# Why is mercury's surface tension so high, when its viscosity is low?

At a basic level, both surface tension and viscosity are the result of forces between particles. Usually we'd talk about intermolecular forces, because liquids are usually molecules, but obviously that doesn't work for mercury, which isn't made of molecules at all. Stronger forces between particles give higher surface tension, and usually also higher viscosity. So water's fairly high surface tension is usually credited to hydrogen bonding, and mercury's exceptionally high surface tension is put down to metallic bonding; while the increasing viscosity of aliphatic hydrocarbons with more carbons is said to be due to increasing London dispersion forces.

It's easy to see that the two are poorly correlated, though. Ethanol has almost identical surface tension to acetone, for example, but it's more than three times as viscous. Most strikingly, mercury has really extraordinarily high surface tension, but is no more viscous than cold water.

Is it completely wrong to expect at least some kind of loose correlation between surface tension and viscosity? Is viscosity just a far more complex phenomenon, a proper explanation of which lies way beyond the hand-wavy school science that chemistry teachers use to give a vague idea about things like trends in the alkanes? Would it be better to emphasise entanglement of long molecules when trying to explain the viscosity of longer alkanes, rather than just stronger forces?

Is mercury's low viscosity mainly down to its small particle size, or is there much more to it than that?

• I'd say it is due to the nature of metallic bond. See, it is undirected. Feb 8 '16 at 6:10
• How is that significantly different from any of the intermolecular forces behind viscosity and surface tension in other liquids, @Ivan? Sep 7 '16 at 8:56
• Sorry, I don't remember what I had in mind back then in February when writing my first comment. As it seems now, yes, it would be better to emphasize the entanglement of long molecules and all. Sep 7 '16 at 9:00
• Related discussion on physics SE: physics.stackexchange.com/questions/148792/… Also, this chemical engineering article developed an empirical relationship between viscosity and surface tension: google.com/… Sep 4 '17 at 16:41
• This is out of my area, so I'll be interested to hear from others with more expertise, but here's how I think of it: The surface tension of a liquid under air is a thermodynamic property resulting from the difference between the free energy of bulk vs. surface liquid molecules (due mostly to liquid-liquid vs. liquid-air bond energies). Typically the former is much more favorable, hence the liquid will try to minimize its surface area:volume ratio. By contrast, viscosity is a kinetic property determined by the activation energy involved in breaking and reforming the liquid-liquid bonds. Jun 17 '19 at 19:44

I think the complex phenomenon here is the nature of the metallic bond. It is commonly said there is a "sea of electrons" that are delocalized across the entire metal and that the metal ions just bash around in the sea against each other. So when they're in the metal bulk phase they feel about the same strong force on all sides (thus as Ivan said, the force is undirected). Therefore in the liquid the atoms can slip past each other OK. The problem with the vapor phase is that it's no longer metallic. An ideal gas (an excellent approximation for mercury or most other vapors at STP) has no forces between molecules, by definition. So you've got to pull the metal atom completely out of the "electron sea" (within which it is strongly-bound) to vaporize it, and that requires a lot of energy and leads to a high surface tension. Surface tension is inherently a two-phase property!

I think the contributing factors are:

Viscosity - liquid only, low energy change for motion, low viscosity
Surface tension - liquid-vapor, large energy change, high surface tension


It's beyond high school level, but I found Rowlinson and Widom's "Molecular Theory of Capillarity" gave very a good and thorough explanation of surface tension.

• Ah, interesting subtlety with the uniformity of the metallic bonds. So it's not just attraction to other particles that makes a liquid viscous, it's the energy required to move from one place in a liquid to another, and in something like glycerol, even though the forces are less strong than in mercury, particles have to navigate a highly non-uniform electrical field. They can't rely on the same forces of attraction as they move from one spot to another. Sep 18 '21 at 6:29