Surface tension and its significance for nozzle technology

The surface tension is usually denoted by the Greek letter σ

Just like viscosity η or ν and the density ρ it belongs to the rheology of a liquid and thus to its specific material properties. It is not important for the flow through the atomizer itself. However, this only applies if no two-phase flow is generated inside the nozzle!

That is to be observed! A pronounced two-phase flow is generated with two-substance nozzles of an internal mixture.

The unity of surface tension - a contradiction?

It is known from mechanics and fluid mechanics that stresses usually have the unit "N/m2". This means a force per unit area.

The unity of surface tension

However, this surface tension has the unit "N/m".

Is that a contradiction or even a mistake?

Figure: Galaktico, Gas liquid boundary, Supplemented by explanations, CC BY-SA 3.0

The special feature is that the surface tension is a line tension. A short explanation.

If, for example, a water molecule is completely inside a resting and homogeneous amount of water in a beaker, the resulting forces acting on this molecule are zero.

However, the situation changes when the molecule in question enters the interface layer between water and the surrounding air.

This results in an effective force which is directed into the liquid. Simplified, one can think of the surface tension as a thin membrane with only a few molecular layers.

Because of the small size of this membrane, the surface tension is defined as the so-called line tension. This results in the unit "force per length".

Why does the surface tension affect the drop size in the spray?

The force directed into the liquid due to the surface tension leads to an internal pressure pi at the curved surface of a drop.

A thought experiment on this subject:

If it were possible to "connect" a pressure gauge to a drop, it would be possible to measure the pressure. And this pressure can be quite considerable, depending on the drop size and the amount of surface tension!

A drop of water with a diameter of 1 µm, i. e. 1/1000 mm, has an internal pressure of almost 2.9 bar! An equally large drop of mercury already at 18.8 bar!

When looking at these values the following fact is immediately obvious! The further splitting of a small drop with a high internal pressure is therefore extremely difficult.

The drop is very stable and resists deformation or fragmentation. And it is precisely this secondary splitting of drops that takes place in a spray field characterized by turbulence.

This is also the reason why technical nozzles and atomizers can only supply extremely fine droplets in a spray with great effort.

Surface tension and droplet diameter - is a drop really a sphere?

The higher the internal pressure pi in a moving drop, the more stable it is. Furthermore, of course, it will exihit an ideal spherical shape, even if external forces attack.

These forces can be caused by a flowing gas (air) from a two-substance nozzle. However, interactions between the liquid and the surrounding atmosphere are also present in pressure nozzles. Mostly the ambient air rests and the drops move.

The surface tension also plays a role in the decay of liquid lamellae and liquid jets.

Surface tension and droplet diameter - Is a drop really a sphere?

Decisive for the real contour of a drop is therefore the surface tension and the drop diameter itself.

Basically, it can be said that the drops in a spray tend to become smaller if the value of the surface tension decreases.

This can be done, for example, by increasing the temperature or by adding surfactants.

Do not confuse surface tension with interfacial tension!

The interfacial tension and the resulting contact angle α determine whether a liquid is wetting or not wetting against a solid surface. This solid can of course also be a nozzle material!

Drops on a solid surface; non-wetting (left) and wetting (right)
A typical example of non-wetting

However, the question of wetting and non-wetting only plays a significant role in so-called quasi-static droplet formation mechanisms and for rotary atomizers.

Do you have questions about surface tension?

Would you like to know whether the surface tension plays a role in your planned nozzle technology? Or would you like to have the surface tension data of special fluids measured? Also as a function of temperature?

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