In this video we are going to talk about another important property of fluids
called surface tension.
So surface tension is one of those things that's kind of abstract to think about
but we see examples of it everyday.
And it has to do with phenomena that take place at the interface
between either two different fluids, or a fluid and a surface.
And so a typical situation that we can think about is a liquid and a gas
For example water and air.
And a crude way to think about it is that thermodynamically it's more favorable for
water molecules to be in contact with and be surrounded by other water molecules
that it is for them to be in contact with air molecules.
So as a result of that, when these two fluids are in contact, the water molecules will tend to
assume a shape that minimizes the interfacial surface area that's in contact with the air.
That kind of shape is a sphere, so for example that explains why
water assumes a spherical droplet shape in air.
Now you can also get similar effects between a fluid and a surface. So for example water on
your car after you wax it tends to bead up and form these droplet shapes.
And that's because, again, the properties of the surface are such that
the water molecules prefer to be in contact with other water molecules than to be in contact
with the surface. So they again assume the spherical shape that minimizes the contact
area with the surface. So that would be an example of a hydrophobic surface.
Another extreme would be a case where you had a coating that
made the water want to spread out over the surface. And so in this case, the surface
properties would be such that it was more favorable for the water molecules to be
in contact with the surface than it was for them to be in contact with other water molecules.
This is an example of a hydrophilic surface.
And so a lot of antifog coatings are examples of
surfaces that would have this hydrophilic property.
But all these examples relate to the same concept. Their origin is with surface tension.
And so surface tension we define in terms of the work associated with increasing
or changing, but generally increasing the interfacial contact area between two fluids.
So it's helpful, at least initially, to think about it in terms of the units of these quantities.
We're talking about energy associated with a change in surface area.
So energy has units of Joules or Newton- meters. Area has units of meters squared.
So when we cancel out one of these meters we get this idea that
surface tension would intuitively have units of Newtons per meter.
And so surface tension is defined in terms of the parameter, gamma,
that has units of force per length or Newtons per meter.
So surface tension is a fluid property just like viscosity or density.
Also, the surface tension parameter is a positive quantity
because we talk about, by convention,
work associated with increasing surface area as a positive work associated to expand
the contact area. The interface between two fluids.
OK, so one thing I want to point out is based on these scaling arguments. So surface tension
depends on the area because it represents, again, a work associated with
a change in the surface area. Let's compare that to a different kind of force like a gravity force
So gravity is a body force. And so mass times gravity is the weight of an object. And this
depends on its volume. Body forces depend on the volume of an object. So if we compare
the magnitudes of these two forces, the ratio of the surface tension force (F sub gamma)
to a gravitational body force (F sub g). Their dependence on length.
The surface tension force depends on area, length squared. The body force depends
on volume, length cubed. So the ratio of these forces scales as 1/L.
That's a very important observation. And we can see by looking at implications in two limits.
So for large sized objects at large length scales, the gravity force is much larger
than the surface tension force because if L is large this quantity is small.
So gravity is much larger than the surface tension force at large length scales.
As we get to smaller length scales very small scales. In the opposite limit the opposite is true.
Now if L is small, 1/L is large.
So surface tension is much more important than gravity.
Surface tension forces, sometimes also refered to as capillary forces, become important
at very small length scales. But they're not so impotant at large length scales.
But they come into play and they can actually be very large at very small length scales.
at very small length scales.