Maximum Spread of Droplet Impacting onto Solid Surfaces with Different Wettabilities: Adopting a Rim-Lamella Shape

Experimental and theoretical investigations are presented for the maximum spread factor (β_m) of an impacting droplet onto solid surfaces with contact angle hysteresis. Experiments were conducted with deionized water on six surfaces with different wettabilities. The examined Weber number ( We) falls between 10^-1 and 10³. A new energetic model adopting a rim-lamella shape is proposed to better represent the droplet shape at the maximum spread. The dynamic contact angle at the maximum spread (θ_β) is introduced in the model to account for the curvature of the surrounding rim induced by surface wettabilities. A lamella-rim thickness ratio κ ≈ AWe^{- B} ( A, B > 0) is utilized successfully to depict the droplet shape at different We in a unifying manner. Comprehensive evaluations of the model demonstrate that the theoretical prediction can well recover the features of the experimental observations. The L2-error analysis demonstrates the improvement of the proposed model in predicting β_m for a wide range of We = 10^-1 to 10³: the calculated errors are smaller than 8% for all six surfaces. Moreover, the proposed model can also be applied to predict energy conversion/dissipation during the droplet spreading process and the effects of surface wettability on β_m in a reasonable manner. The variation of the percentage of the surface energy and viscous dissipation is consistent with that in previous simulations. The weakness of the current model for predicting β_m at extremely low Weber number ( We < 1) is also explained.