Prediction of maximum spreading factor after drop impact: Development of a novel semi-analytical model incorporating effect of surface roughness

In this work, a semi-analytical model based on energy conservation and a term introduced for surface roughness has been developed for the determination of maximum spreading factor in case of different surface roughnesses and resulting contact angles ranging within 10° - 150° for a Weber number spectrum 70–400. Previously published experimental data of water droplets which impacted on glass, stainless steel and aluminum substrates with different velocities, diameters, and surface roughnesses have been taken for comparison and correlation of the model. Six well-known models chosen for comparison either result in an overestimation or underestimation of maximum spreading factor by at least 15% - 50% for measurements on stainless steel substrate, while only two of them satisfyingly agree partially with the experimental data used in this study. The model suggested here achieves a rather good agreement of almost 95% with most of the compared data.