Surface Tension and Capillarity
Surface energy, angle of contact, excess pressure and capillary rise. (Physics › Properties of Bulk Matter, NEET UG syllabus.)
What is Surface Tension and Capillarity?
The property of a liquid surface to behave like a stretched elastic membrane, tending to minimize its surface area. Quantitatively, it is the force per unit length acting tangentially on the surface or the surface energy per unit area.
Key formula / rule: Surface Tension (Force per unit length)
Key points
- Define surface tension and surface energy and state their units.
- Explain the molecular origin of surface tension.
- Define and explain the significance of the angle of contact.
- Derive or recall the expression for excess pressure inside a liquid drop and a soap bubble.
Common exam trap
Confusing excess pressure formulas for a liquid drop (2T/R) and a soap bubble (4T/R). Remember a soap bubble has two free surfaces.
Definitions
- Term
Surface Tension
- Meaning
The property of a liquid surface to behave like a stretched elastic membrane, tending to minimize its surface area. Quantitatively, it is the force per unit length acting tangentially on the surface or the surface energy per unit area.
- Term
Surface Energy
- Meaning
The extra potential energy possessed by molecules at the surface of a liquid compared to those in the bulk. It is numerically equal to the work done in increasing the surface area by unity.
- Term
Angle of Contact (θ)
- Meaning
The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid. It indicates the balance between adhesive and cohesive forces.
- Term
Capillarity
- Meaning
The phenomenon of rise or fall of a liquid in a narrow tube (capillary) due to the combined effects of surface tension, adhesion, and cohesion.
Learning objectives
Define surface tension and surface energy and state their units.
Explain the molecular origin of surface tension.
Define and explain the significance of the angle of contact.
Derive or recall the expression for excess pressure inside a liquid drop and a soap bubble.
Explain the phenomenon of capillarity and its causes.
Apply Jurin's Law to calculate capillary rise or fall.
Analyze the factors affecting surface tension and capillarity.
Formulae
- Name
Surface Tension (Force per unit length)
- Note
F is the force acting on a liquid film, L is the length of the film.
- Expression
T = F / L
- Name
Surface Energy (Work done)
- Note
W is the work done to increase surface area by ΔA, T is surface tension.
- Expression
W = T × ΔA
- Name
Excess Pressure inside a liquid drop
- Note
R is the radius of the liquid drop, T is surface tension. Applies to a single curved liquid-air interface.
- Expression
ΔP = 2T / R
- Name
Excess Pressure inside a soap bubble
- Note
R is the radius of the soap bubble, T is surface tension. Applies to two liquid-air interfaces (inner and outer).
- Expression
ΔP = 4T / R
- Name
Capillary Rise/Fall (Jurin's Law)
- Note
h is the height of liquid rise/fall, T is surface tension, θ is the angle of contact, ρ is liquid density, g is acceleration due to gravity, r is capillary tube radius.
- Expression
h = (2T cosθ) / (ρgr)
Prerequisites
Basic understanding of forces and pressure.
Concept of molecular forces (cohesive and adhesive).
Knowledge of fluid properties and density.
Basic trigonometry (cosine function).
Common mistakes
Confusing excess pressure formulas for a liquid drop (2T/R) and a soap bubble (4T/R). Remember a soap bubble has two free surfaces.
Incorrectly applying the angle of contact (cosθ) in the capillary rise formula, especially for non-wetting liquids where cosθ is negative, leading to capillary fall.
Forgetting the density (ρ) in the denominator of the capillary rise formula.
Using diameter instead of radius (r) in formulae.
Not understanding that surface tension is a tangential force, not a normal force.
Keywords
Surface Tension
Surface Energy
Angle of Contact
Cohesive Forces
Adhesive Forces
Excess Pressure
Liquid Drop
Soap Bubble
Capillarity
Capillary Rise
Jurin's Law
Wetting
Non-wetting
Practice preview
What is the SI unit of surface tension?…
easy
For a liquid that completely wets a solid surface, what is the angle of contact?…
easy
The excess pressure inside a spherical liquid drop of radius R and surface tension T is given by:…
easy