Role of surrounding gas in the outcome of droplet splashing

This study investigates the influence of the surrounding gas on a droplet impacting a smooth dry glass surface at high Weber and Reynolds numbers. It was performed using a flywheel experiment and different gases at ambient pressure. We analyzed the splashing outcome by measuring the size, velocity, and angle of the secondary droplets and by calculating the total volume ejected. We show that gas entrapment is not the mechanism responsible for splashing at high Weber and Reynolds numbers. We demonstrate that splashing is influenced by the density, followed by the viscosity, and last by the mean free path of the surrounding gas. Furthermore, the surrounding gas primarily affects the number of secondary droplets ejected and their ejection angle, whereas the droplet size and horizontal velocity are independent of the surrounding gas properties. We provide the first theoretical expression for the total volume ejected using the theory of Riboux and Gordillo [Phys. Rev. Lett. 113, 024507 (2014)], which attributes the secondary droplet generation to a lift force experienced by spreading lamella. The relationship between the ejected volume and the splashing parameter is described by a power function.

Figure 1

A water droplet of diameter 3.7 mm, traveling at 10 m/s, impacts a smooth dry glass surface surrounded by air. This example of a prompt splash shows the ejection of secondary droplets from the spreading rim at the surface; scale bar 500 $\mu \mathrm{m}$.

Figure 2

Experimental method. (a) Sketch of the flywheel experiment showing the shadowgraph setup, which consists of two high-resolution cameras and one laser light source. (b) Sketch demonstrating the mode of operation and the substrate position where the impact takes place. (c) Schematic representation of a splashing droplet observed from above, showing the depth of field of each camera and the control surface used to calculate the total ejected volume. (d), (e) An example of a large water droplet $D\approx 3.7$ mm impacting the substrate at $U\approx 10$ m/s, recorded at the same instant; scale bars 1 mm.

Figure 3

Footprints of the gas entrapment mechanism. The top image on the left side shows the spreading rim and the entrapped gas within a box. The enlargements highlight the different morphologies that were observed; scale bars 500 $\mu \mathrm{m}$. The diagrams show the diameter of the ring of microbubbles $d_b$ as a function of the gas density and viscosity.

Figure 4

Secondary ejected droplets. Diagram (a) shows the droplet size distribution, which is independent of the surrounding gas. Diagram (b) shows the horizontal velocity as a function of time, which is also independent of the gas. Diagram (c) shows the angle of the droplets relative to the surface as a function of time. The magnitudes of the standard deviations are ${\sigma }_{\tau }=0.1$, ${\sigma }_{u_{x,s}}=0.5$ m/s, and ${\sigma }_{{\theta }_s}=7^{\circ }$.

Figure 5

Total volume ejected during splashing. The images demonstrate the role of the surrounding gas on the splashing outcome; scale bars 500 $\mu \mathrm{m}$. The diagram shows the total ejected volume normalized to the primary droplet volume $V_D$ over the splashing parameter $\beta$. The solid line shows Eq. (6). The red dash line represents the splashing threshold $\beta =0.14$.