The higher the shear stress needed to cause the liquid to deform (flow), the higher the viscosity of the liquid.

The viscosity of different materials changes according to temperature, pressure, and sometimes shear stress. The viscosity of water is lowered by temperature and raised by pressure, but shear stress does not affect it. Honey has a similar viscosity relation with temperature: The hotter the honey, the lower its viscosity. Honey is 200 times less viscous at 160°F (70°C) than it is at 57°F (14°C). For glass, imagine its behavior at the glasshouse. Glass is technically a liquid even at room temperature, because its molecules are not organized into crystals. The flowing glass the glassblower works with is simply the result of high temperatures creating low viscosity. In rock-forming minerals, temperature drastically lowers viscosity, pressure raises it moderately, and shear stress lowers it, as shown in the accompanying figure.

Latex house paint is a good example of a material with shear-stress dependent viscosity. When painting it on with the brush, the brush applies shear stress to the paint, and its viscosity goes down. This allows the paint to be brushed on evenly. As soon as the shear stress is removed, the paint becomes more viscous and resists dripping. This is a material property that the paint companies purposefully give the paint to make it perform better. Materials that flow more easily when under shear stress but then return to a high viscosity when undisturbed are called thixotropic. Some strange materials, called dilatent materials, actually obtain higher viscosity when placed under shear stress. The most common example of a dilatent


These graphs show the relationship of fluid flow to shear stress for different types of materials, showing how viscosity can change in the material with increased shear stress.

Relation of Fluid Flow with Shear Stress

Newtonian viscosity

Recall that viscosity (T)) is defined as shear stress (O) divided by shear rate (£):

and so the slopes of these lines show the viscosities of the materials being graphed.

Shear stress

Shear stress divided by shear rate is constant: Viscosity does not depend upon shear stress.

Shear rate

Bingham plastic viscosity

Power-law viscosity

Low viscosity

Shear stress

Materials called Bingham plastics do not begin to flow until a certain threshold stress is applied.

Shear stress

Mantle materials have •¡J^/ stess-dependent viscosities: The / higher the stress, the lower their viscosity becomes and the Faster they shear (deform).

Shear rate

Shear rate

Rheology, or How Solids Can Flow (continued) material is a mixture of cornstarch and water. This mixture can be poured like a fluid and will flow slowly when left alone, but when pressed it immediately becomes hard, stops flowing, and cracks in a brittle manner. The viscosities of other materials do not change with stress: Their shear rate (flow rate) increases exactly with shear stress, maintaining a constant viscosity.

Temperature is by far the most important control on viscosity. Inside the Earth's upper mantle, where temperatures vary from about 2,000°F (1,100oC) to 2,500°F (1,400oC), the solid rocks are as much as 10 or 20 orders of magnitude less viscous than they are at room temperature. They are still solid, crystalline materials, but given enough time, they can flow like a thick liquid. The mantle flows for a number of reasons. Heating in the planet's interior makes warmer pieces of mantle move upward buoyantly, and parts that have cooled near the surface are denser and sink. The plates are also moving over the surface of the planet, dragging the upper mantle with them (this exerts shear stress on the upper mantle). The mantle flows in response to these and other forces at the rate of about one to four inches per year (2 to 10 cm per year).

Rocks on the planet's surface are much too cold to flow. If placed under pressure, cold, brittle surface rocks will fracture, not flow. Ice and hot rocks can flow because of their viscosities. Fluids flow by molecules sliding past each other, but the flow of solids is more complicated. The individual mineral grains in the mantle may flow by "dislocation creep," in which flaws in the crystals migrate across the crystals and effectively allow the crystal to deform or move slightly. This and other flow mechanisms for solids are called plastic deformations, since the crystals neither return to their original shape nor break.

of years ago.The smallest features discernable in the images are about 10 feet (3 m) across.

Callisto is large enough that it should be at least partly differentiated, based on a combination of its size and the coldness of its position in the solar system. Callisto has the lowest density of any of Jupiter's satellites (114 lb/ft3, or 1,800 kg/m3).This very low density implies that the moon consists mainly of ices and contains less rock than some of Jupiter's other moons. Callisto is thought to have an icy crust about 125 miles (200 km) thick, possibly underlain by a salty liquid ocean. The center of the planet is thought to be a combination of ices and rock, with no differentiated iron core.

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