What is the meaning of end-pinching in fluid mechanics?

[Chuck88]

Main Question or Discussion Point

Dear all,

I want to know the meaning of end-pinching in fluid mechanics. Can someone provide me with the information?

 

[Bobbywhy]

The dynamical mechanisms of drop formation and fluid rupture from a nozzle under the influence of gravity, called the “dripping regime”, and during the application of external force, called the “jetting regime”, have been studied since the mid-19th century. The sequence of events for fragmentation is:

1. The drop evolves to an ellipsoidal shape, then to a dumbbell (bulbous) shape.
2. The necks between the bulbs and the central portion of the drop continue to stretch and become thinner.
3. The bulbs detach. These are called daughter drops. This process is known as “end-pinching”.

The viscosity and surface tension of the liquid strongly affect the drop formation. One of the most cited and famous study of this process is:

J. Fluid Mech. (1989). vol. 198, p p . 399-427
Printed in Great Britain
399
“Relaxation and breakup of an initially extended
drop in an otherwise quiescent fluid”
By H. A. STONE AND L. G. LEAL
Department of Chemical Engineering, California Institute of Technology,
Pasadena, CA 91125, USA
(Received 30 September 1987 and in revised form 24 June 1988)
See especially section 3.2.3 where the mechanism of “end-pinching” is described in exquisite detail:

http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=4&ved=0CFQQFjAD&url=http://authors.library.caltech.edu/31527/1/STOjfm89.pdf&ei=E_YxUNS9MoizqgGYh4GICw&usg=AFQjCNHfWdu86nSz5SHNhW7fu1A08ISYkQ&sig2=MITvEfYNTr6AGhdsCcs6Aw

Here are two websites with great images of “end-pinching”
Droplet formation and Inkjet Rheology and Processing:
http://www.ceb.cam.ac.uk/pages/droplet-formation.html

The role of feedback in microfluidic flow-focusing devices
Excellent images of examples of “pinch-off” (a synonym):
http://rsta.royalsocietypublishing.org/content/366/1873/2131/F2.expansion.html [Broken]

We can experiment at home making drops with an eyedropper, a plastic bottle of water with a small hole in the bottom, and at the sink. At the sink a thin laminar stream will naturally break up into individual drops. Fluid visualization methods such as the inclusion of glitter, bright illumination, and variable strobe lighting all can assist with the observation of the process. All humans excrete fluid wastes several times per day, providing many more opportunities to observe “end-pinching” during droplet formation. We can study fluid mechanics easily in nature. The idea is to be ready to recognize opportunities for research whenever and wherever they appear.

Cheers,
Bobbywhy