# Understanding the concept of surface tension.

The concept of surface tension doesn't seem to be well explained in the first course on Fluid Mechanics. Fundamentals of Fluid Mechanics writes
A tensile force may be considered to be acting in the plane of the surface along any line in the surface. The intensity of the molecular attraction per unit length along any line in the surface is called the Surface Tenison .
There are a few things that are causing me problems:
1. The analogy tensile force is quite hard to understand, I mean the force of attraction looks something like this . As you can see, the molecules at the top have no upward force acting on them and therefore they form something like a surface (this what others writes). Well, okay there is no upward force but we can certainly go for superposition of forces and from the diagram, we can see that the upper molecule should accelerate downwards but it doesn't, why? How all this have any correlation with tension? (the way I have understood tension till now is the force that a string exerts on an object connected to it).
2. The phrase along any line in the surfaceis causing problems because it writes in the surface not on on the surface which is quite hard to comprehend what the book intends.
I request you to please explain the concept of Surface Tension considering the problems that have written over here. If you present your personal understanding of the topic then it will be much appreciated.
Thank you.

#### benit13

Read the quote carefully. It says:

A tensile force may be considered to be acting in the plane of the surface along any line in the surface. The intensity of the molecular attraction per unit length along any line in the surface is called the Surface Tension.
I don't think your picture is really showing what the author is trying to explain.

Surface tension is the same as tension in a string or wire, except that you have a 2D plane to work with instead of a 1D length, so forces can transmit in different directions along the plane.

Grab an A4-sized piece of paper with both hands, one at each side, and try to pull it apart from end to end. It's actually very, very difficult! It is much easier to pull apart for narrower pieces of paper (e.g. if you cut the paper into thin strips). This is surface tension at play.

Fluids, just like solids, have a tension, but it's different in the body of the fluid compared to the surface, as you've already correctly identified.

3D objects also have tension ("volume tension"), but most people call this "stress". Surface tension in solids is basically the same as stress because the inter-molecular forces are very high. For fluids, the difference is more important, hence why you're reading it in a fluid dynamics book.

#### benit13

Well, okay there is no upward force but we can certainly go for superposition of forces and from the diagram, we can see that the upper molecule should accelerate downwards but it doesn't, why?
They do! Molecules in a fluid are a rather big chaotic mess. As molecules move around, the density at any position in the fluid fluctuates very slightly because there will be portions of fluid where more molecules have moved around. These fluctuations in density leave space for other molecules to move into. So, in other words, all fluids are like a massive game of dodgems where all of the molecules are moving around and bumping into each other and then shuffling into areas with space again. Gases are the same.

The phrase along any line in the surface is causing problems because it writes in the surface not on on the surface which is quite hard to comprehend what the book intends.
This might be seen as pedantic or patronising, but it's nice sometimes to clarify basic things in detail so there's absolutely no confusion.

When dealing with surfaces:
- "on" refers to something that's not part of the surface, but instead sits on top of it. "The mug sits on the table-cloth"
- "in" refers to something that's inside or part of the the surface, "The coffee stain is in the table-cloth"

The point I'm trying to make here is that the quote in the book is not only correct, it is specific... it's telling you precisely how the tensile forces act. Good textbooks are specific in this way so careful readers can really figure out exactly what is going on.

Anyway! I hope that helps.

Surface tension is the same as tension in a string or wire, except that you have a 2D plane to work with instead of a 1D length, so forces can transmit in different directions along the plane.
Can you please explain that 2D model of strings with a little more explanation? If you could manage a picture I would be very grateful. All I want to understand how that string tension applies over the molecular attraction.

#### Woody

The molecules of any material create, and experience, attractive forces between them
(otherwise no material would hold together).
Usually the attractive forces between molecules of the same material are greater than the attractive forces to molecules of other materials
particularly where the two materials are in different phases (e.g. liquid and gas).

The diagram you posted indicates the change from these attractive forces all acting equally in all directions in the bulk of the fluid
to the attractive forces being asymmetric on the molecules, higher into the fluid and lower (negligibly small for many purposes) between the fluid and the gas above it.

In the bulk material the molecule if fairly free to move, because the intermolecular forces are evenly balanced in all directions.
Toward the surface, the molecules are less free to move, because of the asymmetry of the forces.
It is this asymmetry of the attractive intermolecular forces that results in the surface tension effect.

Note that in the surface reflects the point that the surface is not infinitely thin, it is a few molecules deep.
Also note not just one molecule deep, since the attractive forces extend beyond just the immediate neighbours
but they fall off quite quickly, so that beyond a few molecules depth the influence is too small to be important.
(I don't know how many a few might be, but would guess between 5 and 10, it probably varies with different materials).

The molecules of any material create, and experience, attractive forces between them
(otherwise no material would hold together).
Usually the attractive forces between molecules of the same material are greater than the attractive forces to molecules of other materials
particularly where the two materials are in different phases (e.g. liquid and gas).

The diagram you posted indicates the change from these attractive forces all acting equally in all directions in the bulk of the fluid
to the attractive forces being asymmetric on the molecules, higher into the fluid and lower (negligibly small for many purposes) between the fluid and the gas above it.

In the bulk material the molecule if fairly free to move, because the intermolecular forces are evenly balanced in all directions.
Toward the surface, the molecules are less free to move, because of the asymmetry of the forces.
It is this asymmetry of the attractive intermolecular forces that results in the surface tension effect.

Note that in the surface reflects the point that the surface is not infinitely thin, it is a few molecules deep.
Also note not just one molecule deep, since the attractive forces extend beyond just the immediate neighbours
but they fall off quite quickly, so that beyond a few molecules depth the influence is too small to be important.
(I don't know how many a few might be, but would guess between 5 and 10, it probably varies with different materials).
Means surface tension is just a manifestation of asymmetric intermolecular forces, am I right? I have understood from your answer and benit13 that the surface molecules are somewhat restricted to move because of the absence of a balancing force, so why don't they move in the direction of resultant force? You have said that they are restricted to move, but force should cause them to move and molecules in bulk shouldn't move because resultant force is zero. I request you to please clarify this doubt of mine.

#### benit13

I'm not sure what specifically what you're wanting because neither the author, nor I, are talking about a 2D model of strings... the author is just explaining that there is a physical phenomenon called surface tension where tensile forces propagate along the plane of the surface. You'll have to look to the textbook to get information about the actual modelling of surface tension because I don't have it to hand.

However, if you're looking for an explanation about the physics of surface tension and why it arises, then it might be easier to explain it by looking at solids and gases first. I don't think an additional picture will help make my explanation any better in this case since your original picture is sufficient for this new purpose.

Most solids are comprised of some sort of lattice structure where any particular molecule is bound to its neighbours by ionic bonds. If any molecule is perturbed (for example, by a force), then energy is transferred throughout the structure through these bonds, depending on the particular perturbation applied and the lattice structure. If the energy eventually makes its way to a surface (which it typically will), then one can say that the 'force' has transmitted throughout the solid. The mathematics that solves these sorts of problems is normally phrased in terms of internal pressures, stress and strain or is skipped in favour of an assumed outcome (c.f. Newton's laws and motion problems). Surface tension is also relevant for solids, explained by the fact that those surface molecules have fewer neighbours, but because the particles are not free to move within the solid, the effect is small; surface tension in solids is effectively the same as tension within the bulk solid; it affects where forces can be transmitted but does not change the material properties of the solid or its shape. I might be wrong here, but it doesn't seem like a common consideration in motion problems of solids.

Most gases are free molecules, which are not bound to their neighbours at all. Those molecules are buzzing around and colliding with each other and the motion of a given molecule is messy (Brownian motion). Perturbations caused by forces/pressures can only be transmitted through the gas by collisions with other molecules. Because of this lack of 'binding' among gas molecules, gases are compressible. Consequently, there is little to no tension at all. If the gas is contained within a volume, one can 'feel' the gas pressure on the walls of the container, caused by collisions, which will affect all walls of the container equally. Increases in pressure affect the pressure measured at all walls. This consideration is important for gas turbine design and other engines which make use of natural gas to drive pistons or other moving objects. Surface tension and bulk tension are not relevant for gases.

Now we get to fluids, which are a mid-way compromise. Fluid molecules interact with their neighbours (like solids) through van der Waal's forces and the difference in surface tension (compared to bulk stress) is due to the lack of van der Waal's forces acting on one side (like in your diagram). However, molecules are also free to move to some degree, so the situations is messy, with many molecules buzzing around and colliding with each. Consequently, fluid dynamics is usually framed in terms of consideration of different parcels/lines of fluid that are incompressible and move together.

So why should we care about surface tension at all? Well, because molecules can move to some degree in a liquid, there are interesting shapes (a meniscus) formed at the boundaries between liquids and other phases of matter. These shapes form are due to surface tension.

topsquark

@benit13 With the explanation that you have given of surface tension I want to know how that explanation explains this phenomena

A pin stays on water surface not due to buoyant force (it doesn't float) but due to surface tension
I want to know how surface tension is involved in this.

#### benit13

Look at the deformation at the sides of the pin... it's a curved surface. The surface tension runs along the plane of the surface, so those intermolecular forces are tugging at the edges of the paper clip at an angle. That will consequently have an upward component that opposes the weight of the pin.