# non-Newtonian fluid

Also found in: Wikipedia.

## Non-newtonian fluid

A fluid that departs from the classic linear newtonian relation between stress and shear rate. In a strict sense, a fluid is any state of matter that is not a solid, and a solid is a state of matter that has a unique stress-free state. A conceptually simpler definition is that a fluid is capable of attaining the shape of its container and retaining that shape for all time in the absence of external forces. Therefore, fluids encompass a wide variety of states of matter including gases and liquids as well as many more esoteric states (for example, plasmas, liquid crystals, and foams). See Fluids, Plasma (physics)

A newtonian fluid is one whose mechanical behavior is characterized by a single function of temperature, the viscosity, a measure of the “slipperiness” of the fluid. For the example of Fig. 1, where a fluid is sheared between a fixed plate and a moving plate, the viscosity is given by Eq. (1).

(1)
Thus, as the viscosity of a fluid increases, it requires a larger force to move the top plate at a given velocity. For simple, newtonian fluids, the viscosity is a constant dependent on only temperature; but for non-newtonian fluids, the viscosity can change by many orders of magnitude as the shear rate (velocity/height in Fig. 1) changes. Typically, the viscosity (&eegr;) of these fluids is given as a function of the shear rate ().A common dependence for this function is given in Fig. 2. For other non-newtonian fluids, the viscosity might increase as the shear rate increases (shear-thickening fluids). See Newtonian fluid, Viscosity

Steady shear flow of a fluid between a fixed plate and a parallel plate, illustrating the concept of viscosity
Typical dependence of the viscosity (&eegr;) on shear rate ( ) for a non-newtonian fluid (Carreau model)

Many of the fluids encountered in everyday life (such as water, air, gasoline, and honey) are adequately described as being newtonian, but there are even more that are not. Common examples include mayonnaise, peanut butter, toothpaste, egg whites, liquid soaps, and multigrade engine oils. Other examples such as molten polymers and slurries are of considerable technological importance. A distinguishing feature of many non-newtonian fluids is that they have microscopic or molecular-level structures that can be rearranged substantially in flow.

Our intuitive understanding of how fluids behave and flow is built primarily from observations and experiences with newtonian fluids. However, non-newtonian fluids display a rich variety of behavior that is often in dramatic contrast to these expectations. For example, an intuitive feel for the slipperiness of fluids can be gained from rubbing them between the fingers. Furthermore, the slipperiness of water, experienced in this way, is expected to be the same as the slipperiness of automobile tires on a wet road. However, the slipperiness (viscosity) of many non-newtonian fluids changes a great deal depending on how fast they move or the forces applied to them.

Intuitive expectations for how the surface of a fluid will deform when the fluid is stirred (with the fluid bunching up at the wall of the container) are also in marked contrast to the behavior of non-newtonian fluids. When a cylindrical rod is rotated inside a container of a newtonian fluid, centrifugal forces cause the fluid to be higher at the wall. However, for non-newtonian fluids, the normal stress differences cause the fluid to climb the rod; this is called the Weissenberg effect. Intuitive understanding about the motion of material when the flow of a fluid is suddenly stopped, for example, by turning off a water tap, is also notably at odds with the behavior of non-newtonian fluids. See Centrifugal force

A non-newtonian fluid also displays counterintuitive behavior when it is extruded from an opening. A newtonian fluid tapers to a smaller cross section as it leaves the opening, but the cross section for a non-newtonian fluid first increases before it eventually tapers. This phenomenon is called die swell.

When a newtonian fluid is siphoned and the fluid level goes below the entrance to the siphon tube, the siphoning action stops. For many non-newtonian fluids, however, the siphoning action continues as the fluid climbs from the surface and continues to enter the tube. This phenomenon is called the tubeless siphon.

Perhaps the most striking behavior of non-newtonian fluids is a consequence of their viscoelasticity. Solids can be thought of as having perfect memory. If they are deformed through the action of a force, they return to their original shape when the force is removed. This happens when a rubber ball bounces; the ball is deformed as it hits a surface, but the rubber remembers its undeformed spherical shape. Recovery of the shape causes the ball to bounce back. In contrast, newtonian fluids have no memory; when a force is removed, they retain their condition at the time the force is removed (or continue moving as the result of inertia). When a newtonian fluid is dropped onto a surface, it does not bounce. Non-newtonian fluids are viscoelastic in the sense that they have fading memory. If a force is removed shortly after it is applied, the fluid will remember its undeformed shape and return toward it. However, if the force is applied on the fluid for a long time, the fluid will eventually forget its undeformed shape. If a sample of a non-newtonian fluid is dropped onto a surface, it will bounce like a ball. However, if the fluid is simply placed on the surface, it will flow smoothly. Viscoelasticity is frequently the cause of many of the secondary flows that are observed for non-newtonian fluids. These are fluid motions that are small for newtonian fluids (for example, swirling motions) but can become dominant for non-newtonian fluids.

Analysis of fluid flow operations is typically performed by examining local conservation relations—conservation of mass, momentum (Newton's second law), and energy. This analysis requires material-specific information (for example, the relation between density, pressure, and temperature) that is collectively known as constitutive relations. The science devoted to obtaining suitable constitutive equations for description of the behavior of non-newtonian fluids is called rheology. The most important constitutive equation for fluid mechanics is that relating the stress in the fluid to the kinematics of the motion (that is, the velocity, the derivatives of the velocity with respect to position, and the time history of the velocity).

Although the non-newtonian behavior of many fluids has been recognized for a long time, the science of rheology is, in many respects, still in its infancy, and new phenomena are constantly being discovered and new theories proposed. Advancements in computational techniques are making possible much more detailed analyses of complex flows and more sophisticated simulations of the structural and molecular behavior that gives rise to non-newtonian behavior. Engineers, chemists, physicists, and mathematicians are actively pursuing research in rheology, particularly as more technologically important materials are found to display non-newtonian behavior. See Rheology

## non-Newtonian fluid

[‚nän·nü′tō·nē·ən ′flü·əd]
(fluid mechanics)
A fluid whose flow behavior departs from that of a Newtonian fluid, so that the rate of shear is not proportional to the corresponding stress. Also known as non-Newtonian system.
References in periodicals archive ?
Guo and colleagues collect and summarize the mathematical theories of non-Newtonian fluid evolution equations, emphasizing various modern approaches and recent developments for researchers and graduate and undergraduate students in fields where such fluids appear, such as biology, physics, and aviation.
Nanoparticles of various materials have a "substantial" impact on the thermal conductivity of non-Newtonian fluid. When added to viscoelastic polydimethylsiloxane non-Newtonian nanofluid flowing around a vertical cone, the fluid's heat transfer increased.
Roussel, "Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: a lattice Boltzmann approach," Journal of Non-Newtonian Fluid Mechanics, vol.
where [u.sub.i] and [F.sup.ext.sub.i] denote, respectively, velocity component of fluid and the external force, p is the fluid pressure, [[rho].sub.f] is the fluid density, and [mu] is the viscosity of the non-Newtonian fluid based on the Carreau model; i.e.,
Rozanova, "Nonexistence results for a compressible non-Newtonian fluid with magnetic effects in the whole space," Journal of Mathematical Analysis and Applications, vol.
A pulsatile flow with non-Newtonian fluid model has not been attempted thus far/yet and it is suggested that this improved method of approach with abovementioned modelling parameters would provide a more accurate estimation of WSS values.
The prize was launched to mark the 40th anniversary of the Journal of Non-Newtonian Fluid Mechanics.
[39] examined the numerical solution for mixed convection boundary layer flow of Casson non-Newtonian fluid about a solid sphere in the presence of thermal and solutal slip conditions.
Within the last thirty years, the study of non-Newtonian fluid flow over a stretching surface has received significant attention due to its industrial applications.
Kahraman and Yuriisoy [4] applied the same approach to study the heat irreversibility in non-Newtonian fluid flow through pipes.
In his other 'crush' videos, which drew millions of views, his machine has obliterated a mighty bearing ball, silver coins, two repelling neodymium magnets, non-Newtonian fluid and reinforced sand, among others.
The Ladyzenskaya [21] model of non-Newtonian fluid dynamics can be formulated in the most general vectorial form of

Site: Follow: Share:
Open / Close