Jannes Kordilla

Effect of Unsaturated Flow Modes on Partitioning Dynamics of Gravity‐Driven Flow at a Simple Fracture Intersection: Laboratory Study and Three‐Dimensional Smoothed Particle Hydrodynamics Simulations

In this work, we study gravity-driven flow of water in the presence of air on a synthetic surface intersected by a horizontal fracture and investigate the importance of droplet and rivulet flow modes on the partitioning behavior at the fracture intersection. We present laboratory experiments, three-dimensional smoothed particle hydrodynamics (SPH) simulations using a heavily parallelized code, and a theoretical analysis. The flow-rate-dependent mode switching from droplets to rivulets is observed in experiments and reproduced by the SPH model, and the transition ranges agree in SPH simulations and laboratory experiments. We show that flow modes heavily influence the “bypass” behavior of water flowing along a fracture junction. Flows favoring the formation of droplets exhibit a much stronger bypass capacity compared to rivulet flows, where nearly the whole fluid mass is initially stored within the horizontal fracture. The effect of fluid buffering within the horizontal fracture is presented in terms of dimensionless fracture inflow so that characteristic scaling regimes can be recovered. For both cases (rivulets and droplets), the flow within the horizontal fracture transitions into a Washburn regime until a critical threshold is reached and the bypass efficiency increases. For rivulet flows, the initial filling of the horizontal fracture is described by classical plug flow. Meanwhile, for droplet flows, a size-dependent partitioning behavior is observed, and the filling of the fracture takes longer. For the case of rivulet flow, we provide an analytical solution that demonstrates the existence of classical Washburn flow within the horizontal fracture.

Smoothed particle hydrodynamics study of the roughness effect on contact angle and droplet flow

We employ a pairwise force smoothed particle hydrodynamics (PF-SPH) model to simulate sessile and transient droplets on rough hydrophobic and hydrophilic surfaces. PF-SPH allows modeling of free-surface flows without discretizing the air phase, which is achieved by imposing the surface tension and dynamic contact angles with pairwise interaction forces. We use the PF-SPH model to study the effect of surface roughness and microscopic contact angle on the effective contact angle and droplet dynamics. In the first part of this work, we investigate static contact angles of sessile droplets on different types of rough surfaces. We find that the effective static contact angles of Cassie and Wenzel droplets on a rough surface are greater than the corresponding microscale static contact angles. As a result, microscale hydrophobic rough surfaces also show effective hydrophobic behavior. On the other hand, microscale hydrophilic surfaces may be macroscopically hydrophilic or hydrophobic, depending on the type of roughness. We study the dependence of the transition between Cassie and Wenzel states on roughness and droplet size, which can be linked to the critical pressure for the given fluid-substrate combination. We observe good agreement between simulations and theoretical predictions. Finally, we study the impact of the roughness orientation (i.e., an anisotropic roughness) and surface inclination on droplet flow velocities. Simulations show that droplet flow velocities are lower if the surface roughness is oriented perpendicular to the flow direction. If the predominant elements of surface roughness are in alignment with the flow direction, the flow velocities increase compared to smooth surfaces, which can be attributed to the decrease in fluid-solid contact area similar to the lotus effect. We demonstrate that classical linear scaling relationships between Bond and capillary numbers for droplet flow on flat surfaces also hold for flow on rough surfaces.