The Kaye effect is a neat phenomenon associated with falling shear-thinning non-Newtonian fluids like shampoo or hand soap. As the falling liquid piles up after hitting a solid surface, it ejects streams of fluid upwards. The effect usually only lasts for a few hundred milliseconds, but it is possible to see it at home without a high-speed camera if you pay close attention. More detailed physics of the effect are discussed in this previously featured video.
Paint vibrated on a loud speaker explodes in multi-colored jets and droplets. Most paints are shear-thinning non-Newtonian fluids (like ketchup, shampoo, or whipped cream), meaning that their viscosity decreases as they are sheared. This allows them to flow more readily once they are perturbed. #
Shear-thinning isn’t just confined to canned whipped cream. It’s also a feature of such non-Newtonian fluids as ketchup, shampoo, latex paint, and blood. The NASA research on shear-thinning the video author refers to is here and comes from the Critical Viscosity of Xenon-2 (CVX-2) experiment flown on the final mission of Columbia. Surprisingly, almost all of the experimental data was recovered from the crash. #
New fissures opened on Mount Kilauea in Hawaii earlier this month, resulting in some fountain-like eruptions of lava. This molten rock is a non-Newtonian fluid with shear-thinning and thixotropic properties. This is what allows the lava to flow long distances before it cools and solidifies. (via jpshoer)
Sure! The Oswald-de Waele relationship (a.k.a. a power-law fluid) is an attempt to generalize the relationship between shear stress and shear rate in fluids. For a Newtonian fluid, that relationship is linear:

This relationship describes many fluids—like air or water—very well. But there are plenty of non-Newtonian fluids as well, both shear-thinning (paint, shampoo, ketchup) and shear-thickening (oobleck). The Oswald-de Waele relationship approximates the behavior of these fluids using:

Values of n less than one correspond to shear-thinning (or pseudoplastic) fluids; a value greater than one is a shear-thickening (or dilatant) fluid. And n = 1 corresponds to a regular Newtonian fluid. #
Non-Newtonian fluids can also be shear-thinning like shampoo. These fluids exhibit a phenomenon known as the Kaye effect. #