Droplets impact on sheet flows: deciphering the physical mechanisms through droplet-induced shear stress

Droplets are prevalent in nature and technology. Under natural conditions, thin layers of water, known as sheet flows, form and move along land surfaces, playing a critical role in the dynamics of erosion and sediment transport related to geophysics. The impact of droplets on the liquid interface makes a quantitative description of these flows very challenging.

This study aims to uncover the complexity of the physical processes and mechanisms of droplet impact on flows in geophysical systems.

We developed an experimental setup capable of directly measuring flow velocity profiles and controlling droplet impacts on the flows. We used the Reynolds-averaged Navier-Stokes equations, which expresses the balance of force on the flow, to deduce from our measurements the shear stress τ_R exerted by the droplets on the flows.

Our results show that the velocity profiles in droplet-impacted flows deviated from the conventional logarithmic law. Droplet impacts induce τ_R by increasing turbulence intensity in the flow and τ_R can be calculated from measurements of velocity profiles. Through dimensional analysis, we proposed a simplified relation expressing the τ_R in terms of the parameters of the problem. We unravel the mechanisms of droplets impact on sheet flows by quantifying τ_R. Our results elucidate the fundamental processes acting on flows of geophysical relevance, and provide a robust description of the force induced by raindrops.