The Splash of a DropWorthington, A. M. (Arthur Mason)
Science
The Splash of a Drop
Worthington, A. M. (Arthur Mason)
Splashes
flow of liquid along the jet; if, for example, we could realize a rod of
liquid of the shape and size of this cylindrical ruler that I hold in my
hand, and liberate it in the air, it would not retain its cylindrical
shape, but would segment or divide itself up into a row of drops
regularly disposed according to a definite and very simple numerical
law, viz. that the distances between the centres of contiguous drops
would be equal to the circumference of the cylinder. This can be shown
by calculation to be a consequence of the surface tension, and the
calculation has been closely verified by experiment. If the liquid
cylinder were liberated on a plate, it would still topple into a regular
row of drops, but they would be further apart; this was shown by
Plateau. Now imagine the cylinder bent into an annulus. It will still
follow the same law,[1] _i.e._ it will topple into drops just as if it
were straight. This I can show you by a direct experiment. I have here a
small thick disc of iron, with an accurately planed face and a handle at
the back. In the face is cut a circular groove, whose cross section is a
semi-circle. I now lay this disc face downwards on the horizontal face
of the lantern condenser, and through one of two small holes bored
through to the back of the disc I fill the groove with quicksilver. Now,
suddenly lifting the disc from the plate, I release an annulus of
liquid, which splits into the circle of very equal drops which you see
projected on the screen. You will notice that the main drops have
between them still smaller ones, which have come from the splitting up
of the thin cylindrical necks of liquid which connected the larger drops
at the last moment.
Now this tendency to segment or topple into drops, whether of a straight
cylinder or of an annulus, is the key to the formation of the arms and
satellites, and indeed to much that happens in all the splashes that we
shall examine. Thus in Fig. 12 we have an annular rim, which in Figs. 13
and 14 is seen to topple into lobes by which the rays are united in
pairs, and even the special rays that are seen in Fig. 9 owe their
origin to the segmentation of the rim of the thin disc into which the
liquid has spread. The proceeding is probably exactly analogous to what
takes place in a sea wave that curls over in calm weather on a slightly
sloping shore. Any one may notice how, as it curls over, the wave
presents a long smooth edge, from which at a given instant a multitude
of jets suddenly shoot out, and at once the back of the wave, hitherto
smooth, is seen to be furrowed or "combed." There can be no doubt that
the cylindrical edge topples into alternate convexities and concavities;
at the former the flow is helped, at the latter hindered, and thus the
jets begin, and special lines of flow are determined. In precisely the
same way the previously smooth circular edge of Fig. 8 topples, and
determines the rays and lines of flow of Fig. 9.
Public-domain text, read in full here on John Shaqi.
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