Plateau - Rayleigh Instability
plateau - Rayleigh instability
The apparatus in the image consists of a standard chemistry stand and clamp. In the Clamp is a syringe full of water dyed with blue food colouring. In the demonstration I applied a constant force to the syringe to obtain a steady flow and i captured an image of the initially smooth stream forming into droplets.
We all know that streams of water whether from a hose or from a syringe, and no matter how smooth will break apart into droplets. The underlying reason for this is surface tension, however this phenomenon is actually alot more complicated. This effect of surface tension is called the Plateau - Rayleigh instability. The proof of this instability is quit mathematical so i will provide a brief explanation. If you want to see the math, see my references at the bottom.
All fluid streams contain perturbations. Perturbations are small changes in a physical system (such as a stream). These perturbations are sometimes compounded into sinusiodal functions and appear as waves. At the trough of the wave, where the radius of the stream is smaller, surface tensions creates a higher pressure. At the crest of the wave where the radius is larger, the pressure will be lower. As a result of the pressure difference the amplitude of some of the waves will increase. The waves will eventually align in what looks like a destructive interference pattern as shown below, however they do not cancel each other out. When the waves become large enough the stream in pinched off and spherical droplets are formed.
the droplest are spherical because the liquid is more stable at a lower energy level, and by decreasing the surface area the number of higher energy molecules is decreased and thus lowers the droplets energy.
the Plateau Rayleigh instability quantifies this phenomenom and shows that where the droplets form is a function of the stream smoothness and the diameter of the stream.
The Link at the very bottom of my references shows a great video of a stream pinching off.
http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture5.pdf This is the math one.