Students: Au Check Chung, Samuel Chan
Diocesan Boys’ School
Lau Wing Kit, Tang Yu Ping
S.K.H. Tsang Shiu Tim Secondary School
Baptist Lui Ming Choi Secondary School
Ho Nga Lei
Belilion Public School
Cheung Kin Wang
PLK Vicwood K.T. Shong Sixth Form College
Surpervisor: Prof. H.K.Wong
Department of Physics, The Chinese University of Hong Kong, PRC
Ferrofluid is a stable colloidal suspension of magnetic particles in a liquid carrier
usually oil. The average size of the particles is about 100Å (10 nm). If the particles
(usually magnetite) are too large, they behave like a fine magnetic powder, clumping
and settling rapidly from the oil. If they are too small, they no longer show the
wonderful magnetic property. They are coated with a surfactant which prevents
particle agglomeration even when a strong magnetic field is applied to the ferrofluid.
The surfactant must be matched to the carrier type and must overcome the attractive
van der Waals and magnetic forces between the particles. Outside a magnetic field,
the particles moves like an ordinary liquid; in a magnetic field, they become a
magnetic liquid. Based on their properties, we explored three applications in this
1. Magnetic field pattern kit
2. Density analyzer
3. Use of ferrofluid to study the data patterns of floppy disk
Ferrofluid consists of tiny magnetic particles suspended in a liquid. It looks
homogeneous but actually contains three constituents: 1. magnetic particle (Fe3O4, ~
10 nm in diameter), 2. surfactant, 3. liquid carrier.
First, consider the magnetic particles. They are essentially tiny magnets, which can
interact with each other. If there is no external magnetic field, the tiny magnets will
attract each other: N S N S
In order to reduce agglomeration, the magnetic particles in the ferrofluid must be very
small and each of them is protected by surfactant molecules for further isolation.
The particles have density higher than water. In theory, they would sink to the bottom
of the liquid. However, the vigorous thermal vibration keeps the particles suspending
in the liquid. To estimate the required particle size, we first consider the dipole-dipole
interaction. (A magnet is a magnetic dipole with magnetic dipole moment m.)
If the two dipoles just touch each other, the dipole interaction energy can be shown to
be Edd = 12 0 M 2V
This equation can be understood by noting the following:
1. Volume of a particle is V = r 3 = (r = radius, d = diameter)
2. Magnetic moment m = MV (V =volume of the magnet, M = magnetic moment per
3. The magnetic field at a distant point along the perpendicular bisector of a dipole
is B= . (x = distance from the moment)
Since there are many magnetic particles in ferrofluid (~ 1023 /m3), collisions between
particles are frequent (Brownian motion). Such thermal agitation is available to
disrupt the agglomeration if thermal energy magnetic energy:
kT ³ 1
12 0 M 2V
For Fe3O4 particles at room temperature, d 8 nm. These tiny particles are well
dispersed in the liquid.
A)The making of a demonstration kit
To visualize the exotic behavior of ferrofluid under a magnetic field, it would be nice
to let it flow freely in a transparent liquid medium. We aimed to make a ferrofluid
demo kit by a simple and cheap method. As we wish someday the demo kit can be a
common teaching material in high school, we have to find a simpler and cheap way to
make the kit.
More demo can be done with the kit. We can use two tiny magnets with N and S poles
facing each other with the kit in between. The ferrofluid can fly around between the
magnets by adjusting the magnet separation. We can use this method to pick up (with
one magnet) a small amount of ferrofluid. Then move it far away from the other
magnet and show the magnetic field pattern.
Theory and experimental method
First, when we discuss how to make the kit, we have to understand the
components of ferrofluid. Our ferrofluid consists of Fe3O4 particles, which are
ferromagnetic substance containing both Fe2+ and Fe3+ ions. The particles, which have
an average size of about 100Å (10 nm), are coated with a stabilizing dispersing agent
(surfactant), which prevents particle agglomeration even when a strong magnetic field
gradient is applied to the ferrofluid. Also, a carrier fluid provides a medium for the
ferromagnetic powder to flow around. Therefore, in order to make it successful, we
must concern four points:
1. The carrier fluid in the ferrofluid must not dissolve in the transparent liquid
medium; otherwise, ferrofluid will change its state to powder form, which affects
the magnetic field pattern.
2. The liquid medium should not dissolve the surfactant gathered around the
magnetic particles. If surfactant is dissolved, it would form an oil layer on the
surface, and the ferrofluid would clump together forming a solid, meanwhile, it
loses its magnetic features.
3. Ferrofluid must be able to sink to the bottom that implies the density of the liquid
medium must be lower than the ferrofluid.
4. We must choose a suitable container. Any stains inside the bottom affect the view
of magnetic pattern.
Different solvents were mixed with the ferrofluid. Fig 1 shows the successful kit.
Results and Discussions
Water was insoluble with the carrier fluid and surfactant. A thin layer of carrier fluid
floated on the top of water; it wet the wall of the container and made it messy. A stain
formed at the bottom of container.
Methanol dissolved the carrier fluid in two or three days, and the transparent liquid
became light brown. A thin layer of carrier fluid floated on the top of methanol; it wet
the wall of the container. A stain formed at the bottom of container.
Ethanol dissolved the carrier fluid in two to three days, and the transparent liquid
became light brown. Ferrofluid wet the wall of container but a stain formed at the
bottom of container.
Propanol dissolved the carrier fluid would dissolved in a short time; the transparent
became brown in color. Surfactant was also dissolved and the ferrofluid became
powder form. If water was added, part of the dissolved carrier fluid could be mixed
with the powder again and became ferrofluid but the viscosity became higher. The
reformed ferrofluid would not wet the wall of the container.
For glycol, both carrier fluid and surfactant would not be dissolved in Glycol in one or
two days. The ferrofluid would not wet the wall of the container. However, the carrier
fluid would be dissolved after two or three days.
We have done another see of experiment to find out the best volume ratio of propanol
If the ratio of propanol to water was 3.26, darkly yellow solution resulted and
magnetic particles stuck together due to the lost of the surfactant and the properties of
the ferrofluid disappeared.
If the ratio was 1.58, darkly yellow solution resulted and ferrofluid with a low
If the ratio was 1.04, golden yellow solution resulted and magnetic pattern was
If the ratio was 0.69, lighter golden yellow solution resulted. Sharp pin shape could be
shown and ferrofluid were free to move.
If the ratio was 0.44, lighter golden yellow solution resulted. Sharp pin shape could be
shown and ferrofluid are free to move, very little ferrofluid stuck on the wall.
If the ratio was 0.26, transparent solution resulted. The problem of ferrofluid sticking
on the wall started to become serious.
If the ratio was 0.11, transparent solution resulted and ferrofluid stuck on the wall in
the bottom of the tube.
The trend was that the sticky problem was less serious when more propanol was used;
more clear solution was obtained when less propanol was used. To summarize all
these results, the ratio with 0.44 and 0.69 were the acceptable result as there was less
sticky problem and clear solution could be obtained. We used glass container as the
ferrofluid would not stain glass easily.
We used propanol and water to solve the sticky problem and the ratio of water and
propanol was the best in around 0.57. We used glass as container as the ferrofluid
would not stain it easily.
B) Density analyzer
This experiment is to demonstrate magnetic Achimedes effect, levitation and to use
ferrofluid as a low cost density analyzer. We use the demo kit we prepared in part A)
to demonstrate the experiment to allow a better results.
Theory and experimental method
There are two types of levitation based on minimum field and field gradient. We are
now using the field gradient.
Bernoulli’s equation for magnetic fluid: p gh 1 v 2 MdB constant
where p is the pressure, is the density, g is the acceleration gravity, h is the height
and v is the velocity. B is the applied magnetic field. Magnetization M is defined as M
= magnetic moment per unit volume. So m = MV (V is the volume of the magnet and
m is the magnetic moment ) Bernoulli’s equation for magnetic fluid tells us that in
magnetic field the fluid is subject to an effective pressure pm MdB (equation 1).
For the magnetic fluid, the higher the field, the larger is the effective pressure (if v and
h are fixed).
As stated in Archimedes principle, suppose you have a small object (with a cubic
shape, area of a face is A and the edge is z ) in the fluid. The force on the upper face
is (pm+ pm)A pointing downward while the force on the lower face is pmA.
The vertical force is then
F = -( p + p )A + p A = - p A ( p m+ pm)A
m m m m m
= -MBA (by differentiation of equation 1)
Fig 2 pmA
In equilibrium, Fm = (S-L)g(Az)
where S is the density of the object (the cube) to be floated,
L is the density of the fluid.
Therefore -M(B/z)(Az) =(S-L)g(Az)
and we get finally -MB/z=(S-L)g or S = L - MgB/z
L can be measured individually. We need a solenoid to generate a magnetic filed
So for different object we need different current in the solenoid to provide suitable
In this experiment, a 12V DC solenoid with metal plates to generate the magnetic
field was used as shown in Fig 3. By varying the current, the strength of the magnetic
field produced can be adjusted.
The field gradient near its opening is just good for this experiment.
Fig 3 Solenoid Fig 4 The setup
Results and Discussions
Table 1 Non-magnetic metals with known densities were first tested and the results
were shown in the table.
Fig 5 A graph of density versus applied current was drawn
A sample with unknown density was tested and the results were compared with the
To obtain an accurate result, the following precautions should be taken.
1. The ferrofluid must be adjusted to the same level as that in the experiments with
2. To avoid heating of solenoid, the measuring time cannot be long and the
connecting of the anode and cathode must be exchanged in each measurement.
This density analyzer is low cost, portable and easy to manage. The accuracy is also
acceptable. It is suitable for some nonmagnetic and small sample. This can be used in
the commercial field; for example, this analyzer can be used to distinguish the crystal
C) The study of the floppy disk
Ferrofluids are extensively used for the study of magnetic domain structures in
magnetic tapes, rigid and floppy disks, magneto-optical disks, crystalline and
amorphous alloys, garnets, steels and geological rocks. In this part, we concentrated
on the floppy disk. We find out the bit size of the floppy and the format of it by using
magnetic property and small magnetic particle of ferrofluid to compare with the
information that we can get in website or in books. This is helpful when teaching
students how the data are stored by the magnetic recording technique because the real
image of the bit can appear by using ferrofluid to do some simple but interesting
experiments. The domains on floopy are well controlled. We hope the demonstration
can give a clear image for students and not just memorize the information directly.
Theory and experimental method
Consider a track of a floppy disk; it is divided into 18 sectors for 5 inches floppy and
36 sectors for 3.5 inches floppy. Each track per sector contains several bytes. A small
amount of ferrofluid is used to coat the disk surface. When the carrier liquid of
ferrofluid evaporates, the magnetic particles congregate at the domain boundaries.
They appear as bright lines in visible light and can be viewed with a microscope. As a
result, the bit length is the distance between two dark lines. This method has several
advantages such as only a small magnetic field change can also be detected and the
instrument is very common and is available in a secondary school.
Each bit can be magnetized in either forward (S to N pole direction is along the
direction of disk rotation) or backward direction. The magnetization direction will be
inversed between the boundaries when the bit is ‘1’. It will also be inversed on a
boundary between two successive ‘0’s. It will not be inversed when a bit ‘0’ following
Fig 6 The magnetic bits represent either 0 or 1 according to the format as shown
In 1931, Bitter invented the method of visualizing the bits using ferrofluid. In this
experiment, we are going to try that method.
1. First, floppy disk was coated with a thin layer of ferrofluid.
2. Then, the ferrofluid was dried by a centrifuge and infrared light.
3. The floppy was checked useful or not (rainbow’s reflection means pattern on
floppy is good)
4. A magnifying glass was used to look for concentric tracks.
5. When optical microscope was used, we saw the bits for better samples. Adjusted
the polarizer for a better contrast.
6. The above test was repeated by controlling the pattern on the floppy with the help
of software, for example, FlopImager and Hex Editor. The formats we use are AA,
FF and FC. They are as shown below.
Fig.7 Image of floppy disk data with FF
(1111 1111). The distance between two
boundaries is also the same as the bit size
of the floppy disk.
Fig.8 Image of floppy disk data with AA
Magnetization (1010 1010). The distance between two
direction boundaries is twice the bit size of the
Fig.9 Image of floppy disk data with FC
Results and Discussions
1) Bit size and track width of 3.5 inches floppy disk
There are 80 tracks located within 2.5cm width on the floppy. Assuming the tracks are
closely packed with each other. The calculated track width is 2.5/80 cm = 0.313mm.
Fig.10 Image using 100X lens and
ferrofliud on a 3.5 inches floopy disk.
The experimental track width found
from the picture 1 is 3.5/100/100 =
The averaged distance from the center of the floppy is 2.5cm. The track length is
(2.5/100)*2* = 0.157 m. Track length per sector is 4.36x10-3m. Then the calculated
bit length is 5.45µm.
Fig.11 Image using 500X lens and
ferrofluid on a 3.5 inches floppy disk
data with FF (1111 1111)
The experimental bit length found
from is 7.5/30/500cm = 5µm.
2) Study of floppy format using ferrofluid
From Fig.11 the distance between two boundaries was 5µm by calculating the
experiment result. Compared with the theoretical result, 5.45µm, the percentage error
was just 8.26%. The two lengths were also very close to each other. The experimental
results matched the MFM format of byte.
Fig.12 Image of floppy disk with data AA
The distance between the two boundaries
was 13.45µm by calculating the
experiment result. It was roughly twice of
the bit length. The experimental results
matched with the format.
Fig.13 Image of floppy disk with data FC
Comparing the calculated and experimental track widths and bit lengths, they all are
in the same order of magnitude. The experiment to find the track width and the bit
length by using ferrofluid is reliable.
Comparing the calculated and experimental track widths, the method to verify format
by using ferrofluid is also reliable. To round up above data, we can use ferrofluid to
detect the format of the floppy and verify the MFM format of byte.
Physical Society of Hong Kong
Department of Physics, Chinese University
Professor H.K. Wong
Mr. C.K. Lee
Mr. F.M. Shiu
Mr .C.W. Yu
Papers and Books:
“Magnetic Fluids” by Ronald E.Rosensweig, Scientific American (1982).
“Magnetic Domain of floppy disk and phone card using toner fluid” by E.S. Bichsel et
al., Physics Teacher Vol. 40, p.150 (2002).
Physics Beyond 2000 by Raymond W.M. Chan