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Does surface tension depend only upon the nature of the fluid or on other factors too like the liquid-solid or liquid-gas interface?

I saw in my book definition that $$S = U/A,$$ where $U$ is the surface energy. Is this, right, or would it be better to say $$S = \text{change in } U/ \text{change in } A~?$$

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    $\begingroup$ It is the derivative, $dU/dA$, although in the case of fluids this is the same as $U/A$. And it is a measure of the tension of the interface rather than just the fluid (or whatever) itself. $\endgroup$ – lemon Feb 22 '16 at 15:08
  • $\begingroup$ But I read in my book and online that it is a characteristic property of the fluid. $\endgroup$ – Shodai Feb 22 '16 at 15:55
  • $\begingroup$ If that were the case then why do reported surface tensions specify what the fluid is in contact with (such as air)? What it's exposed to affects the molecular-scale structure and properties of the surface. It's also not possible to measure (nor to compute in any rigorous way) surface tension that neglects half of the interface. $\endgroup$ – lemon Feb 22 '16 at 20:16
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Surface tension is $S = dU/dA$, or the rate of change of surface energy with respect to area. It is a property of both fluids together. This can be understood by thinking about what happens to a particle near the fluid interface compared to a particle immersed among its own.

On average the immersed particle will be pulled in all directions evenly, whereas the particle at the interface will be attracted toward or away from the interface, depending on the molecular properties of both fluids.

You can imagine fluids with very similar molecules might behave almost as though there was no interface. In fluids with very different molecules, particles might be drawn either more towards their own kind, or more toward the other kind.

The former case is true of water and air, where water is much more attracted to itself that it is to air. It forms a sheet-like interface that supports being deformed into droplets and other complex shapes. By contrast, ethanol is not as strongly attracted to itself, and cannot sustain as much deformation in air.

It is this intuition, based on comparison against a reference fluid, that leads some people to mistake surface tension for a property of an individual substance.

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If we dip a capillary tube in a liquid, say water, we find that water rises in the tube - this phenomenon is associated with surface tension. Similarly when we spray water we find that the droplets of water try to form spherical shapes - as if some surface forces are acting and finally gets to build a shape with minimum surface area. Surface tension is defined as surface energy per unit area.

At liquid-air interfaces, surface tension results from the greater cohesive forces of liquid molecules among each other than to the molecules in the air (due to adhesion). The net effect is an inward force at its surface that causes the liquid to behave as if its surface were covered with a stretched elastic membrane. Thus, the surface becomes under tension from the imbalanced forces, which is probably where the term "surface tension" came from. Because of the relatively high attraction of water molecules for each other, water has a higher surface tension (72.8 millinewtons per meter at 20°C) compared to that of most other liquids.

Quoted from the Wikipedia article on surface tension.

The surface tension does depend on the interface material/gas but the deciding forces are cohesive in nature. By adhesive forces the liquid rises in the meniscus in a glass tube that is concave in nature, whereas in mercury the adhesive forces are so weak that the surface tension leads to a convex shaped meniscus and it dips inside the surface when a tube is dipped in a container of mercury.

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