Physics MECHANICAL PROPERTIES OF FLUIDS

Surface Tension

It is a property of liquid (at rest) by virtue of which its free surface contracts so that its exposed surface area becomes a minimum.

Free surface behaves as if it is under tension, like a stretched elastic membrane.

`text(Cause of surface Tension :)`

Molecule A well inside the bulk experiences force from water molecules form all sides.

Molecule B, at the surface interacts with air molecules from above and water molecules from below.

This asymmetric force distribution is responsible for surface tension.

By surface it means a layer approximately 10-15 molecular diameters.

The force between two molecules decreases as the separation between them increases and it becomes negligible if the separation exceeds 10-15 molecular diameters.

Therefore, 10-15 molecular diameter deep, molecule experiences equal forces from all directions and hence there is no surface tension.

`text(Measurement of Surface Tension :)`

Consider the free surface of a liquid with a line AB drawn on it.

Line AB divides the surface into two parts, surface to the right of it and left of it.

Two parts pull each other with a force proportional to the length of the line AB.

These forces are perpendicular to the line AB and tangential to the surface.

Surface of the liquid behaves like a stretched rubber sheet. The rubber sheet is in state of tension. Any part of sheet pulls the adjacent part towards itself.

Let F be common magnitude of the forces exerted on each other by the two parts of the surface across a line of length `l` .

Surrace Tension `= T= F/l`

`S.l.` unit of `T` is `N//m` and dimensions `[M^1L^0T^-2]`

It is a scalar quantity and depends on nature of liquid.

`text(Alternative method to measure surface tension :)`

Consider a wire frame as shown in figure, equipped with a sliding wire AB.

It is dipped in soapy water which forms a film of liquid.

A force F has to be applied to hold the wire in place.

Since, the soap film has two surfaces attached to the wire; the total length of film in contact with wire is `2 l` .

Surface tension `= T = F/(2l)`

Surface Energy

The molecules on the surface experience a net downward force. Therefore, to bring a molecule from interior of liquid to the surface. some work is required to be done against inter molecular forces.

This work is stored as potential energy of the molecule on the surface.

The potential energy of surface molecules per unit area of the surface is called surface energy.

Its `S.l` unit is `J//m^2` and dimensions are `[M^1L^2T^2]`

It depends on the number of surfaces present. For example, a liquid drop has one liquid-air surface while bubble has two liquid-air surfaces.

`text(Measurement of surface energy)`

Consider a rectangular wire frame ABCD with sliding armAB.

When this frame is dipped in a soap solution. a soap film is formed in frame.

Due to surface tension (T), the film exerts a force on the frame (AB) towards interior of film is given by

`F= T xx (2l)` (Two surface of film)

If arm AB is displaced to new position A'B' through distance (dx) then, work done ( dW) is given by

`dw = F dx = 2Tl(dx)`

`W = int dW = int 2Tldx = 2Tlx`

`W = TA`

Where. `A = 2lx =` Area of both surfaces of film

The work done to form a film is stored as potential energy of the surface. The amount of work done or potential energy per unit area under isothermal conditions is equal to surface energy.

Surface energy `= W/A `
Surface energy is numerically equal to surface tension.

Excess Pressure Inside a Curved Surface

`text(Plane Surface)`

If the surface of liquid is plane. then a molecule on the surface of liquid is attracted equally in all directions along the surface. Hence, resultant force due to surface tension is zero. The pressures just above and below the surface of liquid are equal.

`text(Curved Surface)`
If the surface is curved, there will be net resultant force due to surface tension towards concave side on surface. Since surface is in equilibrium, there must be excess of pressure on the concave side, to balance the force due to surface tension.