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

Abstract

Experimental and theoretical investigations are presented for the maximum spread factor (βm) 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 (θβm) 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 βm 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 βm 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 βm at extremely low Weber number ( We < 1) is also explained.