Meet the 'choc doc'

Christmas and chocolate go hand in hand, resulting in many people making rushed resolutions to lay off the milky goodness for the New Year. But chocolate can also, believe it or not, have an important part to play in maths. Adam Townsend is a PhD student from University College London, and his chocolate fountain provides an important tool in studying what are known as 'non-Newtonian fluids'. He explained more, including why a mayonnaise fountain would work just as well, to Chris Smith, while they engaged in some top level research (called eating)...

Adam - We are trying to answer some science questions about chocolate fountains.  So a good one - the next time you look at a chocolate fountain, as we see here, you can ask "well why when the chocolate falls off the chocolate fountain, does it fall not quite downwards but slightly inwards?"

Chris - I suppose we should explain for people.  So what we've got here is a series of tiers.  There's a top bulb and then there's another one underneath, another one underneath, and then a big dish at the bottom.  The chocolate flows out of the top, it runs down each of these things that look like upside down dishes don't they?...

Adam - Yes.

Chris - And then it drops onto the one underneath it, but when it does so, it doesn't fall straight down like water dripping off the edge.  It actually goes inwards a bit and then down.

Adam - Yes, which is weird, because gravity normally acts downwards, so in this case it's going inwards. So me and my supervisor, we looked at this and thought "okay, well what's going on here?"

Chris - It's important to know that there's key science going on in laboratories around the country looking at important physics principles like chocolate fountains.  But no, I mean more seriously, there's obviously something doing something to this fluid and, more broadly, understanding how fluids move and behave is important isn't it because there are many applications beyond just chocolate fountains?  You're using this as simple model but there are lots of reasons why this is relevant to everyday life in other respects?

Adam - Yes for sure.  I mean knowing how fluids behave, how any liquid moves is clearly very important as liquids and fluids are absolutely everywhere.  Chocolate is a particularly interesting type of fluid; it's what we call non-Newtonian.  What this means is that  the viscosity of the fluid, and that's its thickness, changes as it goes round, so lots of liquids like water and even honey; they have obviously different viscosities; honey is an awful lot thicker.  But their viscosities don't change, when you take a glass or water or something and you stir it, the viscosity, the thickness of the water stays the same.  However, chocolate doesn't behave like this.  So chocolate behaves a bit like mayonnaise, or ketchup...

Chris - It tastes better though.

Adam - It does taste better.  I mean you can try mayonnaise fountains but...  Anyway so...

Chris - I don't think I will actually.  I'll leave that to you Adam.

Adam - So if you take ketchup, for example, and you might know that if you have a glass bottle of ketchup - it's quite difficult to get ketchup out of the bottle...

Chris - If you do not shake the bottle, none comes out and then a lottle.

Adam - Yes, exactly. So ketchup has this weird property that it's quite thick and you can't get it out of the bottle but you need to shake it to give it some sort of sheer before it starts coming out, and chocolate behaves in much the same way.   Other things that behave this way, so say mayonnaise, lava, nail polish, blood - blood behaves this way.

Chris - You don't eat most of those things do you?

Adam - No not so much.

Chris - I'm just kidding. But how did you apply physics and maths to this question?  How can you actually take something like a chocolate fountain and start making mathematical equations to describe that.

Adam - Sure, so we have one big equation that tells you how every fluid moves - it's called the Navier-Stokes equation, it's really important, and it looks horrible, and what you do is you ask  "what's really important in this equation is the viscosity.  How does the viscosity change as it goes through, in this case through the chocolate fountain?"  So what you look for is trying to figure out how does the viscosity...basically, how can you describe the viscosity? So you stick that into the equation and try and get some answers out of it basically?

Chris - So is that what you did?  You now have equations that will describe how this fluid in this situation, moves?

Adam - Yes, so obviously chocolate is a million, possibly billion pound industry and so people have done experiments with chocolate and they can tell you exactly how the viscosity changes as it goes round, and so we try to look these up and convince people to give us some data, and we stuck it in and we got some predictions, and they seem to be pretty good from our kitchen experiments.

Chris - Well you know what they say Adam - proof is in the eating, the proof is in the pudding.  Shall we have a go?

Adam - Yes, so help yourself.  We've got some bananas, we've got some strawberries, and we've got some marshmallows.

Chris - There's a large queue forming behind me as well.

Adam - You're not lying.

Chris - Come on, show us what we do.  Come on let's go for it.

Adam - Yes.  So, from my extensive chocolate fountain research, I can tell you that strawberries are definitely the best to put in here.  So, if you want to be really mean to everyone else, you dip it in the top because that's where you get absolutely best coverage but then you end up sort of...

Chris - Especially if it falls off like that has.  It's gone down inside the machine.

Adam - Yes, but you get full coverage this way which makes it very good and then you stick it in your mouth.

Chris - I think we should let the ladies in because Connie looks like she's about to murder somebody if we don't let her get near it.  What are you going to go for?  We've got banana, we have strawberry or we've got marshmallows.

Connie - I'm going to do what the expert said - I'm going to go for a strawberry.

Chris - Is there a mathematical equation to describe how the chocolates coats the fruit or the marshmallow item?

Adam - Yes.  So, coating is a really important problem because if you're, for example, an airplane manufacturer and you want to paint your aeroplane.  Well this is a coating problem because you end up with a nice thin sheet of paint, and paint: that behaves the same way as chocolate which is amazing.