Forked Fountains

Splitting of a Liquid Jet

Srinivas Paruchuri and Michael P. Brenner

PRL 98, 134502 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e134502


Interesting work --- hard to believe this problem had not been studied earlier! I guess that's the effect of a well-written paper: The ideas are presented so clearly they seem obvious. This was, in my opinion, a very well-written paper.

The authors analyzed the conditions under which a jet of fluid can split. They derive a Navier-Stokes equation for their model jet, then solve it numerically. The numerical results are used as the basis of an analyitc model that captures the essential features of the numerical work. The authors demonstrated a very nice interplay between numerical and analytic work.

The conclusions of the authors are that tangential stress on a jet can lead to splitting, but normal stress cannot. Tangential stress must overcome the surface tension of the fluid; thus, there is a critical stress, below which splitting cannot occur.

Doodling in my notepad, I made a simple model for the pinching and splitting of two surfaces. It is entirely mathematical and does not include any physical parameters. I compared my sketches with the authors results, and was surprised to see sharp cusps in their cross-sections. In my model, there is a linear crossing at one instant in time, but before and after, the surfaces are smooth. It seems to me that a smooth membrane would be vastly lower in energy than one with a cusp. Of course, when the membranes touch, it's got to lead to some kind of singularity in the differential equation, so a numerical routine or an analytic solution to the full equations might not "know what to do" after the membranes meet.