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Excess pressure in drops and bubbles
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Smaller bubbles have greater pressure.
ΔP = 2T/rA curved surface has excess pressure ΔP = 2T/r (drop), 4T/r (soap bubble with two surfaces). Smaller bubbles have higher pressure and the smaller one empties into a larger one.
A 1 mm soap bubble: 4·0.025/0.001 = 100 Pa.
Number of surfaces matters.
In more detail
Surface tension creates an excess pressure inside a drop or bubble. For a drop, P = 2γ/r, and for a soap bubble with two surfaces, P = 4γ/r.
Real-world uses
- Small droplets have high internal pressure, which affects their evaporation.
- Lung alveoli are kept open by surfactants that reduce surface tension.
- Small bubbles in a fizzy drink or a soap bubble have larger internal pressure than big ones, as the surface tension squeezes them.
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Frequently asked questions
Why are small bubbles at high pressure?
Because the surface curvature is greater, so the excess pressure grows as the radius shrinks.
What is a soap bubble's excess pressure?
It is twice that of a single surface with the same radius, because it has two surfaces.
Why does a small bubble shrink into a larger one?
The smaller bubble has higher pressure, so air flows from it into the bigger bubble, which is one reason foams are unstable.
Related topics in Fluids & Elasticity
Reynolds number · Surface tension · Surface energy · Angle of contact · Capillary rise · Cohesion and adhesion