Why do the non Newtonian fluids become solid when we apply force on them ?
Answers
A quick comment on your terminology. The description "non-Newtonian" just means the stress/flow rate graph is not linear i.e. there isn't a single constant viscosity coefficient. The fluid you describe is what we colloid scientists call "dilatant", and it is certainly non-Newtonian. However there are lots of other non-Newtonian fluids such as tomato ketchup and shampoo that behave in different ways. See Are there good home experiments to get a feel for the behavior of yield-stress liquids? for a related question.
Anyhow, kleingordon has explained why the dilatant effect occurs, but let me try a slightly different approach to the explanation.
Oobleck is a suspension of solid (starch) particles in water. Suppose you had a very dilute suspension i.e. lots of water and a little starch. In this case the spacing between the starch grains is large so the grains can flow around without hitting each other, and the suspension just behaves like water. As you increase the amount of starch the spacing between the grains decreases, until at some point the spacing between the grains becomes less than the size of a grain. At this point, when you try apply a large force to suspension the starch grains bump into each other and lock together to form a framework. The water in the suspension now has to flow through the small pores in the starch grain "framework" and this requires a lot of force. Hence you can stand on the suspension for a moment. If the apply a small force the water/starch grains move slowly and this gives time for the starch grains to slide around between each other so they will flow. This is why the chap in the white shirt could run on the oobleck, but when he stood still he gradually sank.