Porosity variation within a porous bed composed of multisized grains

Abstract

We capture the interfacial region of randomly packed porous layers composed of multi-sized spherical or arbitrarily-shaped granules using X-ray computed tomography to explore the porosity-depth variation below a porous media interface. In the case of uni-sized spherical beads, we found in our previous study that the porosity varies from 1 to it's bulk value within a depth of the order of one grain diameter. In this study, we show that for the multi-sized spherical and randomly-shaped granules the porosity reaches it's bulk value within a depth equal to a multiple of the median diameter of the mixture. All multiplication factors for the samples examined here were between 2.6 and 3.8 and mimicked the experimental data with reasonable precision. A direct consequence of this observation is that the diffusion coefficient below the interface can not be considered as a constant. The effect of depth-dependent porosity on the the diffusion coefficient below the porous media interface was examined. It was found that the difference between a constant and a depth-dependent diffusion coefficient in the porous layer is significant and reaches up to 65% for sandy sediment (φb = 0.35) and 20% for highly porous media (φb = 0.90) immediately below the interface. This finding is of great significant when no experimental data of porosity as a function of depth is available. Such situations arise frequently in heat and mass transfer exchanges across fluid-porous or solid wall-porous boundaries.