Fig. 2.

Schematic sketch of the multiphase porous medium modeling the lungs’ smaller airways and blood vessels. At the microscale, the phases and interfaces are discernible (left side), while at the macroscale, the phases are no longer fully resolved but described by their volume fractions, i.e., the volume fraction of air ${\epsilon }^a$, blood ${\epsilon }^b$, and tissue ${\epsilon }^t$ (right side). The thermodynamically constrained averaging theory (TCAT) formally averages the microscale quantities to the macroscale (Miller et al. 2022)