# 10.11 Cohesion and adhesion in liquids: surface tension and capillary  (Page 5/11)

 Page 5 / 11

## Capillary action

The tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube, is called capillary action.

If a capillary tube is placed vertically into a liquid, as shown in [link] , capillary action will raise or suppress the liquid inside the tube depending on the combination of substances. The actual effect depends on the relative strength of the cohesive and adhesive forces and, thus, the contact angle $\theta$ given in the table. If $\theta$ is less than $90º$ , then the fluid will be raised; if $\theta$ is greater than $90º$ , it will be suppressed. Mercury, for example, has a very large surface tension and a large contact angle with glass. When placed in a tube, the surface of a column of mercury curves downward, somewhat like a drop. The curved surface of a fluid in a tube is called a meniscus . The tendency of surface tension is always to reduce the surface area. Surface tension thus flattens the curved liquid surface in a capillary tube. This results in a downward force in mercury and an upward force in water, as seen in [link] . (a) Mercury is suppressed in a glass tube because its contact angle is greater than 90º . Surface tension exerts a downward force as it flattens the mercury, suppressing it in the tube. The dashed line shows the shape the mercury surface would have without the flattening effect of surface tension. (b) Water is raised in a glass tube because its contact angle is nearly 0º . Surface tension therefore exerts an upward force when it flattens the surface to reduce its area.

Contact angles of some substances
Interface Contact angle Θ
Mercury–glass $\text{140}\text{º}$
Water–glass $0\text{º}$
Water–paraffin $\text{107}\text{º}$
Water–silver $\text{90}\text{º}$
Organic liquids (most)–glass $0\text{º}$
Ethyl alcohol–glass $0\text{º}$
Kerosene–glass $\text{26}\text{º}$

Capillary action can move liquids horizontally over very large distances, but the height to which it can raise or suppress a liquid in a tube is limited by its weight. It can be shown that this height $h$ is given by

$h=\frac{2\gamma \phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta }{\rho \text{gr}}.$

If we look at the different factors in this expression, we might see how it makes good sense. The height is directly proportional to the surface tension $\gamma$ , which is its direct cause. Furthermore, the height is inversely proportional to tube radius—the smaller the radius $r$ , the higher the fluid can be raised, since a smaller tube holds less mass. The height is also inversely proportional to fluid density $\rho$ , since a larger density means a greater mass in the same volume. (See [link] .) (a) Capillary action depends on the radius of a tube. The smaller the tube, the greater the height reached. The height is negligible for large-radius tubes. (b) A denser fluid in the same tube rises to a smaller height, all other factors being the same.

## Calculating radius of a capillary tube: capillary action: tree sap

Can capillary action be solely responsible for sap rising in trees? To answer this question, calculate the radius of a capillary tube that would raise sap 100 m to the top of a giant redwood, assuming that sap’s density is $\text{1050 kg}{\text{/m}}^{3}$ , its contact angle is zero, and its surface tension is the same as that of water at $20.0º C$ .

Strategy

The height to which a liquid will rise as a result of capillary action is given by $h=\frac{2\gamma \phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta }{\rho \text{gr}}$ , and every quantity is known except for $r$ .

Solution

Solving for $r$ and substituting known values produces

$\begin{array}{lll}r& =& \frac{2\gamma \phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta }{\rho \text{gh}}=\frac{2\left(\text{0.0728 N/m}\right)\text{cos}\left(0º\right)}{\left(\text{1050}\phantom{\rule{0.25em}{0ex}}{\text{kg/m}}^{3}\right)\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)\left(\text{100 m}\right)}\\ & =& 1.41×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{m.}\end{array}$

Discussion

This result is unreasonable. Sap in trees moves through the xylem , which forms tubes with radii as small as $2\text{.}5×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{m}$ . This value is about 180 times as large as the radius found necessary here to raise sap $\text{100 m}$ . This means that capillary action alone cannot be solely responsible for sap getting to the tops of trees.

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!!

#### Get Jobilize Job Search Mobile App in your pocket Now! By JavaChamp Team By OpenStax By Sandhills MLT By Richley Crapo By Vongkol HENG By Eric Crawford By OpenStax By Brooke Delaney By Michael Sag By Madison Christian