Mix cornflour with water to a thick consitency, that's a non Newtonian fluid, it will flow slowly, but if you try and strir it quickly it will crack like a solid. Have you never made custard or gravy?
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The non Newtonian fluids are studied by a science named "rheology". It comes from the Greek word for flowing.
If you look under it you find informations. One of most known models is the Bingham model which says that as long as a shear threshold has not been reached the fluid does not flow. The Newtonian model is based on a linear relationship between shear stress and speed gradient. Some other models assume a non linear law.
This is it in a nut shell if you want more try under rheology.
There are video clips of people running across a swimming pool filled with non newtonian fluid on you tube. If you want to understand how they work then you'll need to get the books out. The basic principles are really not that difficult to understand and I for one find the science of fluid flow quite interesting.