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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).

Questions & Answers

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Renato
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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biomolecules are e building blocks of every organics and inorganic materials.
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anyone know any internet site where one can find nanotechnology papers?
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Do somebody tell me a best nano engineering book for beginners?
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there is no specific books for beginners but there is book called principle of nanotechnology
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are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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is Bucky paper clear?
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carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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of graphene you mean?
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or in general
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in general
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Graphene has a hexagonal structure
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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