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.

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Karst aquifers provide drinking water for 10% of the world's population, support agriculture, groundwater-dependent activities, and ecosystems. These aquifers are characterised by complex groundwater-flow systems, hence, they are extremely vulnerable and protecting them requires an in-depth understanding of the systems. Poor data accessibility has limited advances in karst research and realistic representation of karst processes in large-scale hydrological studies. In this study, we present World Karst Spring hydrograph (WoKaS) database, a community-wide effort to improve data accessibility. WoKaS is the first global karst springs discharge database with over 400 spring observations collected from articles, hydrological databases and researchers. The dataset's coverage compares to the global distribution of carbonate rocks with some bias towards the latitudes of more developed countries. WoKaS database will ensure easy access to a large-sample of good quality datasets suitable for a wide range of applications: comparative studies, trend analysis and model evaluation. This database will largely contribute to research advancement in karst hydrology, supports karst groundwater management, and promotes international and interdisciplinary collaborations. Background & Summary Karst aquifers are essential sources of drinking water to about 10% of the world's population 1. In many regions across the globe, karst groundwater is also an indispensable resource for ecosystems, agriculture and, economic activities, as well as for tourism and recreation 2,3. For example, in Europe, 21.6% of the land surface is underlain by carbonate rock 4 which contributes up to 50% of supplied drinking water in some countries 5-7. However, groundwater flow in karst aquifers is characterised by a complex interplay of fast-flowing conduit and slow-flowing matrix systems 8,9. Hence, the storage capacity of karst aquifers is variable and systems are extremely vulnerable to climatic pressures, human impacts and contamination 10. In order to ensure adequate protection of karst water sources, in-depth hydrogeological knowledge is necessary. Large-scale modelling and comparative water resource research have shown the great value of large datasets in hydrology 11. Numerous studies have applied these large datasets for several purposes such as model evaluation, global parameter estimations, impact studies, statistical and comparative analyses. For instance, large-scale hydrological models such as WaterGAP 12 used discharge data from the Global Runoff Data Centre (https://www. bafg.de/GRDC) for parameter estimation. Likewise, streamflow data from the Model Parameter Estimation Experiment (MOPEX) 13 and the Global Runoff Data Centre (GDRC) were combined to derive global base flow indexes and recession constants 14. Streamflow observations of near-natural catchments obtained from UNESCO's European Water Archive (EWA) were used to investigate the streamflow trends across Europe and differentiated the impacts from climatic variability and anthropogenic dri...

Abstract. The objective of this work is the simulation of saturated and unsaturated flow in a karstified aquifer using a double continuum approach. The HydroGeoSphere code (Therrien et al., 2006) is employed to simulate spring discharge with the Richards equations and van Genuchten parameters to represent flow in the (1) fractured matrix and (2) conduit continuum coupled by a linear exchange term. Rapid vertical small-scale flow processes in the unsaturated conduit continuum are accounted for by applying recharge boundary conditions at the bottom of the saturated model domain. An extensive sensitivity analysis is performed on single parameters as well as parameter combinations. The transient hydraulic response of the karst spring is strongly controlled by the matrix porosity as well as the van Genuchten parameters of the unsaturated matrix, which determine the head dependent inter-continuum water transfer when the conduits are draining the matrix. Sensitivities of parameter combinations partially reveal a non-linear dependence over the parameter space. This can be observed for parameters not belonging to the same continuum as well as combinations, which involve the exchange parameter, showing that results of the double continuum model may depict a certain degree of ambiguity. The application of van Genuchten parameters for simulation of unsaturated flow in karst systems is critically discussed.

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.