# Understanding the meaning of tension at molecular level.

I'm having hard time understanding the term tension in fluid mechanics. What I understand by tension is the force that string exerts on some object which is pulling it. But when it comes to surface tension it is said that each molecule experiences a force from all four directions, all of them are symmetric hence there develops a tension on the surface. I can't understand why the tension develops when all forces are symmetrical and hence should cancel each other and there should be no force (after all, tension is a force only). I asked it to one of learned man and he replied

let's consider the one-dimensional case of a long molecule under tension. To put it under tension we hold the ends of the molecule a little further away from each other than they would normally be, so each atom is further away from its neighbours than it would normally be, and so is being pulled to the right by its neighbour on the right, and pulled to the left by its neighbour on the left, so there is no resultant force on the atom, but there would be if we cut the molecule!
I'm having trouble understanding his last line, but there would be if we cut the molecule! .

Thank you. Any help will be much appreciated.

#### SDK

You are correct that if all forces are symmetric then they cancel out. But that isn't what happens at the surface is it? The molecules at the top of the surface are interacting with the molecules below but there are no molecules above to interact with. To be more precise, there are still molecules above but they are molecules of air instead of fluid so they are much less dense. In fact they are so much less dense that this force is essentially negligible for most fluids.

However, I also don't understand the other person's comment about cutting the molecule.

You are correct that if all forces are symmetric then they cancel out. But that isn't what happens at the surface is it? The molecules at the top of the surface are interacting with the molecules below but there are no molecules above to interact with. To be more precise, there are still molecules above but they are molecules of air instead of fluid so they are much less dense. In fact they are so much less dense that this force is essentially negligible for most fluids.

However, I also don't understand the other person's comment about cutting the molecule.
With all due respect, I disagree with your conception of surface tension. It's not due to the absence of upward force.

#### DarnItJimImAnEngineer

Surface tension arises at curved surfaces of insoluble fluids (liquid-liquid or liquid-gas) because the attractive forces from the similar molecules are stronger than the attractive forces from the other fluid's molecules. I haven't done a lot of liquid interface MD simulations, but I assume it has to do with the similar molecules forming crystalline mini-structures, whereas two substances with different atomic packing structures and lattice sizes have a hard time getting as close to each other, on the whole.

Truth-be-told, I don't think most continuum fluid mechanics people spend that much time thinking about the molecular causes of surface tension. We care that there is a pressure discontinuity at curved interfaces, and the pressure is proportional to the mean local curvature; that's about it. Molecular physics-based fluids guys, I believe, are probably more likely to think of surface tension as surface energy -- as in, being surrounded by tightly packed molecules on all sides puts you at a lower energy state than being at a surface.