A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces

• We developed a Smoothed Particle Hydrodynamics model to study droplet flow on rough surfaces.
• The model is verified using empirical and semi-analytical solutions for a wide range of parameters.
• Gravity driven flow on initially dry and prewetted surfaces is investigated.
• Flow regimes based on Reynolds numbers and static contact angles are delineated.
• Surface roughness is shown to systematically decrease droplet velocities.

Flow on fracture surfaces has been identified by many authors as an important flow process in unsaturated fractured rock formations. Given the complexity of flow dynamics on such small scales, robust numerical methods have to be employed in order to capture the highly dynamic interfaces and flow intermittency. In this work we use a three-dimensional multiphase Smoothed Particle Hydrodynamics (SPH) model to simulate surface tension dominated flow on smooth fracture surfaces. We model droplet and film flow over a wide range of contact angles and Reynolds numbers encountered in such flows on rock surfaces. We validate our model via comparison with existing empirical and semi-analytical solutions for droplet flow. We use the SPH model to investigate the occurrence of adsorbed trailing films left behind droplets under various flow conditions and its importance for the flow dynamics when films and droplets coexist. It is shown that flow velocities are higher on prewetted surfaces covered by a thin film which is qualitatively attributed to the enhanced dynamic wetting and dewetting at the trailing and advancing contact lines. Finally, we demonstrate that the SPH model can be used to study flow on rough surfaces.