Where is the Air?

July 25, 2012

Dynamics of drop splashing

When a liquid drop hits a surface, it may rebound, spread smoothly, or shatter violently in a splash.  Controlling whether a liquid splashes has important consequences in many applications, including fuel dispersion in the automotive industry, splat formation in coating technologies, and pesticide application in agriculture.  Liquid and surface properties obviously influence impact dynamics; it is quite counterintuitive, however, that lowering the ambient pressure eliminates splashing altogether.  To measure transient air-layer dynamics, we developed a technique that combines the high spatial precision of interferometry (nm scale) with high time resolution (15 µs). 

At impact, a small amount of air is trapped beneath the falling drop, creating a bubble.  Recent theoretical work has suggested that this air pocket is linked to splashing dynamics.  In a sufficiently viscous liquid, splashing occurs at late times, several tenths of a millisecond after impact.  This temporal separation between impact and splashing creates an ideal system to test whether the initial air pocket influences the later-time splashing dynamics. Using our interference technique, we found the initial air-cavity dynamics to be consistent with theoretical predictions.  However, we found no significant air layer that persists beneath a spreading drop until the time of thin-sheet ejection—a necessary precursor to splashing in high-viscosity liquids.  Thus, in contradiction to theoretical predictions, an underlying air layer is not responsible for splashing in this high viscosity regime.

The drops used in this study were mixtures of water and glycerol, with dynamic viscosities µ between 8 and 48 mPa s.  Over this range there is minimal variation in surface tension and density.  Drops of uniform radius, r0 = 2.05 mm, were created using a syringe pump. The impact velocity u0 was varied between 1.5 and 4.1 m/s by releasing drops from various heights within an acrylic tube that could be evacuated to varying ambient pressures P between 2 and 102 kPa.  Using a high-speed camera, we imaged drop impacts as shown in (a).  To determine the thickness of the liquid as a function of position and time, we measured the local optical absorption of a spreading drop of colored liquid (µ = 8 mPa s) as shown in (b); we converted the transmitted light intensity to liquid thickness by calibrating with a liquid wedge of known proportions.  By modifying our setup as shown in (c), we also measured the thickness of any air layer underneath the spreading liquid using interferometric high-speed imaging at speeds up to 67 000 frames/sec.

We used a monochromatic LED (wavelength660 nm) with a small coherence length, ~10 µm, as a light source, so that there would be no interference between the two sides of the glass substrate.  Adding a small amount of dye to our liquid minimized the reflected light from the upper liquid surface and eliminated any interference generated within the liquid itself.  The addition of dye to the water-glycerol mixtures did not change the liquid viscosity or surface tension nor alter the threshold pressure for sheet ejection Psh.  Images of a splash with or without the dye were virtually indistinguishable. 

(a)  Side view showing thin-sheet ejection and splashing for a drop with viscosity µ = 13 mPa s, and impact speed u0 = 3.5 m/s.

(b)  Bottom view and intensity profile of a dyed µ = 8 mPa s, u0 = 3.3 m/s drop used to measure liquid thickness: the ejected sheet is approximately 1/10 the thickness of the lamella.  Arrows indicate measured regions.

(c)  Schematic for reflected-light interference: a half-silvered mirror (M1) directs light from a monochromatic LED onto the impacting drop from below; a standard mirror (M2) redirects reflected light into a high-speed camera.

(d)  Example time-series interference image of an impacting drop with µ = 18 mPa s and u0 = 3.5 m/s. The lamella is uniform in intensity, indicating an optically flat region.  The thin sheet is ejected in the third panel.

(e)  Magnified images of initial air cavity.  This initial air cavity closes completely well before the thin sheet is ejected. 

(f )  Radius of curvature of cavity normalized by drop radius rc/r0vs time showing the cavity is slender (rc ~r0), and gently flattens in time.  Complete cavity closure occurs ~150 µs after impact, well before splashing occurs.

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