Excess Pressure inside a Liquid Drop and a Bubble
On the concave face of a curved surface there is always an excess pressure over the convex face of the surface. The magnitude of excess pressure can be obtained by studying the formation of air and soap bubbles.
Excess Pressure in an Air Bubble in Liquid:
Figure below shows one half cross section of an air bubble formed inside liquid. It is in equilibrium under the action of three forces:
1. Due to external pressure p₁
2. Due to internal pressure p₂
3. Due to surface tension of the liquid σ
If R is the radius of the air bubble, then the forces due to external and internal pressures are p₁ (πR²) and p₂ (πR²), respectively. Since the surface tension acts around the circumference of the bubble, therefore the force of surface tension is σ (2πR).
Thus, from the condition of equilibrium:
p₂ (πR²) = p₁ (πR²) + T (2πR)
p₂ – p₁ = 2T/ R.
Excess Pressure in Soap Bubble:
A soap bubble forms two liquid surfaces in contact with air, one inside the bubble and the other outside the bubble. The below figure shows one half cross section of the soap bubble, by considering its equilibrium, we get:
p₂ (πR²) = p₁ (πR²) + T [2 (2πR)]
p₂ – p₁ = 4T/ R