and void
distribution patterns.
