Re: What is the maximum size for a drop of water?

On Fri, 1 Sep 2006 12:34:34 +1000, j.wilkins1@xxxxxxxxx (John Wilkins)
wrote:

Nic <harrisondalen@xxxxxxxxxxx> wrote:

Manny Feld wrote:
r norman wrote:


The problem, as has already been mentioned, is the drop breaking up by
wind shearing forces as it falls through air. I seem to recall
astronauts playing with enormous globules of water floating in zero
gravity. Surface tension holds it together, but is a rather weak
force especially as the surface area grows more slowly with drop size
than the inertial or gravitational disruptive forces on the mass.

In free fall one can assemble some rather large water drop.

But there still must be a limit. Water isn't very dense, so it would
be interesting to know whether in the case of a very large drop, the
event horizon would be below the surface.

Surely it would be at the point where (on average) the stresses of
internal thermal agitation and prior kinetic energy imparted to the
water exceeded the cohesion provided by surface tension? Assuming that
there are no internal stresses at the limit, and the water needs to be
at least 0°C, how big could a stable drop get? I guess that you have to
factor out tidal stresses too in microgravity.

The event horizon bit was obviously a drop so enormous it became a
black hole. On the other hand, thermal agitation is not a factor
because the stresses generated on the surface do not depend on drop
size. Thermal agitation allows for evaporation but not breakup of the
drop into smaller pieces.

The physics is completely known and anybody who studied surface
tension in Freshman Physics should know how to solve this question.
I vaguely remember calculating the size of drops falling from nozzles
of different diameter way back in those days.

Basically, LaPlace's Law specifies that the pressure holding together
the drop by surface tension is sigma/D where sigma, the surface
tension for a water-air interface, is about 0.07 N/m and D is the
diameter of the drop. Compare that with the pressure tending to
disrupt the drop caused either by either the need to support the drop
under gravity or the drag force of air on a drop falling at terminal
velocity. In either case, that pressure is on the order of rho g D,
where rho is the density of water, g the acceleration of gravity. You
end up with drops on the order of several millimeters in size Without
wind stress or the need for the drop to support its own weight, you
get drops of unlimited size, as demonstrated by astronauts or by the
Pacific Ocean.




.

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