Definition: Surface tension is a physical property of liquids that arises from the cohesive forces between molecules at the surface, causing the liquid to behave like a stretched elastic membrane. It is defined as the force per unit length acting perpendicular to an imaginary line drawn on the liquid surface, tending to minimize the surface area.
The Molecular Origin of Surface Tension
To understand why liquids have surface tension, we must look at the behavior of molecules at the interface. Inside a liquid, a molecule is surrounded by neighbors on all sides, resulting in a net attractive force of zero due to symmetry. However, a molecule at the surface experiences an imbalance; it is pulled inward by the bulk liquid but has no upward pull from the gas or vacuum above it.
This inward pull creates a potential energy state for surface molecules that is higher than those in the interior. Because systems in nature naturally seek to minimize their potential energy, the liquid surface contracts to the smallest possible area for a given volume. This is why small droplets of water are spherical—the sphere represents the shape with the minimum surface area for a fixed volume.
Surface energy is the extra potential energy associated with the molecules at the surface of a liquid, numerically equal to the work done in increasing the surface area by one unit.
Surface Energy and Work
If we want to increase the surface area of a liquid, we must perform work against the inward cohesive forces. This work is stored as surface energy. If the surface area of a liquid film is increased by an amount ΔA, the work done (W) is given by the relation W = S × ΔA, where S is the surface tension coefficient (measured in J/m² or N/m).
It is crucial to remember that a liquid film (like a soap bubble) has two surfaces: one in contact with the air inside and one in contact with the air outside. Therefore, when calculating the energy of a soap bubble, you must account for both surfaces, effectively doubling the area involved in your calculations.
Excess Pressure in Drops and Bubbles
Because the surface of a liquid acts like a stretched membrane, it exerts a pressure on the interior fluid. This is known as excess pressure. For a curved surface, the pressure on the concave side is always higher than the pressure on the convex side.
The excess pressure (ΔP) depends on the surface tension (S) and the radius (r) of the curvature. The relationship is derived from the work-energy principle:
- Liquid Drop: ΔP = 2S / r (Only one surface)
- Air Bubble in Liquid: ΔP = 2S / r (Only one surface)
- Soap Bubble in Air: ΔP = 4S / r (Two surfaces)
Capillary Action and Jurin’s Law
Capillarity is the phenomenon where a liquid rises or falls in a narrow tube (capillary) due to the competition between cohesive forces (between liquid molecules) and adhesive forces (between liquid and tube molecules). When adhesive forces are stronger, the liquid wets the surface and rises; when cohesive forces dominate, the liquid is depressed.
The height (h) to which a liquid rises is governed by Jurin’s Law: h = (2S cos θ) / (rρg), where θ is the angle of contact, ρ is the density of the liquid, and g is the acceleration due to gravity. This formula is a staple in competitive exams and requires careful attention to the contact angle.
Important Facts and Formulas
| Quantity | Formula | Units (SI) |
|---|---|---|
| Surface Tension (S) | F / L | N/m or J/m² |
| Excess Pressure (Drop) | 2S / r | Pascal (Pa) |
| Excess Pressure (Bubble) | 4S / r | Pascal (Pa) |
| Capillary Rise (h) | (2S cos θ) / (rρg) | Meters (m) |
Key Points to Remember
- Surface tension decreases with an increase in temperature as cohesive forces weaken.
- Adding impurities can significantly change surface tension; soluble salts increase it, while detergents decrease it.
- The angle of contact is measured inside the liquid, between the tangent to the liquid surface and the solid surface.
- For water and glass, the angle of contact is acute (θ < 90°), leading to capillary rise.
- For mercury and glass, the angle of contact is obtuse (θ > 90°), leading to capillary depression.
- The shape of the meniscus is concave for wetting liquids and convex for non-wetting liquids.
- Surface tension is a scalar quantity, but the force associated with it is a vector acting along the surface.
Quick Revision Summary
- Surface tension arises from unbalanced cohesive forces at the liquid-air interface.
- Work done to increase surface area is stored as surface potential energy.
- Soap bubbles have two surfaces, making their excess pressure twice that of a simple drop.
- Capillary rise is inversely proportional to the radius of the tube and the density of the liquid.
- Temperature increase generally reduces surface tension.
- The contact angle dictates whether a liquid will rise (wetting) or fall (non-wetting) in a capillary.
- Always check for the number of surfaces (1 or 2) when calculating pressure or work.
