Yesterday while cleaning my kitchen stove, i witnessed a wonderful physical phenomena happening in a complete different way than I would have expected.
A drop/ little blob of water fell into the concave center of the stove plate. The stove was still very hot at a temperature well above the boiling point of water. I knew about the thin layer/cushion of vapor that forms under the water in such case, insulating it from the stove's surface . (Later I found out its called leidenfrost effect) However i didnt expect the oscillations and the geometric patterns associated with it. And immediately my brain got on fire and i started seeing the common snowflake shape and thinking about crystallization of water and its dependency on temperature and humidity but realised quick enough that its the wrong place to start , then thought of the circular grooves in the surface of the stove and the cavity where the water sat as resonance cavities ..
It did not get clear till I learned about normal oscillations happening during the leidenfrost effect which take place at fixed frequencies.
With some degree of confidence one can say that these oscillations are responsible for the shapes seen in my video. Thinking of the water blob as being levitated by the vapor cushion and being excited by sound pressure from the air/vapor layer itself !?
See this video on shape oscillation of a levitated drop in an acoustic field. By W. Ran & S. Fredericks, Clemson university,
Still fascinated with the topic, so i went and recreated the experiment, filmed it and processed the video with imovie (crop, shadows, etc ) then processed it again in matlab and did some macgyvering on the video to get mathematical.
Its clear to me now that the excitation is not related to the acoustics of the environment but somehow connected to the temperature. The critical temperature for the oscillation to start was above 200 and also above the limit of my IR temperature sensor.
Here is the processed video!
I had no idea how to treat shape oscillations in matlab, but two things came to mind; The peaks in the video and the frequency of the hiss sound i recorded in another video (mobile phone),
Plotting the Peaks would show me the number of modes (or at least that what i think) and the hiss would tell me something about the frequency of the oscillation.
The video processing in matlab was straight forward, creating a video object and getting its parameters then reading it in a struct. later on reading every single frame and getting its grayscale twin .. then calculating and plotting the peaks. Now peaks in matlab is a function of 2 variables, and it does return a 49 x 49 matrix with the maximas and minimas and the surf function displays the peaks in the z axis, Check the next video for the matlab plot animation.
Now remains the question, what the excitation source excitation and relation to temperature.
A paper published by the American physical society (2012) states in the Abstract that "The geometry of the vapor pocket depends primarily on the drop size not the substrate temperature". In another place its states that "Larger drops have higher modes of amplitude variation. I look again at the plot animation of the peaks in matlab and i see 2 normal/orthogonal modes. Apparently you think of these problems in terms of Eigenvalues and Eigenvectors like good people do. The eigenvalues representing the resonance frequencies of the amplitude peaks. In the matlab animation i only show the first 50 frames of the normal speed video.