Alistair Fitt, University of Southampton, Southampton UK



Yummy! A lovely cool ice cream coated in chocolate – just perfect after a hard day’s golf at Troy Country Club. And named after the world’s most powerful handgun too.[1]


By the way, the chocolate used on this bar is real Belgian chocolate – not the nasty stuff that usually passes for real chocolate.


Just one thing – how did the chocolate get there?




The answer is almost certainly that it was curtain coated onto the ice cream bars. Bars of ice cream (with the stick already frozen into them) were passed, upright, beneath a “chocolate curtain” which allowed a layer of hot (molten) chocolate to run over the surface, coating all of the ice cream bar faces (see the not-too-well drawn figure on the next page).




As always, the manufacturer would like to know more details of the process. Experiments are probably possible, but some theoretical predictions would be of great help as well. As usual, one possibility would be to use a “black box” CFD package. However, this would just give pages full of numbers (and probably some nice colour pictures as well). What is really required is help in predicting and understanding what the key problem parameters are and how they influence the results. For example, some of the questions that could be posed include:


  1. Is it possible to control the process so that the coating has the same width at the top and the bottom of the ice-cream?
  2. Excess chocolate that drips off the bottom of the ice cream can be used again to a certain extent, but is not as pure as the original chocolate. What is the minimum size of “curtain” required to completely coat all sides of the ice cream?
  3. If productivity is increased by increasing the speed U of the belt carrying the ice creams, how will the delivery of the curtain need to be changed?
  4. For how long must the newly-coated ice creams be left before they can be packaged? In other words, how long does the coat take to dry?
  5. Will any of these conclusions be changed if a different type of chocolate is used?
  6. Do both sides of the ice cream get coated in the same way? What about the sides? What happens if a different sized ice cream bar is used?


The problem is a modelling one, which is likely to require fluid dynamics, asymptotics, heat transfer/phase change and possibly numerical analysis as well.




In some ways this is a simple problem – but if a really detailed look at the process is required, then there are some extra complications to take care of, including:



The chocolate curtain coating process




1. Tayler, A.B. Mathematical Models in Applied Mechanics (2002, Oxford University Press) (good for general modelling advice and also examples of how to cope with freezing and melting problems)


2. Acheson, D.J. Elementary Fluid Dynamics (1990, Clarendon Press) (good for fluid mechanics equations)


3. Morton, K.W. and Mayers, D.F. Numerical Solution of Partial Differential Equations: An Introduction (2005, Cambridge University Press) (for numerically solving some of the PDEs that might arise)

[1] Or was it the other way around perhaps?