Bubble entrapment by drop impact: Combined effect of surface tension and viscosity

Abstract

In this study, we systematically investigate the effect of surface tension on bubble entrapment after drop impact in the pinching regime. Experiments are conducted using three different systems: pure water, aqueous solutions with ethanol, or with surfactant molecules, both at various concentrations. Results are compiled for a large set of values of the surface tension $\gamma$ and the drop impact velocity $U$. Across all solutions, the cavity development dynamics exhibit similarity and are effectively characterized by dimensionless gravito-capillary parameters. Whatever the surface tension, our measurements indicate that only $40\%$ of the impact energy is converted into potential energy of the cavity. However, a notable distinction arises when considering bubble entrapment. We have constructed a bubbling diagram in the ($U,\gamma$) plane, and observed that the conditions for bubble entrapment are altered with changing surface tension in water-ethanol mixtures. More intriguingly, these conditions are modified in a distinctly different manner for surfactant solutions. To interpret our experimental findings, we compile a comprehensive set of experimental and numerical results from the literature. We demonstrate the possibility of unifying results across all systems and our water-ethanol mixtures through an empirical law including the influence of surface tension and viscosity. Although no physical justification exists at this stage, this empirical law suggests the significant role of capillary waves traveling along the cavity interface in bubble entrapment. Within this context, the behavior of surfactant-laden solutions aligns with other homogeneous solutions by considering the elastic properties conferred upon the interfaces by surfactant molecules.