Dilatant
Encyclopedia
A dilatant material is one in which viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 increases with the rate of shear strain. Such a shear thickening fluid, also known by the acronym STF, is an example of a non-Newtonian fluid
Non-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

.
A shear thickening fluid, also called a dilatant, is a Non-Newtonian fluid
Non-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

 where the shear viscosity increases with applied shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

. This behavior is only one type of deviation from Newton’s Law, and it is controlled by such factors as particle size, shape, and distribution. The properties of these suspensions depend on Hamaker theory
Hamaker theory
After the explanation of van der Waals forces by Fritz London several scientists soon realised that his definition could be extended from the interaction of two molecules with induced dipoles to macro-scale objects by summing all of the forces between the molecules in each of the bodies involved. ...

 and Van der Waals force
Van der Waals force
In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

s and can be stabilized electrostatically or sterically. Shear thickening behavior occurs when a colloidal suspension transitions from a stable state to a state of flocculation. Such behavior is currently being researched for use in body armor applications by companies like Dow Corning
Dow Corning
Dow Corning is a multinational corporation headquartered in Midland, Michigan, USA. Dow Corning specializes in silicon and silicone-based technology, offering more than 7,000 products and services...

 with their Active Protection System. A large portion of the properties of these systems are due to the surface chemistry of particles in dispersion, known as colloids.

This can readily be seen with a mixture of cornstarch
Cornstarch
Corn starch, cornstarch, cornflour or maize starch is the starch of the corn grain obtained from the endosperm of the corn kernel.-History:...

 and water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

 (sometimes called oobleck), which acts in counterintuitive ways when struck or thrown against a surface. Sand that is completely soaked with water also behaves as a dilatant material. This is the reason why when walking on wet sand, a dry area appears underneath your foot.
  • Rheopecty
    Rheopecty
    Rheopecty or rheopexy is the rare property of some non-Newtonian fluids to show a time-dependent change in viscosity; the longer the fluid undergoes shearing force, the higher its viscosity. Rheopectic fluids, such as some lubricants, thicken or solidify when shaken...

     is a similar property in which viscosity increases with cumulative stress or agitation over time.
  • The opposite of a dilatant material is a pseudoplastic.

Definitions

There are two types of deviation from Newton's Law that are observed in real systems. The most common deviation is shear thinning behavior, where the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 of the system decreases as the shear rate is increased. The second deviation is shear thickening behavior where, as the shear rate is increased, the viscosity of the system also increases. This behavior is observed because the system crystallizes under stress and behaves more like a solid than a solution. Thus, the viscosity of a shear-thickening fluid is dependent on the shear rate. The presence of suspended particles often affects the viscosity of a solution. In fact, with the right particles, even a Newtonian fluid can exhibit non-Newtonian behavior. An example of this is cornstarch in water and is included in the Examples section below.

The parameters that control shear thickening behavior are: particle size and particle size distribution, particle volume fraction, particle shape, particle-particle interaction, continuous phase viscosity, and the type, rate, and time of deformation. In addition to these parameters, all shear thickening fluids are stabilized suspensions and have a volume fraction of solid that is relatively high.

Viscosity of a solution as a function of shear rate is given via the Power Law equation, where η is the viscosity, K is a material-based constant, and γ̇ is the applied shear rate.


Dilatant behavior occurs when n is greater than 1.

Below is a table of viscosity values for some common materials.
Material Viscosity (cP)
Benzene 601
Carbon Tetrachloride 880
Ethanol 1,060
Mercury 1,550
Pentane 2,240
Sulfuric Acid 27,000
Water at 298K 1–5
Water at 460K 1 to 5
Blood 10
Anti-Freeze 14
Maple Syrup 150–200
Honey 2,000–3,000
Chocolate Syrup 10,000–25,000
Peanut Butter 150,000–250,000
Ketchup 50,000–70,000

Stabilized suspensions

A suspension (chemistry)
Suspension (chemistry)
In chemistry, a suspension is a heterogeneous fluid containing solid particles that are sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The internal phase is dispersed throughout the external phase through mechanical agitation, with the use of certain...

 is composed of a fine, particulate phase dispersed throughout a differing, heterogeneous phase. Shear-thickening behavior is observed in systems with a solid, particulate phase dispersed within a liquid phase. These solutions are different from a Colloid
Colloid
A colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...

 in that they are unstable; the solid particles in dispersion are sufficiently large for Sedimentation
Sedimentation
Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained, and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration...

, causing them to eventually settle. Whereas the solids dispersed within a colloid are smaller and will not settle. There are multiple methods for stabilizing suspensions, including electrostatics and sterics.

In an unstable suspension, the dispersed, particulate phase will come out of solution in response to forces acting upon the particles, such as gravity or Hamaker attraction. The magnitude of the effect these forces have on pulling the particulate phase out of solution is proportional to the size of the particulates; for a large particulate, the gravitational forces are greater than the particle-particle interactions, whereas the opposite is true for small particulates. Shear thickening behavior is typically observed in suspensions of small, solid particulates, indicating that the particle-particle Hamaker attraction is the dominant force. Therefore, stabilizing a suspension is dependent upon introducing a counteractive repulsive force.

Hamaker theory
Hamaker theory
After the explanation of van der Waals forces by Fritz London several scientists soon realised that his definition could be extended from the interaction of two molecules with induced dipoles to macro-scale objects by summing all of the forces between the molecules in each of the bodies involved. ...

 describes the attraction between bodies, such as particulates. It was realized that the explanation of Van der Waals force
Van der Waals force
In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

s could be upscaled from explaining the interaction between two molecules with induced dipoles to macro-scale bodies by summing all the intermolecular forces between the bodies. Similar to Van der Waals forces, Hamaker theory describes the magnitude of the particle-particle interaction as inversely proportional to the square of the distance. Therefore, many stabilized suspensions incorporate a long-range repulsive force that is dominant over Hamaker attraction when the interacting bodies are at a sufficient distance, effectively preventing the bodies from approaching one another. However, at short distances, the Hamaker attraction dominates, causing the particulates to coagulate and fall out of solution. Two common long-range forces used in stabilizing suspensions are electrostatics and sterics.

Electrostatically-stabilized suspensions

Suspensions of similarly charged particles dispersed in a liquid electrolyte are stabilized through an effect described by the Helmholtz double layer model. The model has two layers. The first layer is the charged surface of the particle, which creates an electrostatic field that affects the ions in the electrolyte. In response, the ions create a diffuse layer of equal and opposite charge, effectively rendering the surface charge neutral. However, the diffuse layer creates a potential surrounding the particle that differs from the bulk electrolyte.

The diffuse layer serves as the long-range force for stabilization of the particles. When particles near one another, the diffuse layer of one particle overlaps with that of the other particle, generating a repulsive force. The following equation provides the energy between two colloids as a result of the Hamaker interactions and electrostatic repulsion.



Where:

V = Energy between a pair of colloids

R = Radius of colloids

-H = Hamaker constant between colloid and solvent

h = Distance between colloids

C = Surface ion concentration

k = Boltzmann constant

T = Temperature in Kelvin

= Surface excess

= Inverse Debye length

Sterically-stabilized suspensions

Different from elecrostatics, sterically-stabilized suspensions rely on the physical interaction of polymer chains attached to the surface of the particles to keep the suspension stabilized; the adsorbed polymer chains act as a spacer to keep the suspended particles separated at a sufficient distance to prevent the Hamaker attraction from dominating and pulling the particles out of suspension. The polymers are typically either grafted or adsorbed onto the surface of the particle. With grafted polymers, the backbone of the polymer chain is covalently bonded to the particle surface. Whereas an adsorbed polymer is a copolymer composed of lyophobic and lyophilic region, where the lyophobic region non-covalently adheres to the particle surface and the lyophilic region forms the steric boundary or spacer.

Theories behind shear thickening behavior

Dilatancy in a colloid, or its ability to order in the presence of shear forces is dependent on the ratio of interparticle forces. As long as interparticle forces such as Van der Waals forces dominate, the suspended particles remain in ordered layers. However, once shear forces dominate, particles enter a state of flocculation and are no longer held in suspension; they begin to behave like a solid. When the shear forces are removed, the particles spread apart and once again form a stable suspension. This is opposite of the shear thinning effect where the suspension is initially in the state of flocculation and becomes stable when a stress is applied.
Shear thickening behavior is highly dependent upon the volume fraction of solid particulate suspended within the liquid. The higher the volume fraction, the less shear required to initiate the shear thickening behavior. The shear rate at which the fluid transitions from a Newtonian flow to a shear thickening behavior is known as the critical shear rate.

Order to disorder transition

When shearing a concentrated stabilized solution at a relatively low shear rate, the repulsive particle-particle interactions keep the particles in an ordered, layered, equilibrium structure. However, at shear rates elevated above the critical shear rate, the shear forces pushing the particles together overcome the repulsive particle-particle interactions, forcing the particles out of their equilibrium positions. This leads to a disordered structure, causing an increase in viscosity.

The critical shear rate here is defined as the shear rate at which the shear forces pushing the particles together are equivalent to the repulsive particle interactions.

Hydroclustering

When the particles of a stabilized suspension transition from an immobile state to mobile state, small groupings of particles form hydroclusters, increasing the viscosity. These hydroclusters are composed of particles momentarily compressed together, forming a irregular, rod-like chain of particles akin to a logjam or traffic jam. In theory the particles have extremely small interparticle gaps, rendering this momentary, transient hydrocluster as incompressible. It is possible that additional hydroclusters will form through aggregation.

Silly Putty

An integral part of many childhoods, Silly Putty was first made from silicone oil and boric acid during World War II in an attempt to make synthetic rubber. This material can stretch without tearing yet parts can be broken off, it has a rebound of 80% when bounced like a ball, and even keeps its shape when hit with hammer yet it flattened by a child's palm.

Corn Starch and Water (Oobleck)

Cornstarch is a common thickening agent used in cooking. It is also a very good example of a shear thickening system. When a force is applied to a 1:2.5 mixture of water and cornstarch, the cornstarch acts as a solid and resists the force. For a great demo of this behavior, check out this video.

Silica and poly(ethylene glycol)

Silica nano-particles are dispersed in a solution of poly(ethylene glycol). The Silica particles provide a high strength material when flocculation occurs. This allows it to be used in applications such as liquid body armor and brake pads.

Traction control

Dilatant materials have certain industrial uses due to their shear thickening behavior. For example, some all wheel drive systems use a viscous coupling unit
Viscous coupling unit
A viscous coupling is a mechanical device which transfers torque and rotation by the medium of a viscous fluid. It is made of a number of circular plates with tabs or perforations, fitted very close to each other in a sealed drum. Alternate plates are connected to a driving shaft at one end of the...

 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
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

 transferred to the secondary drive wheels increases proportionally, until the maximum amount of power possible in the fully thickened state is transferred. See also: limited slip differential
Limited slip differential
A limited slip differential is a type of differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical bound on the disparity...

, some types of which operate on the same principle.....
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.

Body armor

Various corporate and government entities are researching the application of shear thickening fluids for use as body armor
Bulletproof vest
A ballistic vest, bulletproof vest or bullet-resistant vest is an item of personal armor that helps absorb the impact from firearm-fired projectiles and shrapnel from explosions, and is worn on the torso...

. Such a system could allow the wearer flexibility for a normal range of movement, yet provide rigidity to resist piercing by bullet
Bullet
A bullet is a projectile propelled by a firearm, sling, or air gun. Bullets do not normally contain explosives, but damage the intended target by impact and penetration...

s, stabbing knife
Knife
A knife is a cutting tool with an exposed cutting edge or blade, hand-held or otherwise, with or without a handle. Knives were used at least two-and-a-half million years ago, as evidenced by the Oldowan tools...

 blows, and similar attacks. The principle is similar to that of mail
Mail (armour)
Mail is a type of armour consisting of small metal rings linked together in a pattern to form a mesh.-History:Mail was a highly successful type of armour and was used by nearly every metalworking culture....

 armor, though body armor using a dilatant would be much lighter. 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. However, against slow attacks which would allow flow to occur, such as a slow but forceful stab, the dilatant would not provide any additional protection.

In one study, standard Kevlar
Kevlar
Kevlar is the registered trademark for a para-aramid synthetic fiber, related to other aramids such as Nomex and Technora. Developed at DuPont in 1965, this high strength material was first commercially used in the early 1970s as a replacement for steel in racing tires...

 fabric was compared to a composite armor of Kevlar and a proprietary shear-thickening fluid. The results showed that the Kevlar/fluid combination performed better than the pure-Kevlar material, despite having less than one-third the Kevlar thickness.

Two current examples of dilatant materials being used in personal protective equipment are d3o
D3o
D3O formally "D3o" is a dilatant material commonly used for impact protection. It has been categorized into smart fabrics and intelligent textiles by the Research and Markets....

, and Active Protection System, manufactured by Dow Corning
Dow Corning
Dow Corning is a multinational corporation headquartered in Midland, Michigan, USA. Dow Corning specializes in silicon and silicone-based technology, offering more than 7,000 products and services...

.

See also

  • Newtonian Fluid
    Newtonian fluid
    A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...

  • Non-Newtonian fluid
    Non-Newtonian fluid
    A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

  • Bingham plastic
    Bingham plastic
    A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form....

  • Colloid
    Colloid
    A colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...

  • Double layer (interfacial)
    Double layer (interfacial)
    A double layer is a structure that appears on the surface of an object when it is placed into a liquid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The DL refers to two parallel layers of charge surrounding the object...

  • Rheology
    Rheology
    Rheology is the study of the flow of matter, primarily in the liquid state, but also as 'soft solids' or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force....

  • DLVO theory
    DLVO theory
    The DLVO theory is named after Derjaguin and Landau, Verwey and Overbeek.The theory describes the force between charged surfaces interacting through a liquid medium....

  • Hamaker theory
    Hamaker theory
    After the explanation of van der Waals forces by Fritz London several scientists soon realised that his definition could be extended from the interaction of two molecules with induced dipoles to macro-scale objects by summing all of the forces between the molecules in each of the bodies involved. ...

  • Suspension (chemistry)
    Suspension (chemistry)
    In chemistry, a suspension is a heterogeneous fluid containing solid particles that are sufficiently large for sedimentation. Usually they must be larger than 1 micrometer. The internal phase is dispersed throughout the external phase through mechanical agitation, with the use of certain...

  • Power-law fluid
    Power-law fluid
    A Power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid for which the shear stress, τ, is given by\tau = K \left^n where:...

  • Pseudoplastic
  • Silly Putty
    Silly Putty
    Silly Putty , is the Crayola-owned trademark name for a class of silicone polymers. It is marketed today as a toy for children, but was originally created by accident during research into potential rubber substitutes for use by the United States in World War II...

  • Thixotropy
    Thixotropy
    Thixotropy is the property of certain gels or fluids that are thick under normal conditions, but flow over time when shaken, agitated, or otherwise stressed...

  • Liquid Armor
    Liquid Armor
    Liquid Armor is a material under research by United States Army Research Laboratory . It is liquid under low or normal pressure and solid under high pressure. This liquid is made with polyethylene glycol and the solid part is made of nano-particles of silica...

  • d3o
    D3o
    D3O formally "D3o" is a dilatant material commonly used for impact protection. It has been categorized into smart fabrics and intelligent textiles by the Research and Markets....


External links

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