Rheological behavior

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Introduction

The design of the earliest rheometers dictated the design of the earliest rheological experiments.

To measure non-Newtonian fluids, both the shear stress and the shear rate need to be known. Two experiments are common: the first is to control the shear rate, say by using a steady circular rotation with a Couette rheometer; the second is to control the shear stress and measure the shear rate, as in many modern rheometers.

In any case the experimental data is a plot of the shear rate against the shear stress.

Typical data and common empirical equations that fit the data are given:


Bingham

<math>\sigma =\sigma _{B}+\eta _{pl}\dot{\gamma }</math>

Casson

<math>\sigma =\left( \sqrt{\sigma _{C}}+\sqrt{\eta _{pl}\dot{\gamma }} \right)^{2}</math>

Herchel-Bulkley

<math>\sigma =\sigma _{HB}+\left( \eta _{pl}\dot{\gamma } \right)^{n}</math>

Morrison, Fig. 2.11
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-> Nice graph that summarized all the different types of flows from "Chemical and Functional Properties of Food Components" (By Zdzisław E. Sikorski)p.185

Table.jpg
[1]


The types of flow mentioned in the above figure can be briefly summarized as follows.

  • Newtonian: an "idea" liquid, where shear rate and shear stress are proportional. In other words, it always behaves like a liquid. Water is a good example of a Newtonian liquid.
  • Plastic: a material which can be made to flow with some critical amount of applied stress (the yield point), below which it will not flow at all. Therefore, once the stress is no longer applied, it will generally not flow back to its original configuration, and therefore can be "molded." Notice that the viscosity of a plastic decreases at higher shear stress. Typical examples are many plastics, or more interestingly, rocks and ice.
  • Pseudoplastic: Pseudoplastics exhibit behaviors both of Newtonian flow and plastic flow. The liquid flows as a plastic at high shear rates, but does not have a yield point and so will always flow under a shear stress, like a Newtonian liquid. This behavior is also called shear thinning: the more stress is applied, the more freely it flows. This is a useful property for materials like paint and nail polish, which you want to flow only when brushing it! Typical examples are ketchup, whipped cream, blood, paint, and nail polish.
  • Dilatant: These materials are also called shear thickening, since their viscosity increases as more shear stress is applied. A classic example of this is cornstarch and water. Some interesting applications include traction control and body armor, described below.


Random fact: The Deborah number is a dimensionless number that describes how fluid a material is. This stressed the importance of time scale in the definition of states. You can use the Deborah number to define whether the material can be categorized as a solid, liquid, or gas. I thought it was interesting that according to wikipedia, the origin of the name " coined by Prof. Markus Reiner, is the line "The mountains flowed before the Lord" in a song by prophetess Deborah recorded in the Bible (Judges 5:5)."

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Pseudoplastic flow

Morrison Fig. 2.7
Rheograms of 20 w% deionized kaolin slurries at several levels of tetrasodium pyrophosphate* addition. The figures on the curves indicate percent TSPP per weight of clay. An extrapolation of the linear region determines an apparent yield point.


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Dilatancy

Morrison Fig. 2.9
Rheograms for a series of curves of deflocculated paper-coating-grade clay, at weight-percent solids indicated, showing development of shear thickening behavior.

Application: Traction Control

From Wikipedia: Dilatant materials have certain industrial uses due to their shear thickening behavior. For example, some all wheel drive systems use a viscous coupling unit full of dilatant fluid to provide power transfer between front and rear wheels. On high traction road surfacing, the relative motion between primary and secondary drive wheels is the same, so the shear is low and little power is transferred. When the primary drive wheels start to slip, the shear increases, causing the fluid to thicken. As the fluid thickens, the torque transferred to the secondary drive wheels increases proportionally, until the maximum amount of power possible in the fully thickened state is transferred.

To the operator, this system is entirely passive, engaging all four wheels to drive when needed, and dropping back to two wheel drive once the need has passed. This system is generally used for on-road vehicles rather than off-road vehicles, since the maximum viscosity of the dilatant fluid limits the amount of torque that can be passed across the coupling.

Application: Body Armor

From Wikipedia: Various corporate and government entities are researching the application of shear thickening fluids for use as body armor. Such a system could allow the wearer flexibility for a normal range of movement, yet provide rigidity to resist piercing by bullets, stabbing knife blows, and similar attacks. The principle is similar to that of chainmail armor, though body armor using a dilatant would be much lighter and could be cut like cloth[citation needed]. The dilatant fluid would disperse the force of a sudden blow over a wider area of the user's body, reducing the blunt force trauma; against slow attacks, such as a slow but forceful stab, the dilatant would not provide any additional protection.

Two current examples of dilatant materials being used in personal protective equipment are d3o, and Active Protection System, manufactured by Dow Corning.

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Thixotropy

The dictionary definition of thixotropy is "a property of certain gels which liquefy when subjected to vibratory forces like simple shaking, and then solidify again when left standing." All in all, using scientific terms, thixotropy is the property of some non-Newtonian pseudoplastic fluids to show a time-dependent change in viscosity; the longer the fluid undergoes shear stress, the lower is its viscosity. A thixotropic fluid is a fluid which takes a finite time to attain equilibrium viscosity when introduced to a step change in shear rate. A thixotropic fluid displays a decrease in viscosity over time at a constant shear rate.

Morrison Fig. 2.12
Rheograms of a thixotropic system at different sweep rates. The "up" curves are measured at steadily increasing stresses and the down curves are measured at steadily decreasing shearing stresses. The are of the loop is a measure of thixotropic breakdown. The less rapid the cycling the less the thixotropy as more time is given for healing.

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Silly Putty: a classic example

The main structure of Silly Putty is polydimethylsiloxane,a polymer. These polymers form layers, which are linked together by boric acid. This cross-linking connects most of the polymers together, but not all of them, creating the possibility of movement when force is applied (the diagram to the right shows the boric-linked-polymers that make up Silly Putty.
alt text

The molecules that make up the polymers are covalently bonded, where as the molecules, themselves, are linked by hydrogen bonding to boric acid. When stress is applied to the putty the viscosity (resistance to flow) is affected. Silly Putty’s viscosity is not only dependent on temperature, but also stirring or spreading can also change it. This process causes the Silly Putty’s viscosity increases under increased stress. In rheological terms the Silly Putty can be explained as being distorted over a range of Deborah numbers.[2]

Silly Putty.jpg[3] Rheology: There are two mechanisms (and hence two characteristic time scales) at work in this material. The high molecular weight PDMS has a characteristic polymeric relaxation time, λrelax (defined by the time that a random walk allows the chain to relax from a stretched state through thermal vibrations). However due to the Boric acid there are also transient Boron mediated “crosslinks” arising from associating Boron linkages. These act to give the Silly Putty™ a behavior more like an elastic solid than a liquid. However since these “crosslinks” are dynamic (with a characteristic time, λassoc that is much shorter than λrelax) the material is not permanently locked in place and can consequently flow under the correct conditions. Therefore at time scales longer than λassoc the Silly Putty™ behaves like a high molecular weight polymeric fluid (with a characteristic relaxation time of λrelax). Over time scales much shorter than λassoc Silly Putty™ behaves like a crosslinked elastic solid.

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Quicksand

What is quicksand?

Quicksand is an interesting natural phenomenon -- it is actually solid ground that has been liquefied by a saturation of water. The "quick" refers to how easily the sand shifts when in this semiliquid state.

alt text

Quicksand is not a unique type of soil; it is usually just sand or another type of grainy soil. Quicksand is nothing more than a soupy mixture of sand and water. It can occur anywhere under the right conditions, according to Denise Dumouchelle, geologist with the United States Geological Survey (USGS).

Quicksand is created when water saturates an area of loose sand and the ordinary sand is agitated. When the water trapped in the batch of sand can't escape, it creates liquefied soil that can no longer support weight. There are two ways in which sand can become agitated enough to create quicksand:

  • Flowing underground water - The force of the upward water flow opposes the force of gravity, causing the granules of sand to be more buoyant.
  • Earthquakes - The force of the shaking ground can increase the pressure of shallow groundwater, which liquefies sand and silt deposits. The liquefied surface loses strength, causing buildings or other objects on that surface to sink or fall over.

Vibration tends to enhance the quickness, so what is reasonably solid initially may become soft and then quick, according to Dr. Larry Barron of the New South Wales Geological Survey.

The vibration plus the water barrier reduces the friction between the sand particles and causes the sand to behave like a liquid. To understand quicksand, you have to understand the process of liquefaction. When soil liquefies, as with quicksand, it loses strength and behaves like a viscous liquid rather than a solid, according to the Utah Geological Survey. Liquefaction can cause buildings to sink significantly during earthquakes.

While quicksand can occur in almost any location where water is present, there are certain locations where it's more prevalent. Places where quicksand is most likely to occur include:

  • Riverbanks
  • Beaches
  • Lake shorelines
  • Near underground springs
  • Marshes


How to get out of quicksand?

  1. Avoid quicksand. Any time you are in an area of wet ground, such as along beaches, marshes and rivers, or if you are in a place where underground springs bubble up, you might encounter quicksand. Be on the lookout for ground that appears unstable. Often, you can't detect quicksand just by looking at it. If you step on ground that ripples or shifts beneath you, step backward quickly and smoothly: quicksand usually takes a second or two before it liquefies.
  2. Walk softly and carry a big stick. When hiking, especially in an area you suspect contains quicksand, carry a long, stout pole. You can use the pole to test the ground in front of you, and you can also use it to help extract yourself should you sink (see step 9)
  3. Drop everything. Because your body is less dense than quicksand, you can't fully sink unless you panic and struggle too much (which will cause the sand to further liquefy) or you're weighed down by something heavy. If you step into quicksand and you're wearing a backpack or carrying something heavy, immediately take off your backpack or drop what you're carrying. If it's possible to get out of your shoes, do so; shoes, especially those with flat, inflexible soles (many boots, for example) create suction as you try to pull them out of quicksand. If you know ahead of time that you are highly likely to encounter quicksand, change out of your boots and either go barefoot or wear shoes that you can pull your feet out of easily.
  4. Relax. Quicksand usually isn't more than a couple feet deep, but if you do happen to come across a particularly deep spot, you could very well sink quite quickly down to your waist or chest. If you panic you can sink further, but if you relax, your body's buoyancy will cause you to float.
  5. Breathe deeply. Not only will deep breathing help you remain calm, it will also make you more buoyant. Keep as much air in your lungs as possible. It is impossible to "go under" if your lungs are full of air.
  6. Get on your back. If you sink up to your hips or higher, bend backward. The more you spread out your weight, the harder it will be to sink. Float on your back while you slowly and carefully extricate your legs. Once your legs are free you can inch yourself to safety by using your arms to slowly and smoothly propel yourself. If you are very near the edge of the quicksand, you can roll to hard ground.
  7. Take your time. If you're stuck in quicksand, frantic movements will only hurt your cause. Whatever you do, do it slowly. Slow movements will prevent you from agitating the quicksand—the vibrations caused by rapid movements can turn otherwise relatively firm ground into more quicksand. More importantly, quicksand can react unpredictably to your movements, and if you move slowly you can more easily stop an adverse reaction and, by doing so, avoid getting yourself stuck deeper. You're going to need to be patient; depending on how much quicksand is around you, it could take several minutes or even hours to slowly, methodically get yourself out.
  8. Get plenty of rest. Other than panic, exhaustion is your worst enemy. Since it can take a long time to get yourself out of quicksand, be sure to take breaks and just float on your back if you feel your muscles getting tired. If you're in a dangerous tidal zone, however, you may be in a race against time (see warning below).
  9. Use a stick (optional). A stick is not necessary to extricate yourself from quicksand, but it can be helpful if you have one.
    • As soon as you feel your ankles sink, lay the pole on the surface of the quicksand horizontally behind you.
    • Flop onto your back on top of the pole. After a minute or two, you will achieve balance in the quicksand, and you'll stop sinking.
    • Work the pole towards a new position, under your hips. The pole will prevent your hips from sinking, so you can slowly pull one leg free, then the other.
    • Stay flat on your back with your arms and legs fully touching the quicksand and use the pole as a guide. Inch sideways along the pole to firm ground.


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Novel Materials

Picture 15.png

Liquid Body Armor The term "liquid body armor" can be a little misleading. For some people, it brings to mind the idea of moving fluid sandwiched between two layers of solid material. However, both types of liquid armor in development work without a visible liquid layer. Instead, they use Kevlar that has been soaked in one of two fluids. The first is a shear-thickening fluid (STF), which behaves like a solid when it encounters mechanical stress or shear. In other words, it moves like a liquid until an object strikes or agitates it forcefully. Then, it hardens in a few milliseconds. This is the opposite of a shear-thinning fluid, like paint, which becomes thinner when it is agitated or shaken.

The fluid is a colloid, made of tiny particles suspended in a liquid. The particles repel each other slightly, so they float easily throughout the liquid without clumping together or settling to the bottom. But the energy of a sudden impact overwhelms the repulsive forces between the particles -- they stick together, forming masses called hydroclusters. When the energy from the impact dissipates, the particles begin to repel one another again. The hydroclusters fall apart, and the apparently solid substance reverts to a liquid.

The fluid used in body armor is made of silica particles suspended in polyethylene glycol. Silica is a component of sand and quartz, and polyethylene glycol is a polymer commonly used in laxatives and lubricants. The silica particles are only a few nanometers in diameter, so many reports describe this fluid as a form of nanotechnology.

To make liquid body armor using shear-thickening fluid, researchers first dilute the fluid in ethanol. They saturate the Kevlar with the diluted fluid and place it in an oven to evaporate the ethanol. The STF then permeates the Kevlar, and the Kevlar strands hold the particle-filled fluid in place. When an object strikes or stabs the Kevlar, the fluid immediately hardens, making the Kevlar stronger. The hardening process happens in mere milliseconds, and the armor becomes flexible again afterward.

In laboratory tests, STF-treated Kevlar is as flexible as plain, or neat, Kevlar. The difference is that it's stronger, so armor using STF requires fewer layers of material. Four layers of STF-treated Kevlar can dissipate the same amount of energy as 14 layers of neat Kevlar. In addition, STF-treated fibers don't stretch as far on impact as ordinary fibers, meaning that bullets don't penetrate as deeply into the armor or a person's tissue underneath. The researchers theorize that this is because it takes more energy for the bullet to stretch the STF-treated fibers.

Picture 16.png

Magnetorheological Fluid

The other fluid that can reinforce Kevlar armor is magnetorheological (MR) fluid. MR fluids are oils that are filled with iron particles. Often, surfactants surround the particles to protect them and help keep them suspended within the fluid. Typically, the iron particles comprise between 20 and 40 percent of the fluid's volume. The particles are tiny, measuring between 3 and 10 microns. However, they have a powerful effect on the fluid's consistency. When exposed to a magnetic field, the particles line up, thickening the fluid dramatically. The term "magnetorheological" comes from this effect. Rheology is a branch of mechanics that focuses on the relationship between force and the way a material changes shape. The force of magnetism can change both the shape and the viscosity of MR fluids.

The hardening process takes around twenty thousandths of a second. The effect can vary dramatically depending on the composition of the fluid and the size, shape and strength of the magnetic field. For example, MIT researchers started with spherical iron particles, which can slip past one another, even in the presence of the magnetic field. This limits how hard the armor can become, so researchers are studying other particle shapes that may be more effective.

As with STF, you can see what MR fluids look like using ordinary items. Iron filings mixed with oil create a good representation. When no magnetic field is present, the fluid moves easily. But the influence of a magnet can cause the fluid to become thicker or to take a shape other than that of its container. Sometimes, the difference is very visually dramatic, with the fluid forming distinctive peaks, troughs and other shapes. Artists have even used magnets and MR fluids or similar ferrofluids to create works of art.

With the right combination of density, particle shape and field strength, MR fluid can change from a liquid to a very thick solid. As with shear-thickening fluid, this change could dramatically increase the strength of a piece of armor. The trick is activating the fluid's change of state. Since magnets large enough to affect an entire suit would be heavy and impractical to carry around, researchers propose creating tiny circuits running throughout the armor.With the right combination of density, particle shape and field strength, MR fluid can change from a liquid to a very thick solid. As with shear-thickening fluid, this change could dramatically increase the strength of a piece of armor. The trick is activating the fluid's change of state. Since magnets large enough to affect an entire suit would be heavy and impractical to carry around, researchers propose creating tiny circuits running throughout the armor.

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d3o

This is adilatant material developed by the British company d3o Lab. This lightweight material is very flexible and malleable, until subjected to abrupt force, making it useful in protective clothing in situations where the wearer may be exposed to blunt trauma. Recently, the material has been used in the production of protective garments used by US and Canadian skiers during the 2006 Winter Olympic Games. Since 2005 d3o has been incorporated in several product ranges:

- Within the snowsports market d3o has been used by Olympic GS in racing suits for the US and Canadian teams, outerwear in jackets and pants, base layers, beanies and gloves Football (soccer) shin guards and goalkeeping gloves have been developed by Sells Goalkeeper Products

- Integrated into motorcycle gloves for protection of the back of the hands and the knuckles

- Early building blocks of molecular armor

- A d3o skin is available on the Apple Store to protect iPhone 3G.