Magnetic Fluids

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David Vader - Final Wiki Entry for APPHY 225, Fall 2008

FINAL PROJECT: Fun with Magnetic Fluids

Introduction

When I first learned about mechanical properties of solids and fluids in school, I first found out about static properties such as the elastic modulus, the viscous modulus, the yield stress and the Poisson ratio. It makes sense, at the beginning, to think of very simple models to describe materials, speak of properties that are independent of the rate at which deformations/stresses occur, of how much deformation/stress has been accumulated or of the mechanical history of a sample. However, I quickly realized that the most interesting and relevant models are those that account for the time and frequency dependence of these mechanical properties. They are the most interesting, because they begin to hint as to what may be happening microscopically when macroscopic deformations and/or stresses are applied.

We have seen some of these material models throughout this course, specifically in the section on Viscosity,_elasticity,_and_viscoelasticity. The most simple addition to a simple elastic solid is that of plastic deformation, which starts to occur once a certain yield strain or yield stress is reached. This can be easily interpreted, at the microscopic scale, as spring-like bonds breaking once they are too extended. Beyond the simple models of elastic and plastic behavior, we see interesting behaviors such as:

  • dilatant fluids, which show an increasing viscosity as shear rate goes up;
  • pseudoplastic materials, which show a decreasing viscosity as shear rate increases.
  • strain-stiffening materials, which display a higher elastic modulus at higher strains
  • strain-softening materials, which have a lower elastic modulus at higher strains, a behavior very often associated with plastic deformation.

In many cases, the changes observed in the viscosity (respectively Young's modulus) as a function of shear rate (respectively shear strain) are rather small, i.e. stays in the same order of magnitude. Exciting materials, I find, are those that show changes of several orders of magnitude in their material properties when deformations or deformation rates are changed. Even more exciting are those that display drastic changes in their mechanical behavior when an external variable - e.g. magnetic field or temperature - is changed. In this final project, I present a very brief overview of materials, which display changes from fluid to solid behavior in the presence of a magnetic field, along with applications seen in the purely engineering world. I will also present some of the important observations I made over the Christams break with my international team of scientific experts: my two kids (2 and 4 years old) and two nieces (3 and 5 years old).


Magnetorheological fluids vs ferrofluids

In the category of fluid materials that are strongly influenced by the presence of a magnetic field - which we will subsequently call "magnetic fluids" -, there are two main subcategories:

  • magnetorheological (MR) fluids;
  • ferrofluids.

In terms of their composition, both of these materials are typically composed of three simple ingredients:

  1. a continuous oily fluid phase;
  2. 10-20% volume solid ferromagnetic particles;
  3. surfactant.

The continuous oily phase provides the default rheological properties of the material, i.e. the viscosity in the absence of an external magnetic field. The ferromagnetic particles confer the dependence on the external magnetic field. And because of mismatches in density, as well as the tendency for particles to form aggregates, surfactant must be added for long-term stability. Note that other ingredients may be added to change the baseline properties of the material.

What is the difference between an MR fluid and a ferrofluid in terms of composition? The main difference is in the size of the magnetic particles included in the fluid: for MR fluids, the typical size of solid particles is on the order of 10 microns, whereas for ferrofluids, the typical size is on the order of several nanometers.

How is this change in composition reflected in the material's mechanical properties in the presence of an external magnetic field? When an external field is applied on an MR fluid, particles tend to self-assemble along field lines and create structures that span lengths on the order of millimeters. If the thickness of the fluid sample is on that same order, then the fluid is retained by these structures and behaves more like a solid; the strength of this solid and how easily it will yield depends on the strength of the magnetic field [1].


MRfluid.jpg

[2]


Ferrofluid, on the other hand, really behaves like a magnetic fluid as we would intuitively describe it: in the presence of an external magnetic field, the fluid is strongly attracted to the source of the magnetic field, and will try to adapt its shape, location and orientation to minimize its magnetic energy. Most of the images of ferrofluids seen on the internet are of a special property of ferrofluids called the "normal-field instability", seen below. Briefly, the fluid is attempting to minimize its total free energy, of which the main components are gravitational energy, surface free energy and magnetic energy; when the magnetic field is strong enough, surface free energy and gravitational potential are increased to allow the fluid to decrease its magnetic energy. This makes for very cool effects!


Ferrofluid.jpg

[3]


Note that similar effects - formation of microstructures in the presence of an external field and change in rheological properties - can also be obtained using electrorheological (ER) and thermorheological (TR) fluids. I was initially planning on discussing those materials as well, but instead decided to report on homemade magnetic fluid and cool experiments done with my international team of experts (see acknowledgements). For more information on cool and responsive materials, there's plenty of resources on the web, starting with Wikipedia [4].

Applications of magnetic fluids

Without going into a long enumeration, I'd like to briefly mention some of the interesting applications I've read about for magnetic fluids. In general, the properties of MR fluids are used in situations where fluid-like behavior is the preferred default state, but where it may be useful to have a stiffer material present in exceptional circumstances. Or vice-versa.

  • A typical example is that of large engineering structures, such as buildings. In general, it is desirable to have strong hard foundations to support the building. However, when an earthquake strikes, hard foundations break to dissipate all the energy associated with this large-scale natural phenomenon. In this case, it is preferable to partially "fluidize" some of the components of the building foundations and building support, so that the energy can be dissipated without inducing any breakage.
  • In the automotive industry, similar applications have been implemented for a car's suspension system. Ferrari uses magnetic fluids in the suspensions, so that those can be instantly stiffened or softened using a computer-controlled electromagnet. Very cool!


Building.jpg[[5]] Ferrari.jpg[[6]]


  • Another example, already mentioned on the wiki, is that of a human body armor, where the rapid stiffening of MR fluid inside a body suit can protect from bullet shots (see Rheological_behavior).
  • One final example, is that of hard drives and other similar electronics. In this case, engineers have really used the lubricating properties of oils in electronics, while taking advantage of the attraction of ferrofluid to a magnetic field. Essentially, ferrofluid is used in rotating heads as a lubricant, but in smaller quantities than would otherwise be needed, because it is localized and maintained in place by a magnetic field; so hardly any fluid is lost in the process of lubrication, be it due to excessive friction, shear or gravity. That's cool too!

For more applications, check out Wikipedia's page [[7]] and branch from there.

Short digression on a cool rheology technique

Before reporting on cool home experiments on magnetic fluids, I'd like to insert a short digression on a cool rheological technique I encountered in my graduate years here at Harvard. We have seen some very cool theoretical derivations in this course; a lot of them initially performed by de Gennes. We have also seen at least one example of a cool experimental technique, that used by Langmuir and Blodgett to measure the surface tension of liquids and how it changes in the presence of various amounts of surfactant [8].

The technique I want to mention here is related to this final project, in the sense that it's a rheological protocol and analysis that allows one to study the mechanical properties of materials, which are typically fluid-like but which may display, due to jamming or to some other external factor, a rapid stiffening and/or brief solid-like behavior. This method was implemented in the Weitz Lab [[9]] by Ryan Larsen during the final months of his PhD, while he was trying to characterize the jamming of a colloidal suspension.

The main idea is that of creep-ringing for a viscoelastic medium. When applying a step stress on a sample with a viscous and elastic component to it, one expects to see an interesting mechanical response: because the inertia of the sample and tool are never zero, the system will initially overshoot the equilibrium strain or strain-rate required for that stress. The material will then pull back and reduce strain/strain-rate, but due to non-zero inertia will overshoot that target value once more. And so on and so forth, with the amplitude of oscillations around the target value gradually decreasing. The frequency of the oscillations and the rate at which their amplitude will decrease is directly related to the elastic and viscous components of the material's mechanical properties; those can be calculated as long as the value of the inertia is known. This method is called creep-ringing, because in a creep experiment, you apply a step-stress and measure the response in the strain; again, with non-zero inertia, you should expect to see the oscillatory response described above.


CreepRinging.jpg


Ryan Larsen used this during his PhD to measure the properties of jamming materials. He applied a constant shear rate on these colloidal systems until they started jamming, at which point there was a sharp increase in the sample stress. This step stress, as described above, generates a creep-ringing oscillatory response. From the frequency and amplitude decrease of the oscillations, the elastic properties of the jammed colloid can be measured. Note that these jamming events disappear as suddenly as they appeared, so it was important to find a rapid and clever way to characterize them. I find this quite creative, because Ryan used the rapid, and temporary, change of mechanical properties to his benefit.

Anyway, back to magnetic fluids...

FUN WITH THE KIDS: homemade MR fluid

As the bulk of this final project and as a way to spread scientific education to the next generation, I thought I'd experiment myself - along with my two toddler kids and their two toddler cousins who were visiting over the Christmas break! - with magnets and magnetic fluids, using very simple materials. Here are our findings...


Materials

  • iron powder: we used 325- and 100- mesh iron powder I had in the lab, which corresponds to particle sizes of 10-30 microns;
  • olive oil: extra virgin, from Trader Joe's;
  • glass vial, 3mL or 10mL, from the lab;
  • Parafilm paper, from the lab;
  • magnet, from thrift store, see comment below;
  • digital camera, 2MP or more is better.


IMPORTANT! Note that care must be taken with iron powder - especially around kids - to avoid inhalation and ingesting, as this could lead to metal poisoning.

Though we did not know the exact strength of the magnetic field generated by our toy magnet, we did find out subsequently that it is comparable to that generated by a 5mm by side cube of NIB N40 grade magnet; the magnet we used was bought second-hand from a thrift store, but looks exactly like one of those displayed in the pyramid below:

ToyMagnets.jpg

[10]

Sample preparation

We prepared a couple of <math>0.5cm^3</math> aliquots of 325- and 100- mesh iron powder I had in the lab. After putting some powder in 3mL or 10mL vials, which have a diameter of roughly 1-2cm, samples were sealed using extensive Parafilm paper; the sealing serves two purposes:

  1. avoiding spill accidents, which could create not only a mess, but also dangerous metal poisoning;
  2. avoiding oxidation, which causes iron to lose its ferromagnetic properties.


Iron powder observations

Though most of our results focus on iron powder immersed in olive oil, here are a couple of brief observations on dry iron powder in a vial, interacting with a magnet.

General observations

As most people know, iron powder tends to form nice patterns in the presence of a strong magnetic field; the iron particles tend to line up along the field lines and form structures over several millimeters to centimeters, depending on the magnetic field strength. In our case, 1 or 2cm was about the limit of the structures we could form. Nonetheless, forming structures can be a lot of fun, especially when playing with the sample geometry, i.e. the confinement within a glass vial. This yields some cool-shaped structures, depending on whether the magnet is working along, against or perpendicularly to the gravitational force. This is a good way to keep kids busy for a while. :)

Coarse1.jpg Fine1.jpg

To the left, the spikes formed using 100-mesh iron powder (30 micron particles) vs the image to the right, showing the "finer" spikes formed using 325-mesh iron powder (10 micron particles).

Iron powder as a granular material

A very interesting observation we carefully noted and played around with a bit, was the following, made with dry iron powder in a glass vial. Proceed in the following order:

  1. place the vial in its original vertical position, with all iron powder at the bottom;
  2. lift up the vial;
  3. place the magnet under the vial, which causes all the powder to be attracted even more to the bottom of the vial, due to the combined strength of gravity and magnetism;
  4. turn the vial upside down while the magnet is still touching the same side, thus causing iron powder to be held upside down by magnetism, even though it's pulled down by gravity;
  5. slowly and very carefully remove the magnet, while holding the vial upside down steadily.

Vertical upside down.jpg


What we can observe, if the experience is carried out carefully, is that all the iron powder remains suspended at the top of the vial, even though the magnetic force has been removed from it and gravity should be pulling it down. This is not related to MR fluids at all, but shows some interesting jamming effects one can observe in granular materials. What we have observed in this simple experiment, is that the system can be stable at least over tens of hours in this state. It could be interesting to test the dependence of this stability on the thickness of the particle layer, the particle size and the diameter of the glass vial. But that's a whole other final project.

Sample preparation (cont'd)

After playing around with the dry iron powder vials for a few days at home and seeing the results described above, my team of experts and I unanimously decided, after seeing the cool pictures of ferrofluids online, to add some oil to this sample; so that's what we did. We added about 0.5mL of extra virgin olive oil to the roughly <math>0.5cm^3</math> of iron powder. Though we exceeded the typical 10-20% iron volume fraction people recommend for ferrofluids, the iron didn't seem to form too many clumps and our subsequent experiments worked just fine. Note that you wouldn't want to put a water-based fluid, because it would cause the oxidation of iron.

This is what the sample looked like after the additional of oil and some slow mixing; slow, due to the relatively high viscosity of the olive oil.


Vertical reference.jpg


Note that typical MR fluids or ferrofluids also require some surfactants as well to prevent particles from aggregating and forming permanent structures. However, to simplify sample preparation and because I didn't have any adequate surfactant, we decided to go without it, and still ended up having a blast with the sample as it was. The downside of not having the surfactant, was that after several hours of leaving the sample intact, there was a thin layer of oil floating at the top. But a few minutes of slow mixing made it all good.

If you are patient - and kids can be patient, sometimes -, you can position your vial horizontally and after a few minutes, have most or all of the fluid at the bottom, as illustrated below.


Horizontal no corrugations.jpg

Solidifying of the magnetic fluid

Why would you want to position your vial in a horizontal position? Well, the reason is quite simple. As explained above, MR fluids display cool properties when magnetic particles form, along the magnetic field lines, structures that span the whole thickness of the sample. That is what causes them to go from a fluid-like to solid-like state. The length and strength of these spanning structures inside a fluid is dependent on the strength of the applied magnetic field, and with a small toy-magnet, the field strength is only sufficient to create structures over a range of a few millimeters, so spreading out the ferrofluid was an essential part of some of our experimenting.

The strength of these structures can be seen in action with the magnet keeping the fluid from falling in the horizontal vial.


Horizontal upside down.jpg Vertical upside down.jpg


When placed in the vertical position, as seen above, the magnetic fluid has a thickness of roughly 1cm. The magnet was barely strong enough to hold the fluid in place when the vial was turned upside down in the vertical position, and sometimes a few drops of the oil were seen leaking down due to gravity, while the the rest of the magnetic fluid was held in place.

Formation of corrugations and mound

One common observation people make with ferrofluids and already described earlier, is that when the magnetic field is very strong, the fluid itself wants to align with the field lines, but is prevented to do so by gravity and surface tension effects. However, when the magnetic field is strong enough, an interesting phenomenon occurs, in which corrugations form on the surface of the fluid, which represent a balance between these three forces:

  • gravitational;
  • surface tension;
  • magnetic.

You can find many pictures of this "normal-field instability" posted on the internet, one of which [11] is here below:


Ferrofluid corrugations.jpg


We observed two related phenomena with our magnetic fluids:

First, we saw corrugations, when the magnet is pulling the magnetic fluid AGAINST the solid surface. Essentially, the same geometry as that of the magnet keeping the fluid from falling when the vial is upside down. This means that the magnet is effectively repelling some of these newly-formed structures and causing some particles to push against the fluid surface. The free surface energy and gravitational energy are increased, while the magnetic energy is decreased.


Horizontal corrugations.jpg


Second, when we use a geometry where the magnet is placed above the sample rather than under it, we observe the following: rather than multiple corrugations, we see one big hump of magnetic fluid slowly forming and moving up, gradually accelerating until it's as close to the magnet as it can be. Essentially, we see the formation of a mound of solidified magnetic fluid moving up toward the magnet. Interestingly, when we mix up the sample a bit and perform this test initially, the formation of the mound takes several seconds and appears slow; however, if we take away the magnet, don't mix the sample and repeat this experiment, the mound forms very quickly, typically in a second or so. So it appears that after the first mound formation, some pre-formed structures remain even after the magnet has been removed, which allows for quicker formation the second time.

It is also possible that the first mound formation locally changes the composition of the fluid, perhaps increasing the density of iron particles near the magnet even after it is removed. Such fluctuations in density would be expected to be less significant in the presence of a good surfactant, which we didn't include in our sample preparation. Moreover, it is expected that the shape of the mound will change with the addition of surfactant, due to the reduction in surface tension. It would be interesting to see if any type and amount of surfactant could cause us to see normal-field instability, i.e. multiple corrugations in this geometry as well.


Mound0.jpg Mound1.jpg Mound2.jpg

Suspended thin layers of magnetic fluid

One more cool observation on our magnetic fluid is the formation of what I call "suspended thin layers". Essentially, as long as the magnet's strength was felt, we typically saw a thin film - thickness on the order of 1mm - spanning the whole cross-section of the vial (~1cm^2). This film is stable over the course of at least an hour.

How is this done?


Thin film.jpg


Experimentally, it's quite simple:

  • begin with all the magnetic fluid on one side of the vial, by having the vial in a horizontal position and waiting for the fluid to settle;
  • bring the magnet against the fluid, toward the end of the vial;
  • while holding it against the vial, bring the magnet against the bottom end of the vial, and slide it across the vial diameter;
  • bring the magnet against the vial on the side across from that where most of the fluid lies; because a good amount magnetic fluid is following the magnet, it will force some of the fluid to detach from the surface and be suspended across the vial (see image above).

This effect looks particularly nice, because the magnetic fluid sheet has a shiny, silvery appearance to it; seeing it suspended in the vial looks cool. But perhaps it is not so unexpected, as once more, it is a competition between surface energy and magnetic energy. If the fluid-glass surface tension is comparable to fluid-air, then in fact, it is not unexpected at all to see something like this happen. But as soon as the magnetic field loses its strength locally, the magnetic fluid regains its fluid-like properties and "melts" in a very dramatic way over the course of a second or so, depending on the oil viscosity. It's fun to watch every time! A sequence of images from the first half-second shown below:


Falling04.jpg Falling05.jpg Falling06.jpg Falling07.jpg

In the pictures above, the magnet is not visible, but was in fact held between my fingers as I was moving them away. It was the only way I could get a consistent timelapse, without having the vial move around too much due to the attraction between the magnet and the iron.

Acknowledgements

My highly-qualified team of naturally curious scientists, with whom I was happy to collaborate and would gladly do such work again:


International experts.jpg


From left to right: my nieces Emma and Olivia from Switzerland, my daughter Sonia and son Milo.

More fun with ferrofluids

For higher quality (i.e. more stable) ferrofluids, you can get a nice kit with a couple of ounces of ferrofluid, a pipetter and a magnet on eBay for about $20 [12]. Similar deals can be found elsewhere on the internet, with specific quantities of fluid and accessories varying; it makes for a fun little gift for your geeky friends, or for yourself.

Additionally, though much of the description of the behavior of magnetic fluids is still phenomenological, there are some constitutive models out there, for those interested. For example, the recent work of Ciocanel et al. provides extensive equations that explain and predict some of MR fluids' behavior [13].


References

[1] http://www.springerlink.com/content/t461j211175wp11h

[2] http://www.brlsi.org/proceed05/postgrad0505.html

[3] http://www.ferrotec.com

[4] http://en.wikipedia.org/wiki/Smart_fluid

[5] http://simplyweb.blogspot.com/2007/05/lighthouse-skyscraper-4000-solar-panels.html

[6] http://frankschilling.typepad.com/my_weblog/2007/07/new-ferrari.html

[7] http://en.wikipedia.org/wiki/Ferrofluid#Applications

[8] http://en.wikipedia.org/wiki/Langmuir-Blodgett_trough

[9] http://www.seas.harvard.edu/projects/weitzlab

[10] http://en.wikipedia.org/wiki/Neodymium_magnet

[11] http://scienceblogs.com/moleculeoftheday/2006/09/ferrofluids.php

[12] http://cgi.ebay.com/Ferrofluid-Kit-Neodymium-Magnets-Dish-Dropper_W0QQitemZ120316670945QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item120316670945&_trksid=p3286.c0.m14&_trkparms=72:1205%7C66:2%7C65:12%7C39:1%7C240:1318%7C301:1%7C293:1%7C294:50

[13] http://www.springerlink.com/content/t461j211175wp11h