Full-field spreading velocity measurement inside droplets impinging on a dry solid-heated surface

Abstract

This study investigates the radial velocity distributions during the early phase of spreading inside the water droplets impinging onto a heated sapphire glass surface as the second part of the author’s previous paper about the droplet impacts onto an unheated surface (Erkan and Okamoto in Exp Fluids 55:1–9, 2014). The surface was heated to the temperature values above the saturation temperature of the water and the droplets impinge with low-Weber numbers (in the range of 4–5) and high-Weber numbers (in the range of 10–15). Planar full-field velocity distributions were measured inside the expanding liquid lamella using time-resolved particle image velocimetry (TR-PIV), and the results were presented with the quantitative uncertainties. The PIV results revealed that radial velocity distributions demonstrated nonlinear and linear behaviors, as in the case of unheated surface impacts, at a single instant of time. By the time, they gained nonlinear forms, particularly in the outer radial positions owing to the vertically upward flows. An empirical time-dependent correlation in power-law form was proposed to formulate the temporal evolution of the velocity distributions covering all radial positions in the spreading droplet. The rate of change in the droplet radii was also measured from the time-sequential shadowgraph images. Spreading speeds resemble an extension of the PIV-velocity profiles, which verified the two different measurement methods. For the low-Weber number cases, the radial velocity magnitudes were detected to be lower than those of the unheated surface impacts, specifically in the later stages of the spreading. That is likely to be related to the increasing effect of thermocapillary flows or with the degree of curvature on the outermost interface of the spreading liquid lamella. The radial velocity measurements inside the droplets impinging onto the unheated surface were compared with an analytical model and a numerical simulation (OpenFOAM-VOF). The analytical model could predict spreading speeds of the droplets, while, as anticipated, it could not reproduce the nonlinearity of the velocity profiles, which might be responsible for the nonuniform convection of heat inside the expanding droplets on the hot surfaces. The numerical simulation could estimate the velocity profiles, even though some deviations detected between the experimental results and numerical results.

Graphical abstract