Model of drop infiltration into a thin amphiphilic porous medium

Water drop infiltration into a thin amphiphilic porous medium is influenced by wettability. Due to the reorganization of amphiphilic matter in contact with water, polar interaction changes the wettability in the bulk porous medium and at the liquid/porous substrate interface. To model out of equilibrium water transfer, we propose a thermodynamics approach derived from Onsager's principle.

A 2D macroscopic gradient-dynamics model coupling the drop infiltration and the water dynamic into an amphiphilic porous medium is developed and applied to rhizospheric soil in presence of exopolysaccharides (EPS) as an example. The free energy of the entire drop and porous medium system is defined by taking into account the free surface energy of the water and the effective interaction between the porous matrix and the amphiphilic matter.

The temporal evolution of the 2D drop volume and contact angle are studied during infiltration using the new formulation. Depending on amphiphilic concentrations and initial water saturation, numerical simulation captures similar scenarios to those described in the literature for powder media, as well as a latency phenomenon occurring in dry soil. The latter has been until now poorly modeled.