Porosity variation below a fluid–porous interface

• Derivation of a depth-dependent porosity relation below a fluid–porous interface.
• Assumption is based on spheres, randomly packed as a porous medium.
• Validation of relation by non-invasive laser method and numerical simulations.
• Comparison of the results with literature data on biofilm porosity.
• Showing effect of variable porosity on solute concentration profile in a biofilm.

The correct quantification of porosity is essential in all studies pertaining to porous media. A host of existing works employs a constant, bulk value for porosity, even when the porous sample is attached to a free fluid. Since the volume fraction of the solid matrix near the interface region differs from that in the core, the porosity undergoes a spatial variation. Here we present a novel relation for the porosity as a function of depth below the interface, using the concept of surface roughness applied on the classical definition of open porosity. This relation has been verified by computational modeling as well as non-invasive laser experiments. It has been shown that this depth-dependent porosity relation applies also to a non-granular porous layer such as a biofilm.