Droplet Lamella Lift Dynamics and Surface Wettability

Droplet impact on dry, smooth surfaces remains an issue for a variety of important applications such as fuel injection, spray cooling, metallurgy, pesticides and coatings. The mechanisms that initiate splashing are highly complex and differ from those on rough or pre-wetted surfaces. In this work, droplet wettability on a smooth, dry surface is examined to quantitatively evaluate its influence on splashing. Water droplets of approximately 3.5 mm diameter and velocities ranging from 2.2-3.5 m/s were dropped onto a smooth, Plexiglas surface. Hydrophobic and hydrophilic coatings were applied to the surface in order to change wetting characteristics. It was found that the hydrophilic surface required higher gas densities for splashing to occur and vice versa for the hydrophobic surface. Focusing on the spreading lamella, a momentum balance was derived with consideration of the chemical affinity or adhesive force of the liquid to the impact surface. The lamella lift from the surface was assumed to be induced by the displaced surrounding gas during spreading. This provides an explanation for the vertical velocity component of corona splashing on dry, smooth surfaces. Consideration of the adhesive force between the lamella and impact surface may also provide an explanation for the seemingly paradoxical effect of droplet viscosity to both promote and inhibit splashing. Introduction The ability to accurately predict the occurrence of splashing of single droplet impacts remains of interest due to a number of important applications including materials processing, ink printing, spray cooling, fuel injection, fire suppression and irrigation. Many mechanisms for splashing have been proposed, however a complete picture of the phenomenon is yet unattained. The phenomenon was first studied by Worthington [1]. Since then, many mechanisms have been proposed to explain splash formation. At high droplet impact velocities over 100 m/s, an internal pressure shockwave may form to initiate splashing [2, 3]. At lower velocities, splashing may still be initiated through a redirection of spreading momentum to the location of lowest surface energy [4-6]. Surface roughness plays an important role by obstructing to flow of momentum along the impact surface, forcing a redirection vertically. Splashing of this form has been referred to as “prompt” splashing [7]. However, splashing may also take place on smooth surfaces, though of a distinctly different nature. Splashing of this type is labeled “corona” splashing because of the distinct crown shape that forms at the leading edge of spreading [7]. It is this, lesser-studied mechanism of splashing that we examine further in this paper. Recent research has shown that changing the pressure or density of the surrounding air may significantly alter the threshold of splashing [8-10]. Accordingly, the shear stress between the droplet and the surrounding gas becomes a key parameter to prediction of splashing. In a recent study, Xu [8] provided supporting evidence for this claim by discovering that as the ambient pressure drops to 0.17 atm, splashing was suppressed. Further description of the interaction between a water droplet and ambient gas during impact was presented by Jepsen et al. [9], who used the Schlieren photography method to provide experimental evidence of gas movement, which varied with the ambient pressure during a water slug impact onto a solid surface. Recently, Liu et al. [10] confirmed the validity of this effect under super-atmospheric conditions. Many experimental correlations exist to predict the quantitative threshold of splashing during droplet impact and most are based on the Weber number (We) and the Reynolds number (Re) or some combination of the two [5, 10-12]. These studies have related the threshold of splashing to liquid properties, most importantly the surface tension and viscosity, droplet size and velocity, and to the impact surface characteristics. Correlations may often be divided into those that predict a direct relationship between droplet viscosity and impact kinetics required for splashing [5, 11], and those that predict an inverse relationship [8, 10, 12]. A direct relationship means that increasing viscosity would have a tendency to suppress splashing (following intuition) and vice versa for the latter. Clearly these correlations would diverge widely in their splash predictions through a broad range of fluid properties. Xu [8] also found a transition point in which the gas density required to splash changes from an inverse to direct function of viscosity. A recent work [13] examined splashing through a wide range of liquid viscosities, and adjusted existing splash correlations for low and high viscosity regimes, separated by a transition Re ≈ 500. Causes for the observed phenomena, however, could not be fully explained. In this study, a more in-depth study of the mechanisms of splashing is presented by focusing on the spreading lamella, which has been found recently by Bird et al. to be critical to splashing [14]. By considering the forces acting on the lamella, the as yet unknown mechanism for the vertical velocity component of splashing on dry, smooth surfaces may be determined. This analysis also brings to consideration an adhesive force, dependent upon the chemical affinity or wettability between the liquid and solid surface. Surface wettability has been shown to play an important role in droplet impact dynamics [15, 16], affecting the spreading and recoil behavior during impact. But to the authors’ knowledge, this parameter has not been studied specifically for its effects on splashing. Some experiments are performed using water droplets impinging onto surfaces treated to be hydrophilic and hydrophobic to verify the existence of an adhesive force. Consideration of this adhesive force may also explain transition of viscosity from a direct to inverse relationship with air density with respect to splashing. Lamella Lift Dynamics As noted before, it has already been proven that the ambient air pressure has a significant effect on splashing. This has been explained by Jepsen [9] as a compressive effect in which the gas below the droplet is compressed and forced outward, while causing a shearFigure 1: A schematic of lamella lift and the rele-