Surface Tension | General Awareness for SSC CGL PDF Download

Surface Tension

• When a small amount of water is poured onto a clean glass plate, it spreads out thinly.
• Mercury, when poured onto a glass plate, forms a round drop instead of spreading out.
• Water on a greasy glass plate forms small drops like mercury does.
• This behavior shows that besides gravity, another force affects how liquids take shape based on the surfaces they touch.
• When the liquid is very light, it becomes a perfect ball shape like raindrops or soap bubbles.
• For a certain amount of liquid, a sphere has the smallest surface area.
• Liquids tend to minimize their surface area due to surface tension.

Definition of Surface Tension

Imagine an imaginary line AB on a liquid surface. The surface on either side of this line exerts a pulling force on the other side, lying in the plane of the surface and perpendicular to AB. The surface tension of the liquid is measured by the force per unit length of AB. If F is the total force on either side of line AB of length l, the surface tension T is given by T=F/l. Hence, surface tension is defined as the force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn in that surface. Its unit is Newton/meter, with dimensions [MT^-2].

The value of surface tension depends on the liquid's temperature and the medium on the other side of the surface. It decreases with rising temperature and becomes zero at the critical temperature.

Surface Energy

Increasing the surface area of a liquid requires work against the force of attraction among molecules, which is stored as potential energy in the new surface. Additionally, there is cooling due to the increased surface area, so heat from the surroundings is added to maintain constant temperature. This additional energy per unit area of the surface is called surface energy.

Relation Between Surface Tension and Work Done in Increasing Surface Area

Consider a liquid film between a bent wire ABC and a straight, movable wire PQ. As the film tends to contract, PQ moves upward, requiring a downward force F to keep it in equilibrium. F is directly proportional to the length l of the film in contact with PQ. Since there are two free surfaces, F∝2l or F=T×2l, where T is the surface tension.

If PQ is moved downward by a small distance Δx, increasing the film's surface area, the work done by the force F is W = F × Δx = T × 2l × Δx. Since 2l × Δx is the total increase in area (ΔA), W = T × ΔA. Thus, the surface tension T equals the work required to increase the liquid film's surface area by unity at constant temperature, expressed in joules per square meter.

Excess Pressure Inside a Drop

Let us consider a spherical drop of liquid of radius R. If the drop is small, the effect of gravity may be neglected and shape may be assumed to be spherical.
If the pressure just outside the surface is P₁ and just inside the surface is P₂.
P₂ - P₁ = 2T/R
The pressure inside the surface is greater than the pressure outside the surface.

Note:
The pressure on the concave side is greater than the pressure on the convex side.
If there is an air bubble inside the liquid as shown in the figure, is single surface is formed. There is air on the concave side and liquid on the convex side. The pressure in the concave side is greater than the pressure in the convex side, by an amount 2T/R.
P₂ - P₁ = 2T/R

Excess Pressure Inside a Soap Bubble

Let the pressure of the air outside the bubble be P₁, within the soap solution be P′ and that in the air inside the bubble be P₂.

P′ - P₁ = 2T/R
Similarly, looking at the inner surface,
P₂ - P′ = 2T/R
Adding these two equations,
P₂ - P₁ = 4T/R

Angle of Contact

The angle between the tangent to the solid surface and the tangent to the liquid surface at the point of contact is the angle of contact. For liquids that wet the solid, the angle is acute; for those that do not, it is obtuse. For example, pure water and clean glass have an angle of zero, ordinary water and glass have about 8°, and mercury and glass have 135°. For water and silver, it is 90°, keeping the water surface horizontal in a silver vessel.

Capillarity

• When a glass capillary tube that is open at both ends is placed vertically in water, the water moves up in the tube to a specific height above the water level outside the tube. The narrower the tube, the higher the water rises. Conversely, when the tube is put in mercury, the mercury is pushed below the outside level.
  
• The phenomenon of the rise or fall of liquids in a capillary tube is known as capillarity. Liquids that stick to glass (where the angle of contact is sharp) move up in the capillary tube, while those that do not stick to glass (where the angle of contact is wide) move down in the capillary.

Explanation:

The phenomenon of capillarity arises due to the surface tension of liquids. When a capillary tube is dipped in water, the water meniscus inside the tube is concave. The pressure just below the meniscus is less than the pressure just above it by 2T/R, where T is the surface tension of water and R is the radius of curvature of meniscus.

The pressure of the surface of water is atmospheric pressure P. The pressure just below plane surface of water outside the tube is also P, but that just below the meniscus inside the tube is P – (2T/R). We know that pressure at all points in the same level of water must be the same.

Therefore, to make up the deficiency of pressure, 2T/R, below the meniscus, water begins to flow from outside into the tube. The rising force water in the capillary stops at a certain height h. In this position the pressure of the water-column of height h becomes equal to 2T/R, that is,

hρg = 2T/R

where ρ is the density of water and g is the acceleration due to gravity. If r be the radius of the capillary tube and θ the angle of contact of water-glass, then the radius of curvature R of the meniscus is given by R = r/cosθ.
∴ hρg = 2T/r/cosθ
or h = 2Tcos θ/rρg

This shows that as r decreases, h increases, that is, narrower the tube, greater is the height to which the liquid rises in the tube.

Rising of liquid in a capillary tube of insufficient length:
Suppose a liquid of density ρ and surface tension T rises in a capillary tube to a height h.
Then hρg = 2T/R
where R is the radius of curvature of the liquid meniscus in the tube. From this we may write
hR = 2T/ρg = constant (for a given liquid)

When the length of the tube is greater than h, the liquid rises in the tube to a height so as to satisfy the above relation. But if the length of the tube is less than h, say h′, then the liquid rise up to the top of the tube and then spreads out until its radius of curvature R increases to R′, such that h′R′ = hR = 2T/ρg
It is clear that liquid cannot emerge in the form of a fountain from the upper end of a short capillary tube.