A non-Newtonian fluid is a fluid whose viscosity is variable based on applied stress. The most commonly known fluid of this kind is cornstarch dissolved in water. Contrast with Newtonian fluids like water, whose behavior can be described exclusively by temperature and pressure, not the forces acting on it from second to second. These fluids are fascinating substances that can be used to help us understand physics in more detail, in an exciting, hands-on way.
If you punch a bucket full of a shear thickening non-Newtonian fluid, the stress introduced by the incoming force causes the atoms in the fluid to rearrange so that it behaves like a solid. Your hand will not go through. If you shove your hand into the fluid slowly, however, it will penetrate successfully. If you pull your hand out abruptly, it will again behave like a solid, and you can literally pull a bucket of the fluid out of its container in this way.
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A shear thinning non-Newtonian fluid behaves in the opposite way. In this type, the fluid becomes thinner, rather than thicker, when stress is applied. Also called pseudoplastic, examples of this type of fluid include ketchup, toothpaste, and paint. The effect doesn't usually last for long in either type, continuing only as long as the stress is applied.
Non-Newtonian fluids help us understand the wide variety of fluids that exist in the physical world. Plastic solids, power-law fluids, viscoelastic fluids, and time-dependent viscosity fluids are others that exhibit complex and counterintuitive relationships between shear stress and viscosity/elasticity. However, non-Newtonian fluid is probably the most exciting to play with.
A search for non-Newtonian fluid on YouTube brings up some interesting results. On several game shows, hosts or contestants run across big vats of shear thickening non-Newtonian fluid, able to traverse them unless they stop - in which case they sink immediately. When combined with a oscillating plate, these fluids demonstrate other unusual properties, like protruding "fingers" and holes that persist after creating them. An oscillating plate applies stress on a periodic basis, rapidly changing the viscosity of the fluid and putting it in an odd middle ground between a liquid and a solid.
A practical application for shear thickening non-Newtonian fluids may be in body armor of the future. Since such fluids are usually flexible, they would allow soldiers to move freely when not under attack. But if confronted with a speeding bullet, they would quickly harder, performing like traditional armor. More research is necessary to see if non-Newtonian fluids are suitable for the military, but until then, it's sure fun to play with.