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A dilatant (/dˈltənt/, /dɪ-/) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.

A dilatant is a non-Newtonian fluid where the shear viscosity increases with applied shear stress. 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 and Van der Waals forces 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. 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 and water[1] (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 directly underfoot.[2]

Rheopecty 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

A dilatant is a non-Newtonian fluid where the shear viscosity increases with applied shear stress. 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 and Van der Waals forces 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. 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 and water[1] (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 directly underfoot.[2]

Rheopecty is a similar prope

This can readily be seen with a mixture of cornstarch and water[1] (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 directly underfoot.[2]

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

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 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.[3] 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.[4]

Viscosity of a solution as a function of shear rate is given via the Power Law equation,[5] where η is the viscosity, K is a material-based constant, and γ̇ is the applied shear rate.

${\displaystyle \eta =K{\dot {\gamma }}^{n-1}}$

Dilatant behavior occurs when n is greater than 1.

Below is a table of viscosity values for some common materials.[6][7][8]

### StaBelow is a table of viscosity values for some common materials.[6][7][8] A suspension 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 in that they are unstable; the solid particles in dispersion are sufficiently large for sedimentation, 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. Energy of repulsion as a function of particle separation 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 suIn 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 describes the attraction between bodies, such as particulates. It was realized that the explanation of Van der Waals forces 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 HamakeHamaker theory describes the attraction between bodies, such as particulates. It was realized that the explanation of Van der Waals forces 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. 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. ${\displaystyle V=\pi R\left({\frac {-H}{12\pi h^{2}}}+{\frac {64CkT\Gamma ^{2}e^{\kappa }h}{\kappa ^{2}}}\right),}$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 kelvins, ${\displaystyle \Gamma }$ = surface excess, ${\displaystyle \kappa }$ = inverse Debye length. Sterically stabilized suspensions 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.[9]

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.[10]

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.