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Surface tension is proportional to the strength of the cohesive force, which varies with the type of liquid. Surface tension γ size 12{γ} {} is defined to be the force F per unit length L size 12{L} {} exerted by a stretched liquid membrane:

γ = F L . size 12{γ= { {F} over {L} } } {}

[link] lists values of γ size 12{γ} {} for some liquids. For the insect of [link] (a), its weight w size 12{W} {} is supported by the upward components of the surface tension force: w = γL sin θ size 12{W=γL"sin"θ} {} , where L size 12{L} {} is the circumference of the insect’s foot in contact with the water. [link] shows one way to measure surface tension. The liquid film exerts a force on the movable wire in an attempt to reduce its surface area. The magnitude of this force depends on the surface tension of the liquid and can be measured accurately.

Surface tension is the reason why liquids form bubbles and droplets. The inward surface tension force causes bubbles to be approximately spherical and raises the pressure of the gas trapped inside relative to atmospheric pressure outside. It can be shown that the gauge pressure P size 12{P} {} inside a spherical bubble is given by

P = r , size 12{P= { {4γ} over {r} } } {}

where r size 12{r} {} is the radius of the bubble. Thus the pressure inside a bubble is greatest when the bubble is the smallest. Another bit of evidence for this is illustrated in [link] . When air is allowed to flow between two balloons of unequal size, the smaller balloon tends to collapse, filling the larger balloon.

Sliding wire device which is used to measure surface tension shows the force exerted on the two surfaces of the liquid. This force remains a constant until the film’s breaking point.
Sliding wire device used for measuring surface tension; the device exerts a force to reduce the film’s surface area. The force needed to hold the wire in place is F = γL = γ ( 2 l ) size 12{F=γL=γ \( 2l \) } {} , since there are two liquid surfaces attached to the wire. This force remains nearly constant as the film is stretched, until the film approaches its breaking point.
When two balloons are attached to the ends of a glass tube air flows from one to the other if their sizes are different.
With the valve closed, two balloons of different sizes are attached to each end of a tube. Upon opening the valve, the smaller balloon decreases in size with the air moving to fill the larger balloon. The pressure in a spherical balloon is inversely proportional to its radius, so that the smaller balloon has a greater internal pressure than the larger balloon, resulting in this flow.
Surface tension of some liquids At 20ºC unless otherwise stated.
Liquid Surface tension γ(N/m)
Water at 0 º C size 12{0°C} {} 0.0756
Water at 20 º C size 12{"20"°C} {} 0.0728
Water at 100 º C size 12{"100"°C} {} 0.0589
Soapy water (typical) 0.0370
Ethyl alcohol 0.0223
Glycerin 0.0631
Mercury 0.465
Olive oil 0.032
Tissue fluids (typical) 0.050
Blood, whole at 37 º C size 12{"37"°C} {} 0.058
Blood plasma at 37 º C size 12{"37"°C} {} 0.073
Gold at 1070 º C size 12{"1070"°C} {} 1.000
Oxygen at 193 º C size 12{ - "193"°C} {} 0.0157
Helium at 269 º C size 12{ - "269"°C} {} 0.00012

Surface tension: pressure inside a bubble

Calculate the gauge pressure inside a soap bubble 2 . 00 × 10 4 m size 12{2 "." "00" times "10" rSup { size 8{ - 4} } `m} {} in radius using the surface tension for soapy water in [link] . Convert this pressure to mm Hg.

Strategy

The radius is given and the surface tension can be found in [link] , and so P size 12{P} {} can be found directly from the equation P = r size 12{P= { {4γ} over {r} } } {} .

Solution

Substituting r and γ size 12{g} {} into the equation P = r size 12{P= { {4γ} over {r} } } {} , we obtain

P = r = 4 ( 0.037 N/m ) 2 . 00 × 10 4 m = 740 N/m 2 = 740 Pa . size 12{P= { {4γ} over {r} } = { {4 \( 0 "." "037"`"N/m" \) } over {2 "." "00" times "10" rSup { size 8{ - 4} } `m} } ="740"`"N/m" rSup { size 8{2} } ="740"`"Pa"} {}

We use a conversion factor to get this into units of mm Hg:

P = 740 N/m 2 1.00 mm Hg 133 N/m 2 = 5.56 mm Hg . size 12{P= left ("740"" N/m" rSup { size 8{2} } right ) { {1 "." "00"`"mm"`"Hg"} over {"133"`"N/m" rSup { size 8{2} } } } =5 "." "56"`"mm"`"Hg"} {}

Discussion

Note that if a hole were to be made in the bubble, the air would be forced out, the bubble would decrease in radius, and the pressure inside would increase to atmospheric pressure (760 mm Hg).

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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