**CURTAIN COATING OF ICE CREAM BARS**

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Yummy! A lovely
cool ice cream coated in chocolate Ð just perfect after a hard dayÕs golf at
Troy Country Club. And named after the worldÕs most powerful handgun too.[1]

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

Just one thing Ð how did the
chocolate get there?

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**CURTAIN COATING**

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 Òchocolate curtainÓ
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).

**COATING QUESTIONS**

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 Òblack boxÓ 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:

- 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?
- 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 ÒcurtainÓ required to completely
coat all sides of the ice cream?
- 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?
- 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?
- Will any of these conclusions be changed if a different type of
chocolate is used?
- 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?

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

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**COMPLICATIONS**

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

- Hot chocolate is
nice and runny: but it solidifies when it comes into contact with a cool
surface: is this an issue here?
- Conversely, ice
cream is nice and hard when itÕs cold, but tends to melt when a hot
substance is applied to it. It can consist of up to 50% air (the
manufacturers try to maximize the air content since (a) it makes the ice
cream nice and fluffy and (b) itÕs free) so how might this air be
liberated from the ice cream and where will it go?
- The viscosity of
chocolate is a strong function of temperature (as you will know if youÕve
ever had a bar in your pocket on a hot day). This will certainly affect
the way that the chocolate flows. Is it possible to take this variation of
viscosity with temperature into account?
- Chocolate behaves
quite like a standard Newtonian fluid when it is nice and runny, but as
the viscosity increases it resembles much more a pseudoplastic or
shear-thinning fluid. What effect might this much more complicated behaviour have on predictions and
how could it be modelled?
- What can we
reasonably expect to be able to control in the process? What might we ever
really know about the coating of chocolate that is supplied at the ÒtopÓ
of the ice cream? Might this really be quite hard to control? Also, how
does the speed U at which the whole process runs affect the way that the
ice cream bars are coated?

*The
chocolate curtain coating process*

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**References
**

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**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)

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**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)