A Worthington Jet resembling an apple has formed from colored milk being dropped into a pool of differently colored milk.
By Harrison Lien, for Get Wet 2016
A Worthington jet is a phenomenon in fluid flow that occurs after a droplet of a fluid hits the surface of another fluid that is relatively deep. Initially, when a droplet hits a surface, it creates a crater in the surface, and then a crown shape is made from the surface fluid around the crater. While the crater is still in shape but as the crown has fallen from its peak height, a Worthington Jet rises from the center of the crater. Different techniques can be used to analyze the fluid flow beyond the general shapes created from a droplet hitting a surface of a deep liquid.
This photograph demonstrates some different techniques that can be applied to the study of such a flow. The photo depicts a Worthington jet produced from colored milk hitting a pool of differently colored milk. Milk was released, one drop at a time, into the pool of milk from a height of 3 feet from the surface. The saucer that was used was 3.97 inches in diameter on the outside of the dish, and a depth of 0.51 inches from the bottom at the center to the top of the rim of the dish, and the inside edges had a gentle curve to them, going from the rim to a flat circle of diameter 0.98 inches at the bottom. The photograph was taken with a Nikon D3300, with a focal length of 200 mm, an aperture of f/5.6, a shutter speed of 1/640 seconds, and an ISO of 400.
The surface was initially milk with intentionally poorly mixed red and yellow food dye at the surface. The milk dropped into the surface was dyed with blue food dye. Several drops had been dropped onto the surface, prior to this photo, as seen by green areas on the surface – including the base of the jet. It can be observed from the droplets that have separated from the jet, that some of the original blue milk from the impact droplet have not mixed with the milk on the surface, and retain their true blue coloration. It is interesting to note the angle at which the jet is escaping, as most Worthington jets go straight up from the surface. This angling could be due to an unintentional initial horizontal droplet velocity. As part of a series of photographs like this one, it can be observed with consistency that the Worthington jets always seemed to lean over in the direction of the side of the dish in which they were closest to; jets formed in the center went straight up, and ones on the sides were bent toward their respective side. This observation introduces a new hypothesis: perhaps the curvature at the bottom of the relatively shallow dish changes the jet direction: more careful testing and photography could lead to an answer.
In the photograph, there is also some motion blur that is visible, and perhaps even a little distracting from the clarity of the photograph. While this decreases from the artistic value of the photograph, a measurement of this motion blur can be used in combination with the shutter speed to determine the average velocity of a flying droplet during that brief instant. Some caution should be used with this technique, because this type of measurement cannot measure jet motion along the axis of the lens of the camera.
Although this photo depicts some techniques that could be used for analysis, there are also some features of this photograph that are less useful for the scientific method and more employed for artistic value. The first example of this would be the coloring: the surface could have been better mixed and pure and free from color contamination of other tests. With this in play, one could use the color mixing of the base of the jet to determine the speed of fluid mixing in the surface as the jet is formed.
With such a high speed photo, some photographic sacrifices needed to be made to produce a quality photo, given the lighting conditions. The apparatus was lit up using a 1200 lumen light, focused at the saucer 2 feet away. Even with this bright light, the photo settings were a little lacking, the shutter speed could have been higher to make the photo crisper. Given the focal length and the size limitations of the lens being used, the aperture was already at its limit, at f/5.6: parts of the surface are a little out of focus, but this is seen as acceptable, considering the flow being showcased is within the focal range, and this depth of field adds a little bit of an artistic aspect to the photo. The next thing that could account for the exposure was the ISO. An ISO of 400 makes this picture clear of grain, and perhaps an exchange of light grain for motion clarity could be a necessary trade-off for artistic merit.