Experimental and numerical simulation on the dual role of liquid and gas viscosity in the droplet spreading dynamics

The dynamics of droplet impact on a free-slip surface are studied experimentally and numerically. Experimental results and numerical predictions demonstrate good consistency in the dimensionless droplet maximum spreading diameter β max . Non-monotonic droplet maximum spread rate is observed and ascribed to the dual role of liquid viscosity at high Weber number ( W e ≥ 30 , W e = ρ D 0 V 0 2 / σ ), which is different from the small Weber number ( W e < 30). For droplet spreading under relatively small Reynolds number R e = ρ D 0 V 0 / μ (indicating high liquid viscosity), the initial kinetic energy dissipates efficiently, allowing surface energy to dominate the energy budget. Liquid viscosity dominates the viscous dissipation rate, which decreases as R e increases. However, for relatively large R e , the initial kinetic energy cannot be fully utilized, leading to substantial strain rate in the gas phase. The strain rate increases with R e increasing and in turn dominates viscous dissipation. Since gas viscous dissipation becomes more significant under large R e conditions, the impact of gas viscosity on droplet spreading was examined. The dual role of gas viscosity is also observed, where the energy dissipation in the gas phase exhibits a non-monotonic trend concerning R e . A practical model for estimating β max under small Weber numbers is proposed, demonstrating good consistency with previous experimental results.