User:Mundietomnis/sandbox/Fluid thread breakup

Fluid thread breakup is the process by which a single mass of fluid breaks into several smaller fluid masses. The process is characterized by the elongation of the fluid mass forming thin, thread-like regions between larger nodules of fluid. The thread-like regions continue to thin until they break, forming individual droplets of fluid.

Thread breakup occurs when two fluids or a fluid in a vacuum form a free surface with surface energy. If more surface area is present than the minimum required to contain the volume of fluid, the system has an excess of surface energy. A system not at the minimum energy state will attempt to rearrange so as to move toward the lower energy state, leading to the breakup of the fluid into smaller masses to minimize the system surface energy by reducing the surface area. The exact outcome of the thread breakup process is dependent on the surface tension, viscosity, density, and diameter of the thread undergoing breakup.

History
The examination of droplet formation has a long history, first traceable to the work of Leonardo da Vinci who wrote@@:

How water has tenacity in itself and cohesion between its particles. This is seen in the process of a drop becoming detached from the remainder, this remainder being stretched out as far as it can through the weight of the drop which is extending it; and after the drop has been severed from this mass the mass returns upwards with a movement contrary to the nature of heavy things.

He thus correctly attributed the fall of droplets to gravity, but misinterpreted the mechanism which drives thread breakup.

The first correct analysis of fluid thread breakup was determined qualitatively by Young@@ and mathematically by Laplace@@ between 1804 and 1805. They correctly attributed the driver of thread breakup to surface tension properties. Moreover, they also deduced the importance of mean curvature in the creation of excess pressure in the fluid thread. Through their analysis, they showed that surface tension can behave in two ways: an elastic mechanism that can support a hanging droplet and a pressure mechanism due to capillary pressure that promotes thread breakup.

Savart followed in @@ with experimental work, utilizing the stroboscopic technique to quantitatively measure thread breakup.@@ He noted that breakup is a spontaneous process, occurring without an external stimuli. This work allowed him to determine that droplets are produced from a jet flowing from a tank at a distinct rate inversely proportional to the nozzle radius and proportional to pressure in the tank. These observations facilitated Plateau's work that established the relationship between jet breakup and surface energy. Plateau was able to determine the most unstable disturbance wavelength on the fluid thread, which was latter revised by Rayleigh to account for jet dynamics.

As the surface disturbance becomes large, non-linear theory must be applied. The behavior of jets with large disturbances was examined experimentally by Magnus and Lenard. Their experiments helped to characterize satellite droplets, droplets that are produced in addition to the large main droplet, through the introduction of high speed photography. High speed photography is now a standard method for analyzing thread breakup.

Find a couple of numerical papers to put in here as well

Low viscosity
rederive plateu

High viscosity
reynolds & tomotika