While making a cup of coffee I spilled some milk, and it made an interesting pattern. There were approximately 18 small droplets surrounding a larger central droplet (see Photo, above right). It reminded me of a photograph I saw in a textbook during my childhood, where a drop had just fallen into a glass of milk, resulting in a splash like a king鈥檚 crown. Why did my pattern and the one from the book form? Presumably they are related. Do other liquids make similar patterns?
鈥� The pattern of droplets surrounding the larger drop of spilt milk is the result of corona splashing. The study of splashes has a long and distinguished history, dating back to the late 19th century. Arthur Worthington, who was one of the first people to systematically study drop impacts, made it his life鈥檚 work, and his book A Study of Splashes (Longman, 1908) contains many fascinating photographs of splashes. Perhaps the best-known of a corona splash are those captured by starting in 1936.
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鈥淭he study of splashes and droplet patterns has a long and distinguished history, dating back to the late 19th century鈥�
When a drop hits a surface, it can either spread, splash or rebound. The outcome depends on a number of factors, including impact speed, size, density, viscosity and whether the surface is initially dry or damp. For dry surfaces, impact drop morphologies are also influenced by the roughness and 鈥渨etability鈥� of the surface.
On a typical dry, flat and relatively smooth bench, such as the type often found in kitchens, the moment the falling drop strikes the surface, portions of the liquid moving downwards are pushed outwards from beneath the collapsing drop and immediately begin to spread along the bench top. A narrow and highly curved neck therefore develops between the thin liquid layer and the largely uncollapsed spherical drop above it. Provided the impact speed is above a critical value and the surface is not too smooth, surface tension in the necked region gives rise to a force directed at an angle to the horizontal.
In corona splashing, the upward component in the surface tension at the neck causes the leading edge of the radially spreading liquid film to bend upwards, giving rise to the formation of a 鈥渃orona鈥�, or crown, of the type mentioned in the question. Excess pressure caused by the collapsing drop continues to push liquid into the walls of the crown as the impact unfolds, extending it outwards and upwards.
As the crown rises and increases in size the rim slows and thickens, taking on a roughly toroidal shape. The underlying mechanism leading to the rim of the crown breaking up into many smaller droplets is not yet entirely understood. It is thought, however, that at the moment when liquid begins to feed into the walls of the crown, rough anomalies on the bench鈥檚 surface initiate small ripples which rapidly grow and inevitably cause the rim of the crown to form cusps, which break up into thin jets directed upwards and away from the crown. Instabilities in the ejected jets from the rim of the crown cause a droplet to pinch off at each end, giving rise to the distinctive coronet (see Photo, lower right) that is responsible for the observed splash pattern.
Shortly afterwards, the walls of the crown start to thicken as it slows before falling back onto the bench under gravity, together with what remains of the protruding jets, to form the larger central drop. The effects of surface tension are responsible for holding the collapsing coronet together during its final d茅nouement.
Besides milk, corona splashing is found in many other liquids including water, various alcohols and some paints. However, the opaqueness of milk makes it easier to see the droplet ring resulting from a corona splash.
Se谩n Stewart, The Petroleum Institute, Abu Dhabi, United Arab Emirates