Fluid mechanics

Custard, paddling pools, and plasterers’ tools: all part of applied mathematics!

I don’t think I can list walking on custard as one of my hobbies – it’s not exactly a weekly activity – but I have found it a fun way to demonstrate the curious and counter-intuitive behaviour of some fluids. Yes, you can walk on custard. There’s no trick. You just need water and custard powder…and a lot of it!

The last time I did this was at the IMA Festival of Mathematics, a two day event organised by the Department of Mathematical Sciences at the University of Greenwich and the Institute of Mathematics and its Applications that featured many excellent talks and activities on the importance, usefulness, and pleasure of mathematics. Reviews of the festival can be found in PrimeTimes (a magazine written and edited by the University of Greenwich Mathematics Society) and in the latest edition of Mathematics Today. The festival also featured a family-size paddling pool, a plasterer’s bath, and about 200kg of cornflour. You can press “play” on the video below to see this in action.

This video (uploaded to the Twitter account of the Department of Mathematical Sciences, University of Greenwich, @Maths_GRE) shows Greenwich Maths students and staff jumping, running, mixing, and punching a mix of cornflour (the main ingredient of custard powder) and water. Nothing else, but a lot of mess.

Custard, or to be more precise cornflour and water mixed in the right proportions , is an example of a non-Newtonian shear-thickening fluid.  The “non-Newtonian” means the fluid does not follow the law postulated by Sir Issac Newton, which says that the “thickness” or “lack of slipperiness” of fluids remains the same no matter what you do to them (your natural intuition of fluids is probably in-line with  Newton’s law – you don’t feel the sea getting more or less slippery as you swim). The “shear-thickening” means the fluid does something really weird – it gets harder when you apply a force it.

If you slowly dip your hands into a shear-thickening fluid like the custard mix you see in the video then it will behave more-or-less like water. This is because the force you are applying (dipping you hands) is quite gentle. Likewise, if you slowly step into such a fluid you will sink – it is a fluid, after all! The interesting things happen when you hit or punch a shear-thickening fluid. Hitting and punching exerts a much stronger force and this force can actually cause these sorts of fluids to become momentarily thicker and harder. In some fluids this thickening can be so extreme that you will not be able to punch through their surface; you won’t even make a splash. Shear thickening is not a property of most fluids but it is a property of cornflour and water (i.e. custard) when mixed in the right ratio. 

Another way to apply a large and (almost) continuous force to a shear-thickening fluid is to run or jump on it. As long as you keep running or keep jumping then you will not sink. If you stop running then stop applying a force, and if you stop applying a force then the fluid will go back to being runny, and if the fluids is back to being running when you are in it then….well, you are going to get wet and messy!

Sound impossible? It’s not – have a look at the video.

You can do this experiment with regular custard powder or cornflour. You must, however, use a high enough concentration of powder. About 2 parts custard powder (or cornflour) to 1 part water by volume will do it (that’s two cups of powder for every cup of water – closer to 1.5 parts powder should be sufficient but 2:1 puts you on the safe side). Remembering that 1 litre of water weighs 1kg, this means a lot of custard powder to fill the plasterers’ bath you see in the video.

The giant paddling pool was for protection only. It would have been great to fill a 2300 litre pool of custard but I’m afraid our budget wouldn’t stretch that far! And can you imagine disposing of it? (You can’t just tip a highly shear thickening fluid like this down a drain – the consequences are very problematic!). No, the pool was to protect the beautiful Old Royal Naval College, the home of the University of Greenwich. You can probably see from the video that custard walking is fun but messy – the powder gets everywhere. The pool simply contained the mess and protected the World Heritage site. If you want to try this at home then please remember to consider disposal and mess – you’ll regret it if you don’t.

The technical word for the “thickness” or “lack of slipperiness” of a fluid is viscosity. All fluids have viscosity. Some fluids have a constant viscosity  (water), others have a viscosity that decreases under a shear force (shear thinning fluids, e.g.  ketchup), and others such as cornflour-based custard have a viscosity that increases under a force. Scientists who study such things are called rheologists (rheology is the science of deformation and flow). Rheology brings together people from many disciplines – mathematics, physics, chemistry, engineering, computer science…These people bring their expertise to the table and collaborate to better understand fluids and advance the technology around us. If you don’t think rheology is that important or common then have a look around. How many examples of fluid flow have you seen today? Maybe you are having a cup of coffee or a beer. You probably brushed your teeth today (I hope so!) Maybe you washed and conditioned your hair, or had a shave. Think about all the blood circulating your body. The oil that we use everyday, for better or worse, and it’s extraction process. Mud, cement, and lava. How many things made of plastic do you see around you? They were probably in a rheological state before you used them. Then there’s the more classical Newtonian fluid mechanics that’s relevant to aerodynamics (yes, air is a fluid), the design of sports equipment, weather, oceans, and climate….

And, of course, there’s custard.

Perhaps you are wondering why or how some fluids shear thickening. This has been a a source of confusion and interest for a long time. The answer is not a simple one but I’ll try to address it in a future post. In the meantime, try not to put a dense mix of custard into your washing machine. I did this once. It was a very costly experiment.

This activity would not have possible without the hard work and dedication of Tony Mann and Noel-Ann Bradshaw from the Department of Mathematical Sciences at the University of Greenwich. We also had great help and support from our students. Jonathan Histed deserves an special “thank you” for giving up his time (and tools!) to help make this happen.