Equilibrium distribution of the liquid phase in an unsaturated granular material

TL;DR

This paper models the distribution of liquid in unsaturated granular materials using a Boltzmann law, linking gravity and capillary forces, and validates the model with experimental data.

Contribution

It introduces a novel approach using a Langevin equation to describe liquid distribution, connecting static disorder to thermal agitation in the funicular regime.

Findings

Distribution follows a Boltzmann law

Experimental data collapse on a single curve

Model accurately predicts water content profile

Abstract

In an unsaturated granular material, the spatial distribution of the liquid phase results from the competition between gravity and capillary forces. We show that, in the funicular regime, it can be described by a Boltzmann law, with static disorder playing the role of thermal agitation. We propose an approach based on a Langevin equation to derive this distribution, and compare our predictions with conductivity measurements giving the local water content as a function of height in a wet granular medium. We show that experimental data obtained with samples of different polydispersities collapse on a single master curve consistent with our model.