Comment on “Imbibition in layered systems of packed beads” by Reyssat M. et al.

In [1], Reyssat et al. give a succinct theoretical analysis of 1-D capillarity-driven imbibition into layered porous materials, dealing with two-layer and graded-permeability (multi-layer) systems. They provide also some careful experimental data on imbibition into layered glass beadpacks. Quantitative experiments are few and far between in this field, so these results are valuable. It should perhaps be recognized that the capillary absorption of liquids into layered porous materials has been of interest in soil physics, hydrology and construction engineering for many years. The literature goes back at least to Childs and Bybordi [2] who provided equations for the infiltration of water into stratified soils under the combined action of capillarity and gravity (see also Childs [3]). Later Wilson et al. [4] gave the general solution for pure capillary absorption (imbibition) from a liquid reservoir into the two-layer composite with arbitrary permeability and wet-front capillary potential. This was later extended [5] to the 1-D n-layer composite with layers having arbitrary thicknesses and hydraulic (capillary) properties. (These and other results on capillary transport in layered composites are discussed fully also in [6].) In all these analyses it is assumed that the wetted region is saturated, as assumed also in [1]. These are therefore Green-Ampt or Sharp Front models, and are distinct from unsaturated flow models in which a gradient of liquid water content exists within the wetted region. The solutions in [1] are obtained using a KozenyCarman permeability k, and a Young-Laplace wet-front capillary pressure p, with the further simplification that both the wetting index c and the porosity φ are constant throughout the composite system. Thus, the capillary properties scale with the particle diameter d throughout. With these restrictions, the main result for the two-layer [AB] case for s, eq. (11) of [1], follows immediately