The Splash of a DropWorthington, A. M. (Arthur Mason)
Science
The Splash of a Drop
Worthington, A. M. (Arthur Mason)
Splashes
It should be mentioned that it is only in rare cases that the
subordinate drops seen in the last six figures, are found lying in a
very complete circle after all is over, for there is generally some
slight disturbing lateral velocity which causes many to mingle again
with the central drop, or with each other. But even if only half or a
quarter of the circle is left, it is easy to estimate how many drops,
and therefore how many arms there have been. It may be mentioned that
sometimes the surface of the central lake of liquid (Figs. 14, 15, 16,
17) was seen to be covered with beautiful concentric ripples, not shown
in the figures.
The question now naturally presents itself, Why should the drop behave
in this manner? In seeking the answer it will be useful to ask ourselves
another question. What should we have expected the drop to do? Well, to
this I suppose most people would be inclined, arguing from analogy with
a solid, to reply that it would be reasonable to expect the drop to
flatten itself, and even very considerably flatten itself, and then,
collecting itself together again, to rebound, perhaps as a column such
as we have seen, but not to form this regular system of rays and arms
and subordinate drops.
Now this argument from analogy with a solid is rather misleading, for
the forces that operate in the case of a solid sphere that flattens
itself and rebounds, are due to the bodily elasticity which enables it
not only to resist, but also to recover from any distortion of shape or
shearing of its internal parts past each other. But a liquid has no
power of recovering from such internal shear, and the only force that
checks the spread, and ultimately causes the recovery of shape, is the
_surface tension_, which arises from the fact that the surface layers
are always in a state of extension and always endeavouring to contract.
Thus we are at liberty when dealing with the motions of the drop to
think of the interior liquid as not coherent, provided we furnish it
with a suitable elastic skin. Where the surface skin is sharply curved
outwards, as it is at the sharp edge of the flattened disc, there the
interior liquid will be strongly pressed back. In fact the process of
flattening and recoil is one in which energy of motion is first expended
in creating fresh liquid surface, and subsequently recovered as the
surface contracts. The transformation is, however, at all moments
accompanied by a great loss of energy as heat. Moreover, it must be
remembered that the energy expended in creating the surface of the
satellite drops is not restored if these remain permanently separate.
Thus the surface tension explains the recoil, and it is also closely
connected with the formation of the subordinate rays and arms. To
explain this it is only necessary to remind you that a liquid cylinder
is an unstable configuration. As you know, any fine jet becomes beaded
and breaks into drops, but it is not necessary that there should be any
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