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Coanda Effect and Pouring Milk
Name: Dave
Status: Student
Grade: 6-8
Location: N/A
Country: United States
Date: June 2008
Question:
I am pouring a cup
of milk into a mixing bowl. If I pour the milk
quickly, there is no problem, it flows straight
into the bowl with either laminar or turbulent
flow. However if I pour too slowly, the milk
clings to the outer surface of the cup and runs
down to the base of the cup, from where it drips
onto the floor. My questions are:
1) Am I
correct in thinking that this is a demonstration
of the Coanda effect?
2)What factors are
responsible for the flow switching from laminar
flow to adhering to the outer wall of the cup -
i.e. is it possible to predict when this effect
will occur, and what is the equation that
predicts this behaviour? (I am guessing the
following may be involved: velocity, density,
viscosity and surface tension of fluid, and
radius of curvature of the lip of the cup. Are
any other factors involved, e.g. temperature of
the fluid?)
Replies:
1. I suppose this could be considered a 'Coanda effect', if you define it
broadly enough. Coanda studied air flow, and the Reynolds Numbers for air
flow in aircraft are quite different than milk flowing over a cup. So the
physics are dramatically different in the two cases. But, if you consider
any fluid flowing next to a curved surface as Coanda, then your milk-cup
example is in that fold. I would say the novelty of Coanda's discovery had
to do with the counter-intuitiveness of the air clinging to a wing, quite
different than the milk-cup example.
2. With your milk, you have a surface tension effect (water-type liquids
would rather be next to glass than air), and you have an inertia effect
(flowing milk, or any mass, will not change direction without having a force
applied). If you pour fast enough -- e.g. the milk has enough velocity, its
inertia can overcome the surface tension pull. If the flow is too slow, then
the surface tension is strong enough to keep the milk attached to the glass.
Turbulent vs. laminar is not the key factor here. This is why I mentioned
'Reynolds Number'. There are two general kinds of flow regimes. First is
'turbulent flow', where fluids spontaneously form eddies and vortices, and
second is 'laminar flow' where all the fluid particles are moving in the
direction of flow. (These are somewhat 'oversimplified' definitions, but
they should be OK for this discussion.) Finding a flow's Reynolds number is
the best way to predict if it will be laminar or turbulent. For low Reynolds
numbers (low velocity, low density, small size, high viscosity), flow is
laminar -- there is not enough energy in the flow for turbulence to develop.
For high Reynolds numbers (high velocity, high density, large size, low
viscosity), turbulence occurs. Aircraft tend to be high Reynolds numbers,
turbulent. Water flowing slowly tends to be low Reynolds number, laminar.
The point is this: Fluid can cling to a surface in either flow regime. In
the case of Coanda's air, the regime was turbulent. In the case of the milk,
the flow is laminar. Both can display the clinging behavior.
Hope this helps,
Burr Zimmerman
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Update: June 2012
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