Simulations of flow mode distributions on rough fracture surfaces using a parallelized Smoothed Particle Hydrodynamics (SPH) model

Under idealized conditions (smooth surfaces, linear relationship between Bond number and Capillary number of droplets) steady-state flow modes on fracture surfaces have been shown to develop from sliding droplets to rivulets and finally (wavy) film flow, depending on the specified flux. In a recent study we demonstrated the effect of surface roughness on droplet flow in unsaturated wide aperture fractures, however, its effect on other prevailing flow modes is still an open question. The objective of this work is to investigate the formation of complex flow modes on fracture surfaces employing an efficient three-dimensional parallelized SPH model. The model is able to simulate highly intermittent, gravity-driven free-surface flows under dynamic wetting conditions. The effect of surface tension is included via efficient pairwise interaction forces. We validate the model using various analytical and semi-analytical relationships for droplet and complex flow dynamics. To investigate the effect of surface roughness on flow dynamics we construct surfaces with a self-affine fractal geometry and roughness characterized by the Hurst exponent. We demonstrate the effect of surface roughness (on macroscopic scales this can be understood as a tortuosity) on the steady-state distribution of flow modes. Furthermore we show the influence of a wide range of natural wetting conditions (defined by static contact angles) on the final distribution of surface coverage, which is of high importance for matrix-fracture interaction processes.