The post-impact spread, recoil, and shape oscillations of a droplet impinging on a dry horizontal hydrophobic substrate at low Weber numbers (We) (9.0 < We < 25) are modeled as the behavior of a second-order damped harmonic system. Experiments were conducted to capture the spread dynamics of droplets of six different liquids impinging on a Teflon substrate using a high speed digital visualization and image processing. The selected liquids cover a wide range of viscosities and surface tension coefficients, and their Ohnesorge and Capillary numbers vary by three orders of magnitude (0.002 ≤ Oh ≤ 1.57; 0.007 ≤ Ca ≤ 7.59). High-resolution photographic images of the post-impact spread-recoil process at different We are analyzed to obtain the temporal variations of the spread factor (ratio of liquid spread to droplet diameter) and the flatness factor (ratio of liquid height to droplet diameter). These are found to be represented by the damped harmonic response of a mass-springdamper system, where the surface tension force acts as a spring and liquid viscosity provides the damping. Due to contact angle hysteresis, the frequency of oscillations for the transient flatness factor variation is slightly different from that for the spread factor variation. Semi-empirical correlations are developed for both the oscillation frequency and the damping factor as a function of drop Weber and Reynolds numbers. The predictions of temporal variations of the spread and flatness factors from these equations agree very well with experimental measurements on the hydrophobic Teflon substrate.
The postimpact spreading and recoil behavior of millimeter-size liquid droplets of pure water, water-glycerol solution, and non-Newtonian aqueous solutions of medium-grade hydroxyl ethyl cellulose (HEC 250 MR) on dry horizontal hydrophobic (Teflon) and hydrophilic (glass) substrates is presented. The drop spread-recoil dynamics are captured using a high-speed high-resolution digital video recording and image processing. The non-Newtonian effects of aqueous polymeric solutions on postimpact spreading are contrasted with those for a water-glycerol solution with identical surface tension and zero-shear rate viscosity. For a broad range of drop Weber numbers (20 ≤ We ≤ 200), dynamic visualized records of impact, spreading, and recoil are presented along with their measured temporal variations in dropdiameter-scaled spread and film height. The shear-rate-dependent viscosity of the polymer solution is found to give rise to highly complex spread-recoil dynamics compared to Newtonian liquids. During initial spread, because the shear rate tends to be high, shear-thinning or pseudoplasticity effects manifest in polymer solution drops to alter their spread dynamics. Contrarily, during recoil their higher low-shear apparent viscosity tends to retard recoil and dampen shape oscillations. Shear-rate-dependent non-Newtonian behavior is further seen at low We (low shear rate during spreading), where the maximum spread of HEC solution droplets is comparable to that of high-viscosity water-glycerol solution, whereas at high We (high shear rate during spreading), their maximum spreads are closer to those of low-viscosity water droplets.
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