Substrate counts: Quantitative effects of surface roughness on fingering pattern and rim shape of an impacting drop

Abstract

Rim perturbations during the spreading of an impacting water drop are studied to provide quantitative insight into the effects of the substrate surface on the drop spreading process. Water drop impingement experiments on different surfaces confirm that undulations over the spreading rim are affected by surface characteristics. We have obtained a new relation to predict the number of fingers at the maximum spreading, providing a quantitative proof for substrate effects on evolution of the frontal shape. The valid range of the Weber number for this relation is 130–397. Moreover, we suggest a dimensionless “abnormality degree” for estimating the deformation of the rim shape due to instabilities and subsequent undulations. This parameter is quantitatively studied. Through a curve-fitting approach, we show that it can be expressed as a polynomial of three variables, namely, the Weber number and two roughness parameters. This study reveals the role of the solid surface in drop impingement and provides a comprehensive view of this process. The range of average surface roughness in this study is varied between 0.016 μm and 5.894 μm, and the characteristic slope ranges from 0.49 × 10−3 to 53.39 × 10−3.