The force of impacting rain

Abstract

Drop impacts are difficult to characterize due to their transient, non-stationary nature. We discuss the force generated during such impacts, a key quantity for animals, plants, roofs or soil erosion. Although a millimetric drop has a modest weight, it can generate collision forces on the order of thousand times this weight. We measure and discuss this amplification, considering natural parameters such as drop radius and density, impact speed and response time of the substrate. We finally imagine two kinds of devices allowing us to deduce the size of the raindrop from impact forces.

Superhydrophobicity enhancement through substrate flexibility

“…Following the same analysis, we calculated γ d experienced by the droplet in the reference frame moving with the surface. For f b < 1=τ, the substrate velocity just after impact, U s0 , scales as the one for a perfectly inelastic collision (23,24),…”

“…On the other hand, there is a broad palette of surfaces in nature and technology that is characterized by some degree of flexibility [leaves (18), construction materials, textiles (19), etc.]. Studies have been reported with respect to dynamic wetting on hydrophilic, flexible materials (20)(21)(22)(23); however, little work has addressed the interweaving effects of wetting behavior and material flexibility. In addition, the work that has been reported (24) did not focus on the role of surface compliance or flexibility in influencing the physics of the droplet collision process.…”

Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact

“…Then one obtains a typical inertial pressure of P i ≈ ρ l U 2 ∼ 10 3 − 10 4 Pa, a capillary pressure of P c ≈ 4σ cos θ c /d g ∼ 10 3 cos θ c Pa, and a gravitational pressure of P g ≈ ρ l gD 0 ∼ 10 Pa. For the liquids and hydrophilic grains that we used the contact angle stays in a range of cos θ c ∈ [0.3, 1], hence, P c is at least one order of magnitude larger than P g which is therefore neglected. Though P i is again at least one order of magnitude larger than P c , previous simulation and experimental works have shown that P i only acts within an inertial time scale τ i ≈ D 0 /U [17,19]. We correct this time scale as τ i = (D 0 + 2Z m )/U by taking the deformation of the substrate, Z m , into account.…”

The impact of raindrops on sand

“…While it has been shown that the impact force between a droplet and a solid surface is time dependent [36,91], the subsequent analysis justifies equation 2.1 by hindsight.…”

“…We estimate their orders of magnitude with typical parameters for the water droplets used in our experiments: liquid density ρ l = 1.0 × cos θ c Pa, and a gravitational pressure of P g ≈ ρ l g D 0 ∼ 10 Pa. For the liquids and hydrophilic grains that we used the contact angle stays in a range of cos θ c ∈ [0.3, 1], hence, P c is at least one order of magnitude larger than P g which is therefore neglected. Though P i is again at least one order of magnitude larger than P c , previous simulation and experimental works have shown that P i acts only within an inertial time scale τ i ≈ D 0 /U 0 [36,91]. We correct this time scale as τ i = (D 0 +2Z * c )/U 0 by taking the deformation of the substrate, Z * c , into account.…”