The impact and spreading of a small liquid drop on a non-porous substrate over an extended time scale

Abstract

High-speed imaging has been used to analyse the impact and spreading of sub-30 μm drops of Newtonian fluids (diethyl phthalate and glycerol–water mixture) on smooth glass surfaces with controlled wettabilities at velocities from 3 to 8 m s⁻¹. Data on drop height and spreading diameter were generated with high time and spatial resolution, over eight orders of magnitude in time scale. During the initial kinematic phase, the contact diameter followed a simple power-law independent of impact speed and surface wettability. In the spreading phase there was significant influence of impact speed, with the time taken to reach the maximum spreading diameter increasing with speed. During the wetting phase, for a hydrophilic substrate the drop spreading followed Tanner's law for all impact speeds. Measurements of the maximum spreading factor were compared with the predictions of analytical models based on energy balance, and were in reasonable agreement. The final spreading factor, however, showed better agreement with the value predicted from a volume conservation model, and some confusion has been identified in the previous literature over the distinction between these two measures of spreading. Good correlation was found between the deposition dynamics over the whole range of time scales of these small drops, and the data for the much larger, mm-sized drops studied in much previous work, provided that the values of initial Reynolds and Weber numbers were similar.