Georg,
you are quite correct of course about the
cooler water and the cavitation, but I particularly wish to thank you for your
remarks on a kettle striking a particular tone or note. I am embarrassed to say
that though I had heard such tones in the past, I had never stopped to think
about them. In particular I seem to remember them most from my childhood. Have
I just been unlucky, or have the kettles stopped singing? Comments from anyone
would be welcome.
Having slept on the thought, I find the
range of speculation too wide for proper discussion in my state of ignorance,
but a few points strike me as being of immediate interest and I would be
grateful if participants would contribute.
As for my own reactions, first of all, I am
fairly confident that the resonance of the kettle plays an important part. I
seem to remember that a roughly hemispherical copper kettle we had when I was a
child quite commonly would sing as it simmered. Most of the kettles we have
owned since then have had slenderer shapes, and in recent years some of them
have been plastic. Such factors might not have favoured resonance.
Also I suspect that the immersion elements found
in kettles in recent decades do not favour the formation of large areas of
uniform bubbles, but rather produce bubbles that are rapidly detached by
convection currents. This presumably favours efficient transmission of heat and
better cooling of the element, but it would do little to promote musicality. One
cannot have everything...
Now, not long ago I noticed that various
local species of limpets formed surprisingly regular nearly-hexagonal arrays on
flat concrete surfaces on breakwaters. Certain species of sea birds nesting on
level areas form similar patterns. Those patterns result from a short-range
repulsion (territorial behaviour) imposed on opportunistic occupation of
available locations. The two opposing influences, repulsion and attraction,
create negative feedback that results in a stable, near-optimal distribution, which
commonly works out to be roughly hexagonal.
Now, that old copper kettle — its element
was beneath a flat copper bottom. I never paid it much attention, but I have
seen simmering bubbles of uniform size in close, more or less hexagonal array
on similarly flat surfaces. I suspect in fact, given that heat transmission in
boilers and similar devices has been intensively studied, that such bubble
arrays are standard subjects of investigation, but it is a field about which I
know practically nothing, so everything I say here amounts to empty speculation.
I remain under regenerative as usual, partly because empty speculation
sometimes leads to substantial insight, and partly because it is fun. Heat
engineers who have read so far are advised that the worst is yet to be, and
that unless their masochism impels them to contribute, they had better stop now
and cool off comfortably while their tempers still are under control, which I
am not.
At its most naive, my first idea was that
on a flat surface bubbles would form more or less uniformly and that the growth
of each bubble, also more or less uniformly, would be constrained by the supply
of heat from below and the rate of heat loss to the surrounding water. One
might imagine that this would lead to a steady flow of heat, but of course in
practice we get the cavitation effect of simmering, with bubbles repetitively
growing (thereby absorbing heat) and collapsing (and in turn releasing heat).
If such synchronous collapse nearly resonates with a resonant frequency of the
container, there should be positive feedback of the compression pulses, such
that it would be entirely believable that there would be an entrainment effect,
causing the bubbles to synchronise at a resonant frequency.
So far, so persuasive, if just a little
vague. However, on a finer scale of detail, there is room for deeper enquiry. Imagine
that the first bubbles form in isolation at largely random points. As the
bubble expands it rapidly cools the surface below and the surrounding water,
but almost as rapidly loses heat to the water above (which is what causes the
cavitation). The cooling of the surface below, possibly together with the shock
wave from the cavitation, might be expected to repel nucleation sites forming
too closely adjacent. Here we can see the analogy to the limpets and seabirds:
long-range attraction or opportunistic occupation, conditioned by short-range
repulsion. By the time that the surface is fully occupied, the bubble size is
determined by negative feedback as each bubble "competes" with its
neighbours for latent steam, causing neighbouring bubbles to match each other
closely in size, rate of growth, and distance apart. It is immediately obvious
that if such conditions were to pertain in a suitable vessel, we could expect
high degrees of resonance, although possibly octaves apart.
In practice I cannot help suspecting that
high-speed footage of the bubble behaviour not only would reveal resonant
growth and collapse on flat surfaces, but that at various rates of heat flow (as
determined by the temperature of the water, the temperature of the heated surface,
its conductivity and so on) we would get various sub-resonances, with adjacent
bubbles alternating rather than remaining in direct synchrony. This might
reduce the amplitude of the dominant resonance, but double or treble the
frequency.
Anyway, as you can see, if there is any
merit to this speculation, it might well explain certain classes of a
characteristic note of singing simmering. It should be easy to examine in the
laboratory.
Any suggestions anyone?
