2025/07/21 by Náraigh, Lennon Ó, Young, Nicola
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2507.15746
We consider the problem of a cylindrical (quasi-two-dimensional) droplet impacting on a hard surface. Cylindrical droplet impact can be engineered in the laboratory, and a theoretical model of the system can also be used to shed light on various complex experiments involving the impact of liquid sheets. We formulate a rim-lamella model for the droplet-impact problem. Using Gronwall's Inequality, we establish theoretical bounds for the maximum spreading radius Rmax in droplet impact, specifically k1 Re1/3-k2(1-cosϑadv)1/2(Re/We)1/2≤ Rmax/R0≤ k1Re1/3, where Re and We are the Reynolds and Weber number based on the droplet's pre-impact velocity and radius R0, ϑadv is the advancing contact angle (assumed constant in our simplified analysis), and k1 and k2 are constants. We perform several campaigns of simulations using the Volume of Fluid Method to model the droplet impact, and we find that the simulation results are consistent with the theoretical bounds.