# Pressure and surface tension

Please identify what is wrong with my reasoning and help. There is a liquid in a container.

• it's topmost layer is stationary , macroscopically as seen from outside.

• This means there is no net force on the topmost layer.

• On any particle of the topmost layer, pressure P atmospheric acts from all directions , including from the liquid beneath.

• Where is there any chance of unbalanced forces to cause surface tension?

I think that forces are balanced only because there is surface tension in the first place Is this correct??.. please explain how surface tension is balancing the forces if it is the case??

Q2.) If I increase pressure on the free surface of the liquid, The pressure inside increases by the same amount. This implies that an increase in pressure, i.e., extra force applied on the surface of liquid is being balanced by the layer of liquid just below the surface and not surface tension.. Is the above statement correct or is it that some proportion of increased pressure is balanced by increase in surface tension too??

Is there any good book that has logically complete theory of fluids??

Also if you are interested /capable please answer this.. I would be very happy.. Surface Tension-- Sessile drop

## 2 Answers

"Where is there any chance of unbalanced forces to cause surface tension?"

I think it's misreading to talk about surface tension being caused by unbalanced forces. The most convincing simple explanation of ST that I've come across is that the surface is slightly depleted of molecules, that is there are fewer molecules per unit area of surface than there would be in an imaginary plane going through the bulk of the liquid.

[The depletion occurs like this. Suppose we suddenly create a new surface. Molecules will migrate (by random motion) from the surface to the bulk of the fluid at a greater rate than molecules migrate from bulk to surface. Why? Because molecules in the surface don't have molecules above them to hold them back by attractive forces. Very quickly the surface will be depleted and the rates of transport of molecules to and from the surface will be equal - dynamic equilibrium.]

Because of the depletion, molecules in the surface are slightly further apart than their equilibrium separation, and so attract each other. This is the origin of surface tension; the surface is under tension for the same reason that a rope is under tension when stretched.

Owing to contact forces between the edge of the surface and the vessel, the surface acquires a curvature, and if the liquid rises up at the edges where it meets the vessel, the pressure will be less in the liquid than in the air, for points just below and just above the surface. The vessel exerts an upward force on the liquid. This is simply a matter of looking at the directions of forces acting, knowing that the surface is under tension.

• Dear Philip Wood sir, Thank you very much. The picture you painted feels very nice. Apr 10, 2018 at 15:12
• But am unable to make out anything about my second question using your picture of the surface tension. Apr 10, 2018 at 15:19
• "This implies that an increase in pressure, i.e., extra force applied on the surface of liquid is being balanced by the layer of liquid just below the surface and not surface tension.." I think that's right, unless the shape of the surface changes. Thank you for your previous comment. Apr 10, 2018 at 17:10
• Welcome sir.. could you please suggest any source to read about the difference in no. of particles in bulk and on surface and the corresponding dynamic equilibrium that is brought about in the system? Apr 10, 2018 at 17:45
• I remember being worried about the origin of surface tension for quite some time, but I don't remember exactly where I found the explanation I gave in my answer; I came across it a long time ago, and I found it completely satisfying. E M Rogers in $Physics\ for\ the\ Enquiring\ Mind$ (first published 1960 !) has an interesting section on ST, though his treatment is a bit different from mine. Apr 10, 2018 at 18:33

It is easier to understand the action of the surface tension without any vessels or gravity involved.

Under such conditions, liquid would form a spherical droplet in order to minimize its surface tension.

Since molecules on the surface experience a greater pull from the inside of the droplet (cohesion) than from the outside (adhesion), any bump on the surface of the droplet will automatically disappear, since its surface molecules will have a relatively greater exposure to air and therefore, on balance, will be pulled stronger inside, until they are at the same exposure or the same radius as other molecules on the surface of the (spherical) droplet.

As a result of such squeezing action of the surface molecules, the pressure inside the droplet will be higher than the pressure outside the droplet, and that higher pressure will be the force balancing the surface tension. Obviously, without such extra pressure the surface tension would remain unbalanced.

This extra internal pressure can be calculated using the Young–Laplace equation you can google. For a spherical droplet, it will be inversely proportional to the droplet radius:

ΔP=2σ/r

From here you can see that, for a relatively small droplet, your statement "On any particle of the topmost layer, pressure P atmospheric acts from all directions , including from the liquid beneath" would not be quite accurate, because the pressure acting on the topmost layer from beneath would be higher than the atmospheric pressure.

If the pressure outside is increased (Q2) and the droplet does not get compressed, i.e. its radius remains the same, the surface tension will remain the same as well and the pressure on the inside will increase by the same amount as the external pressure, keeping everything in balance.

• I actually already know all this , but still thank you. But when i combined these things with my previous understanding of pressure it led to the Q1 above. It was this understanding of surface tension which you wrote in your answer that i was trying to reconcile with my understanding of pressure Apr 11, 2018 at 10:54