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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).
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