# Mechanical Properties of Fluids

21-MAR-2016 18:09

There are some fluids which offer resistance to motion. This resistance of fluid to motion is like internal friction which is similar to friction when solid moves on a surface. This is called viscosity.

This happens when there is relative motion between the layers of the liquid. Suppose a fluid like oil is enclosed between two glass plates. The bottom plate is fixed and the upper plate is moving with a constant velocity relative to the fixed plate. Now if oil is replaced with honey then a greater force will be required to move the top plate with same velocity. Hence, honey is more viscous than oil. They layer of liquid in contact with top plate moves with the same velocity as that of the top surface and the layer of liquid in contact with the fixed surface is stationary. The velocity of fluid layers increase uniformly from bottom to top. While the top fluid layer pulls it forward, bottom fluid layer pulls it backward. This causes force between the layers. This type of flow is known as laminar.

The SI unit of viscosity is poiseuille (PI). The dimensions of viscosity are ML-1T-1. Viscosity of thin liquids like water, alcohol, etc., is less compared to thick liquids like coal tar, blood, glycerine, etc.

Surface Tension

Liquids don’t have definite shape but have a definite volume and they acquire a free surface when poured in a container. These surfaces have some additional energy. This phenomenon is called surface tension. Gases so not have surface so this phenomenon is there only in liquids.
Some examples of surface tension are, oil and water do not mix; mercury doesn’t wet glass but water sticks to it; hair of paint brush don’t cling together when dry or dipped in water rather form a fin tip when taken out of water, etc.

Surface Energy

There is an attraction between molecules in liquids and this is why a liquid stays together. The intermolecular distance in liquid is such that it is attracted to all the surrounding molecules. This attraction causes negative potential energy for the molecule which further depends on the number and distribution of molecules around the chosen one. This is because to collect and disperse such molecules far away from each other in order to evaporate, the heat of evaporation required is quite large. For water, it is 40 kJ/mol.

Surface Energy and Surface Tension

There is extra energy associated with surface liquids and the spreading of surface or creation of more surfaces requires additional energy. This is because a liquid has fixed volume.

Suppose there is a horizontal liquid film with a bar which can slide over parallel guides. Now if we move the bar by a small distance so that surface area increases, the system will have more energy. This means that some work has been done against the internal force. Now if the internal force is F and the work done by applied force is F*d = Fd. Now as per conservation of energy this is stored as additional energy. Let the surface energy of the film be S per unit area and the extra area is 2dl. Since the film has two sides so there are two surfaces and the extra energy is:

S (2dl) = Fd

The quantity of S will be the magnitude of surface tension. It is equal to the force per unit length exerted by the fluid on the movable bar.
Fluid surface in contact with other fluids or solid surface are also considered. In this case surface energy depends on the materials on both sides of the surface.

The surface tension of liquids falls with temperature.

A fluid will stick to a solid surface if the surface energy between fluid and the solid is smaller than the sum of surface energies between solid-air, and fluid-air.

Angle of Contact

The surface of liquid is curved near the plane of contact with another medium. The angle between tangent to the liquid surface at the point of contact and solid surface inside the liquid is called angle of contact. The value of angle of contact determines whether a liquid will form a droplet or will spread.

There are three interfacial tensions at all the three interfaces, liquid-air, solid-air and liquid-solid. These are denoted by Sla, Ssa and Ssl. The surface forces between the three media must be in equilibrium.

If Ssl > Sla then the angle of contact is an obtuse angle and if Ssl < Sl then the angle of contact is an acute angle. In case of water-leaf interface obtuse angle is formed and in case of water-plastic acute angle is formed.

Molecules of liquid are attracted strongly to themselves and weakly to solid in case angle of contact is obtuse angle. That is why liquid does not wet the solid. On the other hand, if molecules of liquid are strongly attracted to the molecules of solid then acute angle is formed. This is why liquids wet solid.

Drops and Bubbles

Free liquid drops and bubbles are spherical in shape as a result of surface tension. This can be observed in soap bubbles blown. Also the pressure inside a spherical drop is more inside as compared to outside. This is also because of surface tension. In a liquid-air interface, the pressure will be higher on the convex side than on the concave side.

Capillary Rise

Due to pressure difference across a curved liquid-air interface the water level rises up in a narrow tube. If the tube is hair thin then the rise would be very large.

The pressure of the water inside the tube just at air-water interface is less than the atmospheric pressure. The capillary rise is due to surface tension.
Detergents and Surface Tension

We use detergents and soap to wash clothes because just water does not wet grease or dirt on the clothes. But the molecules of detergents are sharp and with one end they are attracted to water and with another end they are attracted to the molecules of grease. This reduces the surface tension (water-oil).

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