Liquid Droplet Impact

What causes a droplet to splash? In spite of its ubiquity, the phenomenon of droplet splashing remains poorly understood. The splash of an impacting liquid drop was thought to occur by the detachment of a shockwave from the liquid-solid interface as the liquid rapidly deformed after contacting the surface on the impact axis [Lesser, 1983]. Such a paradigm ignores both the liquid viscosity and the surrounding air: this paradigm is ostensibly sensible, because the splashing drop typically has an impact Reynolds number exceeding 1000; furthermore, the viscosity and density of the surrounding air are both significantly less than the viscosity and density of the liquid drop. However, recent experiments have shown that indeed, the surrounding air plays a critical role in the splashing transition [Xu et. al. 2005]. Additional experiments have shown that in fact the liquid does not immediately make contact with the surface [Thoroddsen et. al. 2003]; rather, the air fails to drain and instead compresses, and deforms the underside of the drop into a dimple. Theory has implicated the air in the splashing transition [Mandre et. al. 2009, Mani et. al. 2010]; simulations and calculations suggest that a nanometer-thin film of air continues to deflect the liquid away from the surface, and the lubrication by the air acts as a mechanism for a splash [Mandre et. al. 2012]. While much progress has been made with experiments [Kolinski et. al. 2012] and theory [Mandre et. al. 2012], significant questions remain concerning the role played by the air in the impact of droplets, and in the splashing transition.

The Technique

In order to investigate the role played by air at the interface of the impacting drop, we adapt a Total Internal Reflection (TIR) technique used previously in friction experiments [Rubinstein et. al. 2004] that is capable of rapidly probing the height of the liquid from the solid surface with nanometer precision. To achieve this, we shine mono-chromatic light at the surface of a dove prism from below, such that the angle of incidence of the light on this surface is greater than the angle required for total internal reflection from the glass-air interface, but less than the angle required for total internal reflection from the glass-liquid interface; thus we are exciting an exponentially decaying evanescent field immediately above the surface [Kolinski et. al. 2012]. This set-up is shown schematically below. When the liquid enters the evanescent field, light transmits into the liquid; as the liquid gets closer to the surface, exponentially more light transmits into the liquid. Finally, when the liquid makes contact with the surface, all of the light transmits, and none reflects. By recording the reflected intensity on our camera’s imaging sensor, we determine the height of the liquid from the surface as h = d*log(1-I/I0), where d is the decay length of the evanescent field.  

A nanometer-scale film of air & verification of the technique

Using TIR technique, we have shown that indeed, the air mediates the contact of the liquid with the solid: below we show a time series of the liquid as it spreads over a nanometer thin film of air (a). We also show a kymograph (r-t plot), (b), of the height along the dashed red line in (a) ii; here, height is encoded by color, where dark blue indicates liquid-solid contact, and red indicates a distance exceeding 500 nm from the surface. While such high-resolution mapping is possible for slow dynamics, for non-splashing impacts, contact will initiate rapidly at higher impact velocities, and our fastest camera is no longer able to measure the air film at the highest imaging frequencies. Indeed, the asymmetric formation of contact we observe in (a) below prefaces one of the very exciting open questions about what causes the liquid to puncture the thin film of air.

Rapid dynamics beneath splashing drops

In order to probe the dynamics of an impacting drop above the splashing threshold, we needed another technique, since these dynamics occur too rapidly for us to resolve at the highest frame rate that our camera can capture. To do this, we reduce the frame rate to increase the effective sampling rate in a technique we call the virtual frame technique (VFT): since the transition to liquid-solid contact occurs so rapidly above the splashing transition, we assume the liquid wets the surface immediately. This assumption thus enables us to encode the position of the spreading liquid in the intensity of an over-exposed image: by increasing the exposure of the imaging sensor to the inter-frame time, the position is encoded by grayscale on the image, as shown below. Thus, our virtual frame rate is limited only by the camera’s bit-depth and the spatial resolution. The VFT enables measurement of the velocity of the spreading liquid. The wetting front velocity exceeds the liquid capillary velocity for splashing drops, and thus must be spreading over the air, not on contact with the solid.

To verify the assertion that the liquid is spreading over air above the splashing threshold, we directly observe the air film at the highest frequency, using a photodiode as a rapid single-point intensity measurement, at frequencies up to 150 MHz. We sampled the intensity at a single point, and saw that indeed, the air film is formed, and rapidly breaks down behind the spreading liquid front, confirming our assertion from the VFT data; this can be seen by the plateau extending from t = 1 microsecond to t = 6 microseconds.

Many questions remain open...

While we have begun to explore the fascinating dynamics beneath the impacting drop, many mysteries remain. Some of these include:

-What causes the liquid to puncture the thin film of air? The liquid makes contact with the solid through the air by some mechanism. We are currently investigating this phenomenon; we suggest that interfacial forces destabilize the thin film of air, precipitating liquid-solid contact.

-What role does liquid viscosity play in the impact process? The impact Reynolds number is large, exceeding 1000, suggesting that liquid viscosity is irrelevant to the problem of drop impact. However, experiments on the splashing of viscous drops have shown that the ejection of the sheet is both delayed and flatter for more viscous liquids [Driscoll et. al. 2010]. The stress in the liquid and the air are coupled; how does this coupling affect the impact process?

-What happens at low ambient pressure? We know that reduced ambient pressure can completely suppress the splashing phenomenon. Does it completely prevent the formation of the thin film of air, or is it playing some other role? 

For details:

John Kolinski

Above: (Top) Surface height profile of a bouncing drop at four points in the bounce. (Bottom) Side profile and TIR contact profile of the drop at the same four points.