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The Weber number (We) "can be thought of as a measure of the relative importance of the fluid's inertia compared to its surface tension" (Wikipedia):

$$\mathrm{We} = \frac{\rho v^2 l}{\sigma}$$

So assuming a droplet is moving through air, the droplet is the object and the air is the fluid. Clearly, $l$ and $v$ are the characteristic length and velocity of the object (the droplet), but which density $\rho$ and surface tension $\sigma$ of the two should be used?

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As the name suggests, the surface tension is a property at the interface between two phases. As such you should take the surface tension of the liquid-air interface (e.g. water-air)

Since it's the relative importance of the fluid's inertia to its surface tension, it is necessary to use the density of the fluid the droplet is dispersed in. The best way to think of this is to consider that surface tension is trying to keep the droplet spherical, while inertia is trying to deform the droplet by dragging it along in the flow field.

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  • $\begingroup$ "surface tension of the liquid-air interface" as opposed to the surface tension of the liquid alone? what is the meaning of a "joint" surface tension of two materials? $\endgroup$ – Sparkler Apr 8 '16 at 23:09
  • $\begingroup$ @Sparkler they are the same thing, you cannot have a surface tension with only one phase. Imagine a liquid in a vacuum; it will simply vaporize instantly. Surface tension is the energy mismatch between molecules of liquid in the bulk vs that at the interface, therefore an interface is required. $\endgroup$ – nluigi Apr 9 '16 at 5:49
  • $\begingroup$ I thought that surface tension is an absolute property. If it's not (you're saying that it's relative), then to make any prediction we'll have to have data tables of numerous combinations of materials, no? $\endgroup$ – Sparkler Apr 9 '16 at 14:36
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    $\begingroup$ @Sparkler I think it is a common misconception. Often when talking about the surface tension of water, it is implied that it is the surface tension of a water-air system. However, for a water-1-butanol system the surface tension is completely different. For a list of surface tensions for different systems check out the link in my answer. I also suggest to have a look at the first part of the wiki $\endgroup$ – nluigi Apr 9 '16 at 21:59

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