International Baccalaureate
Extended Essay
How does the rate of flow of a ferrofluid through a thin pipe depend upon the
strength of an externally applied magnetic field
Einar A. Rødtang
2011
Physics
Word count: 3906
1
Abstract
This essay attempts to answer the question “How does the rate of flow of a ferrofluid through a thin
pipe depend upon the strength of an externally applied magnetic field” Its scope is restricted to
vertical pipes with flow induced by gravity subject to non-alternating magnetic fields. To answer
this question one experiment will be considered. In this experiment a thin tube was filled with
ferrofluid which was then allowed to flow until the tube was empty. This was repeated with
externally applied magnetic fields of different strengths. Variables measured include time required
for the tube to empty, magnitude and sign of the magnetic field at a point within the coil as well as
basic dimensions of the setup.
Subsequently the results were interpreted and a theoretical approach, relying on the HagenPoiseuille equation, energy density of a magnetic field and related variables was attempted. The
results of this investigation suggested that an increase in magnitude of the magnetic field,
irrespective of its sign, leads to a decrease in the flow rate of the fluid. This is so because when the
fluid flows dipoles that are aligned by the magnetic field are forced out of alignment, the externally
applied magnetic field opposes this change in alignment thus slowing down the fluid. It slows down
because the fluid now uses a part of its energy to force particles out of their alignments, energy that
will not be converted into kinetic energy hence the flow rate decreases.
Furthermore the theoretical approach suggests the following relation between the flow rate Q and
the magnetic field H:
∆𝑃𝜋𝑟4
8 𝑚𝑔 − 8𝐾𝐸 − 4𝐶𝑉𝜀𝑓 𝐻2
Word count: 264
2
=𝑄
Table of contents
Abstract ................................................................................................................................................ 2
Table of contents .................................................................................................................................. 3
Introduction .......................................................................................................................................... 4
Background Literature and Theory ...................................................................................................... 5
Experimental Setup and Procedure ...................................................................................................... 6
Theoretical model ................................................................................................................................ 7
Data Analysis ..................................................................................................................................... 11
Comparing experimental data with the theoretical model ................................................................. 13
Conclusion and Evaluation ................................................................................................................ 15
Improvements..................................................................................................................................... 18
Sources ............................................................................................................................................... 19
Bibliography....................................................................................................................................... 20
3
Introduction
The purpose of this document is to determine how the rate of flow of ferrofluid through a thin pipe
depends upon the strength of an externally applied magnetic field. This was done mainly by
considering an experiment where ferrofluid was allowed to flow through a thin pipe surrounded by
coils inducing a magnetic field. The data was analysed, relevant theoretical treatment attempted and
sources such as research papers and relevant undergraduate textbooks where consulted. Especially
Thomas Franklins master thesis on ferrofluids and the text book “Fundamentals on fluid dynamics”
was useful.
I think ferrohydrodynamics is a topic worthy of investigation due to the many potential applications
of ferrofluids. Applications which would benefit from accurate knowledge of ferrofluid tube flow
include, but are not restricted to: Spacecraft attitude control systems, cancer treatment and treatment
of other medical conditions1. Drugs can be bonded to ferrofluids and after injecting it into the
patient external magnetic fields could be applied in order to guide the drugs to the correct location,
and keep them there. Knowing how ferrofluids flow in tubes would be necessary to do this
accurately.
What originally sparked my interest for ferrofluids was an article referring to research into using
ferrofluids in spacecraft attitude control systems. By applying a magnetic field to a ring filled with
ferrofluid one can change its momentum and thus alter the spin of the spacecraft2. Due to the
accuracy with which it is possible to alter magnetic fields it gives the possibility of altering a
spacecraft’s orientation very precisely while less fuel is necessary for small thrusters. I find such
possibilities fascinating and useful for my later life as I plan on becoming an aerospace engineer.
Furthermore doing my extended essay in this topic has enabled me to explore parts of physics that
strictly speaking are way too complicated for students at my level. However the analysis has
allowed me to apply basic principles in physics: When I considered the conservation of the fluids
potential energy I had to invoke the law of conservation of energy. My knowledge of how magnets
are magnetic due to aligned half-filled electron sub-orbitals helped immensely when trying to
1
"Ferrofluids for Medicine." Ferrolabs, Inc.. N.p., n.d. Web. 22 Jan. 2012.
<http://www.ferrolabs.com/en/information/33/>.
2
"Ferrofluid Application." Ferrofluid Canada. N.p., n.d. Web. 22 Jan. 2012. <http://ferrofluid.ca/application.html>.
4
deduce how the ferrofluid would act when an external field was applied.
Background Literature and Theory
Ferrofluids are fluids composed of magnetic nanoparticles dissolved in a carrier liquid. The
magnetic nanoparticles are coated by a surfactant in order to inhibit clumping caused by external
magnetic fields3.
Magnetization represents the density of magnetic dipole moments in a material.
The magnetic dipole moment of a magnet is a quantity that determines the torque an external
magnetic field will exert on it.
The magnetic susceptibility of a magnet determines how magnetized a material gets when an
external magnetic field is applied to it.
Ferrofluid nanoparticles usually have less magnetization than real ferromagnets but are more
magnetized than paramagnets and are therefore classified as superparamagnets4. Paramagnets are
magnets with a small positive magnetic susceptibility, superparamagnets on the other hand have
significantly higher magnetic susceptibility5. Paramagnets are only magnetized in the presence of an
externally applied magnetic field. They become magnetized because the external field aligns all
individual dipoles or unpaired electrons sub-orbitals parallel to the external field. In the absence of
an externally applied field random thermal motion creates disorder in the individual dipoles making
the net magnetic moment zero.
Viscosity can be defined by considering two parallel large plates of area A separated by a distance y
filled with a fluid of some viscosity. If the topmost plate moves with a velocity u the dynamic
viscosity μ is given by the following equation.
𝐹 = 𝜇𝐴
𝑢
𝑦
Where F is the force necessary to move the topmost plate at a u. The lower plate is fixed6.
3
"Ferrofluid: Magnetic Liquid Technology." Ferrotec. N.p., n.d. Web. 22 Jan. 2012.
<http://www.ferrotec.com/technology/ferrofluid/>.
4
"Ferrofluid - Wikipedia." Wikipedia. N.p., n.d. Web. 22 Jan. 2012. <http://en.wikipedia.org/wiki/Ferrofluid>.
5
"Paramagnetism - Wikipedia." Wikipedia. N.p., n.d. Web. 22 Jan. 2012.
<http://en.wikipedia.org/wiki/Paramagnetism#Superparamagnets>
6
"Physical Chemistry -- Physical Properties of Gases, Liquids and Solids -- Viscosity and the Flow of Fluids Through
5
Experimental Setup and Procedure
List of apparatus used
HQ power PS 3003 power supply
0-30 V and 0-3A
Two coils with 600 turns each
Glass Funnel attached to a 55 cm glass tube with a diameter of 2 mm
Pasco scientific photogate
Me-9204B Accessory photogate
Resolution down to 0.1 millisecond7
Vernier magnetic field sensor
Resolution down to 0.0002 mT 8
Open Tubes.." Physical Chemistry Resources. N.p., n.d. Web. 17 Oct. 2011.
<http://physicalchemistryresources.com/Book2_sections_graphicfiles_08142009/htm_PPGLS_Viscosity.htm>.
7 "PASCO : Accessory Photogate - ME-9204B." PASCO. N.p., n.d. Web. 17 Oct. 2011.
<http://www.pasco.com/prodCatalog/ME/ME-9204_accessory-photogate/index.cfm>.
6
The glass funnel was attached with a clamp and the glass tube was put through 2 coils in series. At
the end of the glass tube a photogate was positioned such that it could register the flow from the
tube. At the bottom there was a beaker used to collect the ferrofluid pouring in from the top. The
magnetic field sensor was fastened with a clamp and positioned inside the coils close to the tube.
Procedure
The lowest end of the glass tube was sealed with a finger then the tube was filled with 40 ml of
ferrofluid. After removing the finger the fluid begins to flow and the photogate measures how much
time it takes before the flow stops.
To ensure that equal amounts of ferrofluid were used every time a measuring glass was used to pour
the ferrofluid into the funnel.
Theoretical model
Flows through long cylindrical pipes can be calculated using the Hagen-Poiseuille equation9;
∆𝑃𝜋𝑟4
=𝑄
8𝜇
Where:
r is the radius of the tube
L is the length or height of the tube
π is the mathematical constant
μ is the viscosity of the fluid
ΔP is the pressure drop over the length of the tube.
The Hagen-Poiseuille equation assumes laminar, viscous and incompressible flows through
cylindrical pipes that have a constant cross-section. The pipe must also be significantly longer than
its radius, such that edge and nozzle effects become negligible. Let us assume that all of these
8 "Magnetic Field Sensor." Vernier Software & Technology. N.p., n.d. Web. 17 Oct. 2011.
<http://www.vernier.com/products/sensors/mg-bta/>.
9
Munson, Bruce Roy. Fundamentals of fluid mechanics. 6th ed. New York, NY: Wiley, 2010. Print.
7
conditions hold true for our experiment.
However the Hagen-Poiseuille equation does not take into account any effects due to externally
applied magnetic fields, so we will have to amend it.
Energy is used by the solenoids in order to make the magnetic field. Therefore the magnetic field
must contain energy. This energy is given by10:
𝐸=
𝜀𝑓 𝐻 2 𝑉
2
Where:
𝜀𝑓 is the permeability of a material, in our case ferrofluid.
H is the magnetic field strength
E is energy stored in the field
V is volume of field
The energy E can be defined as the energy required to change the magnetization of any material
within a volume of the field. The material in our case would be ferrofluid. When the ferrofluid
flows through the magnetic field, electrons in half-filled iron suborbitals attempt to align themselves
with the magnetic field. As the fluid descends the aligned electrons will continually move out of
alignment and then be realigned by the magnetic field. This realignment restricts the motion of the
iron particles, and that which impedes the motion of the particles impedes its velocity. Hence an
increase in magnitude of the magnetic field should slow down the flow
Let the force F required to push the ferrofluid through a circular pipe be:
𝐹 = 𝜇𝑓
Where:
𝜇𝑓 is the viscosity of the ferrofluid
k is a constant representing the properties of the tube. These properties include cross-section,
roughness of the material and any other properties of the tube that may be relevant.
Work W is defined as:
10
"Energy in Electric and Magnetic Fields." Hyper physics. N.p., n.d. Web. 17 Oct. 2011. <hyperphysics.phyastr.gsu.edu/hbase/electric/engfie.html>.
8
𝑊 = 𝐹𝑑
Where d is the distance over which the force moves an object.
Hence the work done moving the fluid through the length L of the tube is:
𝑊 = 𝐹 = 𝜇𝑓
What happens when the fluid flow is impeded by viscosity like this is that ordered kinetic energy is
transformed into random thermal energy TE. Hence:
𝑇𝐸 = 𝜇𝑓
This work is done by the gravitational potential energy of the fluid. However as the fluid moves
through the solenoids, the magnetic field does work on the ferrofluid particles when aligning them.
The gravitational potential energy forces these particles out of alignment as the fluid descends.
Hence the energy stored in the magnetic field opposes the gravitational potential energy. Then the
potential energy of the fluid is given by:
𝜀𝑓 𝑉𝐻 2
𝑃𝐸 = 𝑚𝑔 −
2
However it is unlikely that all energy in the field will be used to realign the ferrofluid particles.
Some particles will be put out of alignment by the thermal energy of the fluid and not by the fluids
gravitational potential energy. Furthermore, all magnetic flux in the field will not necessarily
interact with the ferrofluid, if this was the case you would be able to coat a room with ferrofluid and
then not be able to measure any magnetic fields outside the room. Hence we multiply the magnetic
field energy term with a constant C to account for these effects.
𝐶𝜀𝑓 𝑉𝐻 2
𝑃𝐸 = 𝑚𝑔 −
2
As the fluid flows through the tube this potential energy will be converted into kinetic energy KE
and thermal energy TE caused by viscosity. Hence:
𝐶𝜀𝑓 𝑉𝐻 2
𝐾𝐸 + 𝑇𝐸 = 𝑚𝑔 −
2
𝐾𝐸 + 𝜇𝑓
𝐶𝜀𝑓 𝑉𝐻 2
= 𝑚𝑔 −
2
2𝑚𝑔 − 𝐶𝑉𝜀𝑓 𝐻 2 − 2𝐾𝐸
𝜇𝑓 =
2
We can substitute this expression for the viscosity of ferrofluid into the Hagen-Poiseuille equation.
Thus expressing the volumetric flow rate Q in terms of the magnitude of the magnetic field.
9
∆𝑃𝜋𝑟4
8 (2𝑚𝑔 − 𝐶𝑉𝜀𝑓 𝐻2 − 2𝐾𝐸)
2
∆𝑃𝜋𝑟4
8 𝑚𝑔 − 8𝐾𝐸 − 4𝐶𝑉𝜀𝑓 𝐻2
=𝑄
=𝑄
Other effects
The above derivation assumes a constant and homogeneous magnetic field for the length of the
tube. While this may be true inside the solenoids it is probably not true for the parts of the tube that
are outside the solenoids. A considerable part of the tube is outside the solenoids so the effects of
non-homogeneous magnetic fields are probably significant. The exact consequences of this are hard
to account for quantitatively so the problem should in future experiments be eliminated by covering
the entire length of the tube with solenoids. We can on the other hand consider the problem
qualitatively; the iron particles in the ferrofluid coming from above should be attracted towards the
coil’s magnetic field. When these iron particles leave the coils they should be attracted upwards.
Overall these effects should to some degree cancel each other. Now, it should be noted that the tube
is longer above compared to below the solenoids, so the overall effect may be an acceleration of the
fluid and thus an increase in flow rate.
Because the tube is so thin capillary effects are bound to have some role. Capillary effects arise
when surface tension and adhesion (Which is the attractive force between the walls of the tube and
the fluid resulting from intermolecular attraction) work together to make a fluid flow up against
gravity. The effects of surface tension are likely to be small, partly due to the fact that the surface
area is small but mostly because surface tension is such a weak force.
The adhesion force is significant since it becomes relatively more important the smaller the tube
diameter. However its effects are roughly accounted for by Poiseulles equation and viscosity,
though these effects could be studied in greater detail in future investigations.
Furthermore the fluid will act differently at the nozzle compared to within the tube. At the nozzle
several effects come in to play including pressure drops outside the tube affecting the conditions
just inside the nozzle. The degree of wetting, which is the fluid tendency to stick to a material, also
10
heavily influences how the fluid acts close to the nozzle. However since the radius of the tube is so
small compared to its height, the radius’ length is 0.2% of the length of the tube, all nozzle effects
can safely be assumed to be negligible.
When the ferrofluid is magnetized the ferrofluid itself will generate an additional magnetic field.
The effects of this will not be taken into account because things become way too complicated way
too fast. Furthermore it is difficult to tell the two fields apart empirically.
Data Analysis
Flow rate Vs. Magnetic field
Graph made from the results of the experiment described above.
Due to the high uncertainties it is hard to draw any hard conclusions however it is indicated that
when you increase the magnitude of the magnetic field the flow rate decreases. There is a certain
symmetry around 0 magnetic field. This indicates that the magnitude of the field that affects the
11
flow rate, but that it is independent of the alignment of the field. Though it really just shows that
there is no difference between a positive and a negative magnetic field strength as far as the
ferrofluid is concerned.
If the decrease in flow rate is caused by an increase in viscosity then the direction of the alignment
of ferrofluid particles should not be significant. However forces arising from the interaction
between the field made by the coils and the field made by the ferrofluid may act differently.
It should be noted though that the peak flow rate seems to be to the left of zero magnetic field, this
can be due to uncertainties, however it could be due to the presence of earth’s magnetic field. The
experiment was conducted quite far north so the magnetic field lines should be approximately
normal to the ground and hence parallel to the magnetic field generated by the solenoids. That
earth’s magnetic field is present means that when the magnetic field strength sensor detected zero
tesla inside the solenoids, they were turned on and the net field inside them was zero. Most of the
tube was outside the solenoids where the flow could be affected by earth’s magnetic field. However
the effects of this should be minor as earth’s magnetic field is on the order of 0.1 mT11 while the
highest magnetic fields measured in the experiment where on the order of 8 mT.
Checking the magnetic field at different points at the tube reveals that the effect of different
magnitudes of magnetic fields may have an effect but for analytical purposes it may be justified to
treat it as homogeneous
Uncertainties
The relatively high uncertainties warrant special attention. The uncertainty bars in the flow rate vs
magnetic field were made by comparing the difference between the lowest and highest flow rate
recorded at a given magnetic field strength, consequently due to the relatively modest amount of
trials (5-7 trials for each field strength) some uncertainties will be underestimated. The uncertainties
can be attributed to several factors:
11
"Earth’s Magnetic Field and Climate Variability." Global Warming Science. N.p., n.d. Web. 22 Jan. 2012.
<http://www.megakastro.gr/weather_agro/solar_modulation.htm>.
12
First of all it was difficult to measure the amount of ferrofluid precisely. The ferrofluid clung to the
walls of the measuring beaker, making it hard to read of the exact quantity. Starting the flow relied
on manually removing a finger from the bottom of the tube. Thus human error may be a significant
factor. It is also worth noting that once the flow stopped a few droplets tended to drip, which means
that not all ferrofluid had finished flowing. This introduces an extra uncertainty in time as the
photogate records the time it takes for a gap in the liquid to appear.
The uncertainty is quite high in relation to the change in time, however it is not big in absolute
terms being fractions of a second. This suggests that there perhaps is no relationship between the
flow rate of the ferrofluid and the strength of the magnetic field. Or the field may simply be too
weak for it to be significant. It would be preferable to try with stronger magnetic fields; however the
power suppliers available simply could not deliver enough current to make stronger fields. It is also
a possibility that other ferrofluids may be more responsive. Greater quantities of ferrofluid should
be used to reduce these uncertainties. However an increase in pressure may render the effects of
changing the magnetic field even more minuscule, though for realistic increases in quantity this
should not be too much of an issue. Still, using more powerful fields should be more important.
Comparing experimental data with the theoretical model
It is difficult to do any quantitative comparisons between the theoretical model and the experimental
data since there are so many terms that are unknown. More experiments could have been done to
measure the, viscosity, permeability, etc. However this would take too long time for an EE and for
certain terms and constant the school simply don’t have the equipment necessary to measure them.
However if we collapse all the unknown terms into some neat constants we get:
∆𝑃𝜋𝑟4
8 𝑚𝑔 − 8𝐾𝐸 − 4𝐶𝑉𝜀𝑓 𝐻2
=𝑄
𝐴
=𝑄
− 𝐶𝐻 2
We can take this expression and see whether it fits the experimental data for any values of the constants.
13
The graph could be made to go through two more error bars; however the above constants minimize the
root mean square error down to 0.06021 which isn’t entirely unacceptable. But when even the most
optimal constants can’t make the graph go through all the error bars it makes the theory look somewhat
dubious. It should be noted though that some of the uncertainties may have been underestimated as they
were calculated from the variation between relatively few trials. That the three error bars the graph
doesn’t go through are also the three smallest error bars support this.
During the data analysis there were indications of systematic errors that could shift the graph such that the
maximum is not at zero magnetic field strength. If we incorporate this into our expression by adding
horizontal translation constant we get the following expression:
𝐴
−𝐶 𝐻+
14
2
=𝑄
If we graph this on the experimental data and tweak the constants to get the minimum root mean square
error we get the following plot:
Not only does this graph have nearly half the rmse compared to the last graph, it also goes through
all the error bars. This indicates that the general form of our equation is applicable to the real world.
However if we insert some real values and constants the graph may look nothing like this, so we
should not be too self confident.
In this graph the maximum is shifted to -1.8mT magnetic field strength. This is much more than the
0.1mT magnetic field provided by earth indicating that the shift is not, at least not entirely, due to
earth’s magnetic field.
Conclusion and Evaluation
The question posed in this essay was “How does the rate of flow of a ferrofluid through a thin pipe
depend upon the strength of an externally applied magnetic field”. The experiment had quite big
uncertainties; however a clear trend in the results could be inferred indicating that an increase in the
strength of the magnetic field results in a decrease in the volumetric flow rate. Furthermore the
results indicated that the flow rate was related to the magnitude of the magnetic field irrespective of
whether it was positive or negative. However when the theoretical model allowed a shifting of the
maximum it fit much better with the experimental data, going through all error bars and having a
lower rmse. Still whether this shift is due to random error, systematic error or some property of the
15
ferrofluid is not known. Random error is probable since they are so prominent, systematic errors
that may be relevant include the field being non-homogeneous. The data isn’t certain enough to rule
out properties of the ferrofluid as a cause for this discrepancy, though the theoretical treatment
indicates that maximum flow rate should occur at 0 magnetic field.
The theoretical treatment indicates that the flow rate can be approximated by the following
expression:
∆𝑃𝜋𝑟4
8 𝑚𝑔 − 8𝐾𝐸 − 4𝐶𝑉𝜀𝑓 𝐻2
=𝑄
It was derived by considering the Hagen-Poiseuille equation and as well as the conservation of
energy and the energy stored in the magnetic field.
The Hagen-Poiseuille equation assumes laminar, incompressible flows. However this does not
affect the accuracy of the expression much, since the radius of the tube is 1mm the Reynolds
number is small so the flow is very nearly completely laminar. Only 40 ml fluid was used in the
experiment so the pressure difference across the length of the tube is nowhere near enough to
compress the fluid.
The assumption that the field is homogenous is much more severe as the solenoids cover only a part
of the tube, leading to the iron particles being pushed and pulled on either side of the solenoids.
This variation in field strength was measured; although it was minor it was measurable and may
have had a significant effect on the outcome of the experiment.
To check whether our expression is reasonable or not we could try to substitute in some values and
see how it compares to the experiment. Now, we don’t know most of the values for the experiment
in question, however if we just want to see whether the calculated values are in the same ballpark as
the experimental ones we can just insert some plausible values.
∆𝑃 = 𝜌𝑔 so we can calculate the pressure drop using:
𝑘𝑔
𝜌 = 800 𝑚3 Density of kerosene12, the liquid carrier the ferrofluid is based on.
12
"Liquids - Densities ." Engineering ToolBox . N.p., n.d. Web. 22 Jan. 2012.
<http://www.engineeringtoolbox.com/liquids-densities-d_743.html>.
16
𝑔 = 9.82
𝑚2
𝑠
Acceleration due to gravity in Oslo
= 0.55𝑚 Length of the tube in the experiment
Furthermore these constants will allow us to calculate a flow rate
= 1 I made up the constant k so the literature doesn’t contain any approximations for it, so I will
just let it be 1 for simplicity.
𝑟 = 10−3 𝑚
𝑉 = 4 ∗ 10−5 𝑚3
𝑚 = 𝜌𝑉
𝐻
𝜀𝑓 = 9 ∗ 10−4 𝑚 I don’t have the permeability of the ferrofluid was used, but it contains iron so I
will go with the permeability of steel13 which is made of iron.
𝐶 = 1 This constant describes how much of the energy stored in the field impedes the flow. Letting
it be 1 means we assume that all energy in the field is used to impede the flow.
𝐾𝐸 = 3.7 ∗ 10−3 Which is simply half the gravitational potential energy, the rest is lost due to the
magnetic field and viscosity.
𝐻 = 5.5 ∗ 10−3 𝑇 Which in the experiment lead to a flow rate of 4.1 ml/s
If we substitute all this into our equation we obtain a flowrate 𝑄 ≈ 10
𝑚𝑙
𝑠
This value is off by a factor of 2. So it is not too far from the experimental value, however the
approximate calculation did not use any reasonable value for the constant k. So it is vital that future
investigations figure out the nature of this constant k. If our model is a good approximation, then
the value of k is on the order of magnitude of 0.5.
Though I think it is important to be humble about the accuracy of any theory in this field.
Throughout this investigation I have discovered that electromagnetism and fluid dynamics are two
quite complicated fields, mixing them make things even more complicated. The theories in this
document are first approximations, several effects have not been taken into account and
experimental date is less than conclusive. The reasoning put forth may be flawed and even
contradict itself. However it may have helped provide some indication of what is really going on.
13
"Permeability." Wikipedia. N.p., n.d. Web. 22 Jan. 2012.
<en.wikipedia.org/wiki/Permeability_%28electromagnetism%2
17
Improvements
Throughout the work with the experiment several possible improvements became apparent thought
more experiments could not be done, in part due to lack of ferrofluid and time.
To make the magnetic field uniform several Helmholtz coils should be put around the tube for its
entire length.
In order to measure the quantity of ferrofluid accurately a scale should be used. More ferrofluid
should also be used for each try in order to minimize effects of changing amounts of ferrofluid.
A force sensor should be put under the beaker collecting the ferrofluid. This would make it possible
to measure flow rate versus time directly and enable further and more accurate analysis of the
results.
Measuring different properties of the ferrofluid such as density and particularly viscosity would
greatly benefit the analysis. So would repeating the experiment with a ferrofluid of known
properties given by the producer.
Measuring the voltage and current of the coils would make it possible to calculate the extent and
magnitude of the field at any point along the tube, making more sophisticated analysis possible.
During the experiment it was also discovered that kerosene works very well for cleaning up the
ferrofluid which otherwise was quite difficult to remove.
18
Sources
"Ferrofluids for Medicine." Ferrolabs, Inc.. N.p., n.d. Web. 22 Jan. 2012.
<http://www.ferrolabs.com/en/information/33/>.
"Ferrofluid Application." Ferrofluid Canada. N.p., n.d. Web. 22 Jan. 2012.
<http://ferrofluid.ca/application.html>.
"Ferrofluid: Magnetic Liquid Technology." Ferrotec. N.p., n.d. Web. 22 Jan. 2012.
<http://www.ferrotec.com/technology/ferrofluid/>.
"Ferrofluid - Wikipedia." Wikipedia. N.p., n.d. Web. 22 Jan. 2012.
<http://en.wikipedia.org/wiki/Ferrofluid>.
"Paramagnetism - Wikipedia." Wikipedia. N.p., n.d. Web. 22 Jan. 2012.
<http://en.wikipedia.org/wiki/Paramagnetism#Superparamagnets>.
"Physical Chemistry -- Physical Properties of Gases, Liquids and Solids -- Viscosity and the Flow of Fluids
Through Open Tubes.." Physical Chemistry Resources. N.p., n.d. Web. 17 Oct. 2011.
<http://physicalchemistryresources.com/Book2_sections_graphicfiles_08142009/htm_PPGLS_Viscosity.htm
>.
"PASCO : Accessory Photogate - ME-9204B." PASCO. N.p., n.d. Web. 17 Oct. 2011.
<http://www.pasco.com/prodCatalog/ME/ME-9204_accessory-photogate/index.cfm>.
"Magnetic Field Sensor." Vernier Software & Technology. N.p., n.d. Web. 17 Oct. 2011.
<http://www.vernier.com/products/sensors/mg-bta/>.
Munson, Bruce Roy. Fundamentals of fluid mechanics. 6th ed. New York, NY: Wiley, 2010. Print.
"Energy in Electric and Magnetic Fields." Hyper physics. N.p., n.d. Web. 17 Oct. 2011. <hyperphysics.phyastr.gsu.edu/hbase/electric/engfie.html>.
"Earth’s Magnetic Field and Climate Variability." Global Warming Science. N.p., n.d. Web. 22 Jan. 2012.
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