# 10.11 Cohesion and adhesion in liquids: surface tension and capillary  (Page 2/11)

 Page 2 / 11

Surface tension is proportional to the strength of the cohesive force, which varies with the type of liquid. Surface tension $\gamma$ is defined to be the force F per unit length $L$ exerted by a stretched liquid membrane:

$\gamma =\frac{F}{L}.$

[link] lists values of $\gamma$ for some liquids. For the insect of [link] (a), its weight $w$ is supported by the upward components of the surface tension force: $w=\mathrm{\gamma L}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta$ , where $L$ 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 $P$ inside a spherical bubble is given by

$P=\frac{4\gamma }{r},$

where $r$ 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.

Surface tension of some liquids At 20ºC unless otherwise stated.
Liquid Surface tension γ(N/m)
Water at $0\text{º}\text{C}$ 0.0756
Water at $\text{20}\text{º}\text{C}$ 0.0728
Water at $\text{100}\text{º}\text{C}$ 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 $\text{37}\text{º}\text{C}$ 0.058
Blood plasma at $\text{37}\text{º}\text{C}$ 0.073
Gold at $\text{1070}\text{º}\text{C}$ 1.000
Oxygen at $-\text{193}\text{º}\text{C}$ 0.0157
Helium at $-\text{269}\text{º}\text{C}$ 0.00012

## Surface tension: pressure inside a bubble

Calculate the gauge pressure inside a soap bubble $2\text{.}\text{00}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{m}$ 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 $P$ can be found directly from the equation $P=\frac{4\gamma }{r}$ .

Solution

Substituting $r$ and $\gamma$ into the equation $P=\frac{4\gamma }{r}$ , we obtain

$P=\frac{4\gamma }{r}=\frac{4\left(0.037 N/m\right)}{2\text{.}\text{00}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\text{m}}=\text{740}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}=\text{740}\phantom{\rule{0.25em}{0ex}}\text{Pa}.$

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

$P=\left(\text{740}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}\right)\frac{1.00 mm Hg}{\text{133}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}}=5.56 mm Hg.$

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

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
How we can toraidal magnetic field
How we can create polaidal magnetic field
4
Because I'm writing a report and I would like to be really precise for the references
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!