Liquid migration in sheared unsaturated granular media

We show how liquid migrates in sheared unsaturated granular media using a grain scale model for capillary bridges. Liquid is redistributed to neighboring contacts after rupture of individual capillary bridges leading to redistribution of liquid on large scales. The liquid profile evolution coincides with a recently developed continuum description for liquid migration in shear bands. The velocity profiles which are linked to the migration of liquid as well as the density profiles of wet and dry granular media are studied.

💡 Research Summary

This paper investigates how liquid redistributes in a sheared, unsaturated granular medium by employing a grain‑scale model for capillary bridges combined with Contact Dynamics (CD) simulations. The authors first describe the mechanical framework: CD enforces perfect volume exclusion and Coulomb friction for rigid spherical particles, while capillary forces are modeled using an experimentally validated expression that depends on bridge volume, particle curvature, separation distance, surface tension, and contact angle (set to zero). The rupture distance of a bridge follows a simple scaling, s_c ≈ V^{1/3}.

A central hypothesis is that when a bridge ruptures, its liquid is instantaneously redistributed to all neighboring contacts of the two particles involved. The redistribution rule conserves total liquid mass: the ruptured volume is split equally between the two particles, then divided equally among each particle’s existing contacts (including dry contacts). An upper bound V_max prevents the formation of overly large bridges. This rule is justified by comparing characteristic time scales: bridge formation occurs in milliseconds, bridge equilibration via Laplace pressure takes minutes, and the shear rates considered (10⁻² s⁻¹ ≪ γ̇ ≪ 10³ s⁻¹) ensure that redistribution is much faster than equilibration but slower than particle motion.

The numerical setup consists of periodic simple shear between two rough walls. Particle radii are uniformly distributed between 0.8 R and 1 R, with system dimensions L_x = 20 R, L_y = 12 R, and a wall separation of roughly 78 R. The bottom wall moves at constant speed, imposing a shear strain γ = v_shear t/L_z, while the top wall is pressure‑controlled. Two dimensionless groups govern the dynamics: the inertial number I ≈ 0.008 and the cohesion number η = 2πΓ/(P R), where Γ is the liquid surface tension and P the confining pressure. Initially, the bridge volumes follow a Gaussian profile in the vertical direction, V_b(z) = A exp