Chapter 31 of 2363 min read

Surface tension, capillarity, excess pressure

Why this is asked: Excess pressure is 4T/r inside a soap bubble but only 2T/r inside a plain liquid drop or a submerged air bubble — the extra factor comes from the soap film having two free surfaces instead of one.

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Test yourself

•Consider a water tank shown in the figure. It has one wall at $x = L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $ρ$ , the liquid surface makes an angle $θ_{0}$ ( $θ_{0} ≪ 1$ ) with the $x$ -axis at $x = L$ . If $y (x)$ is the height of the surface, then the equation for $y (x)$ is (take $sin θ (x) \approx tan θ (x) \approx \frac{d y}{d x}$ ; $g$ is the acceleration due to gravity):
•A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If the surface tension of water is $0.07 N m^{- 1}$ , then the excess force required to take it away from the surface is:

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