Newtonian Fluids and Non-Newtonian Fluids
Back in June I attended a taster workshop at UCL for the Arts and Sciences course. As part of the taster day I had the opportunity to go to a few random little activities, one of which was sitting through a presentation about the maths behind chocolate fountains by Adam Townsend. At first I wasn’t quite sure what to expect from the presentation but I knew I was definitely going to like it (obviously not because I’m deeply in love with both chocolate and Maths). So by the end of the presentation, not only did I find out a whole lot of things about how chocolate fountains work, I also got to learn about fluid dynamics and Newtonian fluids.
So what is a Newtonian fluid? Here are two scenarios to compare.
- Imagine you have a bottle of Ketchup. You grab the bottle, twist off the cap and turn the bottle upside down. Nothing happens. The ketchup just sits there in a big lump, defying gravity. You shake it. Nothing. You shake it again more violently and start applying more force. Still Nothing. You shake it really hard this time, and then, disaster. The ketchup starts flowing before you have time to stop the flow.
- You have a water pistol, to make water squirt out of it, you pull the trigger, and instantly the water starts coming out. Next you want to make the water come out faster,so all you have to do is pull the trigger harder and the water will simultaneously start squirting out faster. Simple.
Ketchup behaves this way because it is a non-Newtonian fluid. A Newtonian fluid, like water, has constant viscosity. No matter how much force is applied to it, the viscosity will not change. Picture a flowing liquid as a series of layers of liquid sliding past each other. The resistance to flow happens because of the friction between these layers. If you want one layer to slide over another twice as fast as before, you’ll have to overcome a resisting force that’s twice as great. The slower one layer slides over another, the less resistance there is, so that if there was no difference between the speeds the layers were moving, there would be no resistance. Fluids like water behave according to Newton’s model, and are called Newtonian fluids. Non-Newtonian fluids, however don’t follow this model. They exhibit properties of fluids AND solids
Other non-Newtonian fluids such as blood, yoghurt, gravy, pie fillings, mud, and cornstarch paste also DON’T follow the model. They’re non-Newtonian fluids because doubling the speed that the layers slide past each other does not double the resisting force. It may less than double (like ketchup), or it may more than double (as in the case of quicksand and gravy). That’s why stirring gravy thickens it, and why struggling in quicksand will make it even harder to escape. Another way to talk about the layers sliding past each other, is referring to them as shear factors.
There are two types of non-Newtonian fluids: shear thinning and shear thickening ones. Ketchup is a ‘shear thinning’ fluid. At rest, it is very viscous but the more (shear) force you apply to it, the less viscous it becomes. That’s why it’s hard to get it flowing out of the bottle, and why it’s hard to control the flow once it does. Shear thickening fluids on the other hand flow quite freely under little stress and become almost solid under high stress. A good example is custard. You can slowly sink your hand into a bowl of custard, but if you punch it, it will become solid.
Shear-thickening fluids are pretty helpful, they are used for armour because they’re nice and flexible, but get very hard when hit by a bullet!