# Origin of surface tension

1. Sep 28, 2011

### dEdt

I'm [STRIKE]a little[/STRIKE] very confused about the origin of surface tension. As I understand it, surface tension is a force on the surface of a liquid which is directed parallel to the surface, correct? But the explanation of surface tension is that molecules at the surface are not covered by other molecules above them, hence there is a net force inwards due to cohesive intermolecular forces. But how does that lead to forces parallel to the surface?

2. Sep 29, 2011

### Andy Resnick

Surface tension (more properly called 'interfacial energy') is the name given to energy contained within a surface of discontinuity- typically a fluid-solid or fluid-fluid interface, where the concentration of the materials undergoes a discontinuous change as you cross the interface.

The energy can be thought of as the energy needed to create an interface- low interfacial energies are associated with wetting and spreading, while high interfacial energies are associated with nonwetting (often hydrophobic) interfaces.

A simple result (not simple to derive, but the result is simple to understand) is Laplace's equation- the pressure jump across a surface of discontinuity (say a drop of water in air) is given by $\Delta P = 2\sigma\kappa$, where $\sigma$ is the interfacial energy and $\kappa$ the mean curvature of the surface.

That's for the interface between two materials. When there is a three-phase contact line (say a drop of water resting on a solid surface in air), there is an additional line tension at the three-phase line. Similarly, if there is an intersection of two lines (say, neighboring drops of water and toluene resting on a surface in air), there is an energy associated with the 4-phase point. These contributions (line tension, etc) are orders of magnitude less than "surface tension", and AFAIK, barely measurable.

Some people like the model of 'unbalanced' forces on molecules, but interfacial energy is a continuum concept and thus cannot discuss molecular origins: as a simple example why using a molecular model leads to problems is the fact that at that scale, the interface itself is not precisely located in space.

In the context of the Young-Laplace equation, interfacial energies are represented as forces acting along the various interfaces to model an equilibrium condition, and this is done by representing the forces as gradients of the surface stress. This leads to a whole host of problems regarding continuity at the three-phase line, none of which has been resolved. One proposal is to require that solid-fluid interfacial energies (and the true contact angle) are not thermodynamic quantities- they cannot be measured, are not material properties, and cannot assume arbitrary values.

3. Sep 29, 2011

### dEdt

Energy might be a better way to look at surface tension, but it should still be possible to understand the physical origin of the forces that are created. And that's my problem: I don't see how they emerge.

4. Sep 30, 2011

### Andy Resnick

Nobody else does, either. That's why people are actively researching the issue.

5. Sep 30, 2011

### cmb

This comment is predicated on the assumption that the classic rationalisation of the concept of 'forces' is always correct, viz. that there is always something that mediates the force. It is an intuitive assumption, but personally I don't view it as self-evident.

Surface tension can be described by the rate of change of entropy with respect to a change of surface area (as the degrees of freedom of the liquid molecules is changed as they become 'surface' molecules, or vice versa).

6. Sep 30, 2011

### Sankalp Zeal

Energy has nothing to do with surface tension. Origination of surface tension is only on the surface of water. This is because the molecules below attract it , develop tension in upper molecules ( under stretch) .

The molecules of atmosphere cannot balance this tension because they are far far away.

7. Sep 30, 2011

### cmb

This is naive. Energy has everything to do with the state of everything!

8. Sep 30, 2011

### Sankalp Zeal

Yes , it has to ! But you just can't take energy in respect to origination of surface tension. Have you seen any text doing it ?

9. Sep 30, 2011

Staff Emeritus
Reif, Chapter 5, Problem 15.

10. Sep 30, 2011

### dEdt

I'm not asking anything as complicated as how the forces arise from electrons or anything. My question is a lot simpler (and a lot dumber too).

Imbalances in intermolecular forces on the surface molecules creates a net force perpendicular to the surface. So how does surface tension (which is a force parallel to the surface) come about? Maybe I'm just being stupid, but I don't see it...

11. Sep 30, 2011

### Andy Resnick

I'm not sure how to interpret the phrase "Imbalances in intermolecular forces on the surface molecules". I *do* understand how to interpret a gradient of the chemical potential, which has a maximum in the direction normal to the interface. I'd have to check my texts (Slattery and Brenner both have good interfacial transport texts) and step through their derivations of the young-laplace equation. The books are at my office, tho...

12. Oct 4, 2011

### Andy Resnick

Ok, I re-read the relevant sections in Slattery's "Interfacial Transport Phenomena", and I think we went off-track.

First off, the forces appearing at a three-phase contact line are indeed tangential to the surfaces at the common line, in accordance with the notion of surface stress and momentum balance. So the actual conceptual problem arises from "the explanation of surface tension is that molecules at the surface are not covered by other molecules above them, hence there is a net force inwards due to cohesive intermolecular forces."

My response is simply that the explanation is false. The interface itself is a continuum concept (Gibbs' dividing surface), and MD simulations demonstrate the difficulty of locating a dividing surface due to diffusive transport. Brenner's "Interfacial transport processes and rheology" has a large section on the microscopic theory of interfaces (and references Ono and Kondo's volume 10 in the encyclopedia of Physics "Molecular theory of surface tension in liquids") using a statistical-mechanical approach. The section rapidly went beyond my ability to follow, so I would suggest getting Ono and Kondo's volume or Brenner's book and having a go at it.

13. Oct 4, 2011

### dEdt

I think that makes sense, thanks a lot!