For a fluid to be considered a Newtonian fluid, it must follow that the force is proportional to that equation. However, when a fluid doesn't follow this principle, then we are required to call them a Non-Newtonian fluid. Now, I'm sure we've all heard of this phenomena before (the naturally easiest example of one is the mixture of corn flour and water). What is really cool about Non-Newtonian fluids is the way in which force acts upon the system.
The application of a small force leaves us in a laminar flow region, where we can move the liquid around as a liquid does. When we move up to a large force however, there doesn't become such a thing is turbulent flow, there instead becomes a solid.
In an Non-Newtonian fluid, there is a non-linear relation existing between shear and strain stress, and a viscosity coefficient cannot be defined.
Common examples of these fluids are oobleck (cornflour and water), glurch (borax and white glue), ketchup, shampoo, paint, blood and silicone polymer suspensions.