# Surface tension of solutions and mixtures

The inspiration for this question is over on cooking.stackexchange, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well.

What determines the behavior of surface tension for solutions and mixtures with respect to concentration? Of course, I expect that the answer depends on the liquid, since different liquids have different causes of cohesive forces. I would be interested both in quantitative answers (very approximate/general, probably) and qualitative ones.

Additionally, what is the dependence of surface tension on temperature? Does that have any interaction with dependence on solution/mixture concentration?

(I know this question borders on chemistry, but there's no chemistry stackexchange, and besides, I'm sure at least some surface tension properties admit explanations from statistical mechanics!)

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Surface tension is physics, so this is fine here. By the way, "dependence of surface temperature on temperature"? I'm guessing you meant to say something else there ;-) – David Z Sep 7 '11 at 0:34
@David: Oops! And thanks; it's certainly physics in my book but I figured once you start venturing into solutions, you sometimes get stuck with chemistry-style approximate relations based only on empirical evidence. (This seems especially possible given the sources of cohesive forces between more complex molecules.) – Jefromi Sep 7 '11 at 2:51
If you want some pointers to some of the information about that topic that can be rigorously extracted in simple Ising-like systems, you can have a look at scholarpedia.org/article/Interface_free_energy . Of course, much more is known (in these "simple" models). – Yvan Velenik May 25 '12 at 17:07

## 2 Answers

About the surface tension of mixtures, this is quite complex, and the answer is certainly not straight. However, it looks like the surface tension of the mixture of two fluids is always in between the surface tension of the pure fluids somehow (so it is simpler than azeotropes for the boiling temperatures of mixtures). The dependency of the surface tension on the concentration may be linear, but usually is parabolic. You can find some graphs of surface tension as a fonction of the concentration of the mixture in this paper. About the temperature dependence, as far as I know, surface tension always decreases with temperature. It is due to the fact that higher thermal fluctuations give smaller cohesion.

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The wikipedia section on the influence of temperature and solutes on surface tension is actually pretty decent with some good reference to basic text on this topic.

That said, there is no straightforward answer to your question because it all depends a lot on the liquid(s) that you are looking at. If for example you have a solution of water and surfactant molecules, you will decrease surface tension, but only to the limit of the critical micelle concentration. Moreover, the surfactant (as the word says) will collect at the surface of the liquid and therefore have a greater effect then expected based on the bulk concentration.

About the temperature effect. For most liquids the answer of @Herve that the surface tension decreases with increases temperature is true, but there are some exceptions. Mainly metallic substances can also show an increase in surface tension with temperature.. This is in particular important in the study of welding, where the surface tension gradients due to temperature have a large effect on the quality of a weld. In this case indeed the interaction between temperature and solutes will determine the surface tension (see the article for one of the possible reasons)

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