Fluid thread breakup

The thread-like regions continue to thin until they break, forming individual droplets of fluid.

The examination of droplet formation has a long history, first traceable to the work of Leonardo da Vinci who wrote:[1] "How water has tenacity in itself and cohesion between its particles.

"He thus correctly attributed the fall of droplets to gravity and the mechanism which drives thread breakup to the cohesion of water molecules.

The first correct analysis of fluid thread breakup was determined qualitatively by Thomas Young and mathematically by Pierre-Simon Laplace between 1804 and 1805.

Moreover, they also deduced the importance of mean curvature in the creation of excess pressure in the fluid thread.

In the 1820s, the Italian physicist and hydraulic engineer Giorgio Bidone studied the deformation of jets of water issuing from orifices of various shapes.

[4] Félix Savart followed in 1833 with experimental work, utilizing the stroboscopic technique to quantitatively measure thread breakup.

These observations facilitated Joseph Plateau's work that established the relationship between jet breakup and surface energy.

[6] Plateau was able to determine the most unstable disturbance wavelength on the fluid thread, which was later revised by Lord Rayleigh to account for jet dynamics.

High speed photography is now the standard method for experimentally analyzing thread breakup.

With the advent of greater computational power, numerical simulations have begun to replace experimental efforts as the chief means of understanding fluid breakup.

However, difficulty remains in accurately tracking the free surface of many liquids due to its complex behavior.

The most success has occurred with fluids of low and high viscosity where the boundary integral method can be employed as the Green's function for both cases is known.

These perturbations are always present and can be generated by numerous sources including vibrations of the fluid container or non-uniformity in the shear stress on the free surface.

This would push fluid back toward the thinned regions and tend to return the thread to its original, undisturbed shape.

Numerous solutions have been found for the non-linear behavior of fluid threads based on the forces that are relevant in particular circumstances.

While these numbers are common in fluid mechanics, the parameters selected as scales must be appropriate to thread breakup.

For small Reynolds numbers, viscous dissipation is large and any disturbances are rapidly damped from the thread.

[14] However, his solution has become known as the Rayleigh-Plateau instability due to the extension of the theory by Lord Rayleigh to include fluids with viscosity.

Plateau considered the stability of a thread of fluid when only inertial and surface tension effects were present.

As importantly, unstable modes are only possible when: Reynolds and later Tomotika extended Plateau's work to consider the linear stability of viscous threads.

Examples of when this case would apply are when gas bubbles enter a liquid or when water falls into honey.

coefficients are most easily expressed as the determinants of the following matrices: The resulting solution remains a function of both the thread and external environment viscosities as well as the perturbation wavelength.

The fluid contained in the filament can stay as a single mass or breakup due to the recoil disturbances imposed on it by the separation of the main droplet.

The production of satellite droplets is governed by the non-linear dynamics of the problem near the final stages of thread breakup.

[22] The filament cannot retract sufficiently rapidly to the faucet to prevent breakup and thus disintegrates into several small satellite drops.