THE TWO KINDS OF SPLASHES OF SOLID SPHERES
In the present chapter will be described the splash that follows the
entry of a _solid_ sphere falling vertically into a liquid from a small
height, and I should like to persuade the reader, if possible before he
begins to read, or at any rate afterwards, to make a very simple
experiment. Let a few child's marbles be taken--not glass "marbles," for
these are seldom round enough or smooth enough, but what are sold in the
toy-shops as "stone" marbles--and let one of these be well rubbed and
polished with a dry handkerchief, and then dropped from a height of
about 30 cm., or, say, 1 foot, into a deep bowl or basin of water, the
bottom of which may be conveniently protected from breakage by a few
folds of fine copper gauze.
If the polishing has been good, and the surface of the sphere has not
been dimmed by subsequent handling with hot or greasy fingers, it will
be observed that the splash is singularly insignificant, the sphere
slipping noiselessly into the liquid with very little disturbance of the
surface.
But if the same sphere be fished out of the water, and again let fall
from the same height without being first dried, or, better still, if
another marble be taken, which has been previously roughened with
sand-paper, the resulting splash is totally different. There is now a
noise of bubbles, which may be seen rising through the liquid, and a
tall jet is seen to be tossed into the air.
(1) THE SPLASH OF A ROUGH SPHERE.
To understand the cause of this really surprising difference we must
turn to the photographic record, and we will take first the case of a
rough sphere falling into water to which milk has been added for the
sake of clearness in the photographs. The diameter of the sphere was 1.5
cm. (or 3/5 inch), and the height of fall 15 cm., or just about 6
inches. The sphere on each occasion was fished out, redried, and
re-roughened with sand- or emery-paper. Examination of the first
photographs of Series V shows that the liquid, instead of flowing over
and wetting the surface of the sphere, is driven violently away, so that
as far as can be seen from above the upper portion is, at first at any
rate, unwetted by the liquid. The crater that is subsequently formed is
very similar to that which was thrown by the liquid drop in Series I,
the main difference being that in the present-case the crater is thinner
in the wall and more regular. This greater regularity is chiefly to be
attributed to the fact that the solid sphere enters the liquid with a
true spherical form, and is not distorted by the oscillations and
tremors which disturb a falling drop. The gradual thickening of the wall
and the corresponding reduction in the number of lobes as the subsidence
proceeds is beautifully shown in Figs. 7, 8, 9, and 10, the
last-mentioned figure being hardly distinguishable from the
corresponding Fig. 9 of Series I, p. 17. This stage is in each case
reached in about 58/1000 of a second.
[Illustration: SERIES V
Rough sphere. "Basket splash."
Diameter of sphere, 1.5 centim. Height of fall, 15 centim.
1 T = 0
2 0.003 sec.
3 0.006 sec.
4
5
6]
[Illustration: SERIES V
Rough sphere--(_continued_).
7 0.024 sec.
8 0.032 sec.
9 0.042 sec.
10 0.060 sec.]
Now from the depths of the crater there rises with surprising velocity
the exquisite jet of Fig. 11, which in obedience to the law of
segmentation at once splits up in its upper portion into little drops,
while at the same time it gathers volume from below, and rises
ultimately as a tall, graceful column to a height which may be even
greater than that from which the sphere fell. This is the emergent jet
which one sees with the naked eye whenever a sufficiently rough sphere
is dropped from a small height into water, but if we are to ascertain
how this column originates, we must follow the sphere below the surface
of the liquid. The arrangement already described on p. 69 enables this
to be done. We let the sphere fall into clear water contained in a
narrow, flat-sided, inverted clock-shade and illuminate this from behind
while the camera stands straight in front.
[Illustration: SERIES V
Rough sphere--(_continued_).
11 0.068 sec.
12 0.076 sec.
13 0.088 sec.
14 0.100 sec.]
In this manner were obtained the photographs of Series VI, which require
a little explanation. In the first figure we see the sphere just
entering the liquid. The faint horizontal line shows the level of the
surface. Above this line we see the internally reflected image of the
part that has already entered, while still higher in the figure may be
discerned the summit of the sphere itself. The slight lateral
displacement of the part below the surface is due to refraction
consequent on the camera having been set with its optic axis not quite
perpendicular to the face of the vessel. In the subsequent figures it
will be observed that the sphere, as it descends, drags with it the
surface of the liquid in the form of a gradually deepening pocket or
bag, the upper part of the sphere being for a long time quite unwetted
by the liquid.
The sides of this pocket or bag of air not being quite smooth, give a
somewhat distorted appearance to the sphere within. Also, since the
sides are sloping, their reflected image in the level surface slopes in
the opposite direction and produces an angle where the two meet. This
angle marks very clearly the level of the surface. Above the
surface-line in Figs. 2 to 5 is seen the beaded lip of the crater which
we have already viewed from above, but this is somewhat out of focus,
for the camera had to be focused on the sphere as seen under water, and
the effect of the water is to bring the sphere optically nearer. Hence
only the nearer part of the crater, i.e. the middle part of the front
edge, is distinctly shown.
[Illustration: SERIES VI
The splash of a rough sphere as seen below the surface.
Diameter, 1.5 centim. Height of fall, 15 centim.
1 T = 0
2 0.010 sec.
3 0.018 sec.
4 0.023 sec.
5 0.032 sec.]
Coming now to Fig. 6, we perceive that the long cylindrical hollow has
begun to divide. In this spontaneous division we have another
illustration of the law of instability which regulated the sub-division
of the jets and columns of earlier series. This law is the same whether
the cylinder be of air surrounded by liquid or of liquid surrounded by
air. Hitherto we have only seen it operating in jets of liquid in air;
now we have a jet of air in a liquid.
The lower part of the long cylinder of air splits off into a bubble just
behind the sphere, and follows in its wake to the bottom of the vessel,
and is only detached and rises to the surface when the sphere strikes
the bottom. Many years ago, through the kindness of the curator of the
Brighton Aquarium, I was enabled to watch this bubble of air following
in the wake of the sphere to the bottom of the deepest tank.
Figs. 7, 8, and 9 show the two parts gradually separating.
[Illustration: SERIES VI--(_continued_)
Scale reduced to about 7/10.
6 0.045 sec.
7
8 0.050 sec.
9 0.054 sec.]
Fig. 10 shows specially well the ripples on the surface of the
descending bubble. These undulations sometimes become so accentuated
that the upper part of this descending bubble is detached, and then the
curious phenomenon may be seen of this detached part still following the
rest downwards through the liquid with an unsteady, lurching motion.
Meanwhile the upper half of the divided air-column is seen in Fig. 9 to
resemble a deep basin which now rapidly fills up by the influx of liquid
from all sides. It is from the confluence of this inflowing liquid into
channels which necessarily narrow as the centre is approached that the
great velocity with which the liquid spirts upwards is obtained. In Fig.
11 the jet is just discernible above the surface, and in Fig. 13 it is
well-established.
[Illustration: SERIES VI--(_continued_)
10 0.062 sec.
11
12 0.062 sec.
13 0.070 sec.]
On increasing the height of fall of a rough sphere to 60 cm., we obtain
a higher crater which closes and forms a bubble, exactly as when we
increased the height of fall of a liquid drop. The process as viewed
from above the surface is shown in Series VII. The first figure of this
series shows very well how completely the liquid is driven away from the
surface of the sphere the first moment of contact. The subsequent crater
and bubble are of exquisite delicacy. This bubble, though it closes
completely as in the last figure, is doomed to almost immediate
destruction. For we see, on looking below the surface, that the
proceedings there are of the same kind as in the case of the lower fall
already described, and result in the formation of an upward-directed
jet.
[Illustration: SERIES VII
Rough sphere falling 60 cm. Scale 3/4.
1 T = 0
2 0.003 sec.
3 0.017 sec.
4 0.017 sec.
5 0.033 sec.]
Thus the first three figures of Series VIII show the last moments of a
bubble which has burst, spontaneously, and so has made way for the jet
of Fig. 3. (These are taken from a splash into petroleum with 24.5 cm.
fall.) But the last two figures, 4 and 5 (taken with a 32 cm. fall),
show how a bubble which might otherwise have been permanent, is stabbed
by the rising jet and destroyed. With water and 60 cm. fall the jet
appears sometimes to rise quite unimpeded, and sometimes to be checked
by the still closed bubble.
Before leaving the splash of a rough sphere, I desire to call the
reader's attention to another point.
Such figures as 7, 9, and 10 of Series V, p. 77, show that the surface
of the liquid beyond the walls of the crater is still flat and
undisturbed; yet we now know from the corresponding Figs. 5, 6, and 7 of
Series VI, p. 83, that a large volume of liquid has been displaced, much
larger than the quantity required to form the crater wall. The inference
is that the level of the surface has been slightly raised even at a
great distance from the place of the splash. Figs. 7, 8, and 9 of Series
VI themselves confirm the impression of the undisturbed flatness of the
surface at even a small distance from the splash.
(2) THE SPLASH OF A SMOOTH SPHERE.
The reader who has been sufficiently interested to make for himself the
simple experiment suggested at the beginning of this chapter, will have
already realized that the splash of a smooth sphere is totally different
from that of a rough one. The photographs of Series IX show that the
difference is quite pronounced from the first instant of contact. In
this series the sphere was of polished stone 3.2 cm. in diameter and
fell 14 cm. The scale of magnification is 3/4. The second figure shows
that the liquid, instead of being driven away from the surface as was
the case with a rough sphere, now rises up in a thin, closely-fitting
sheath which (see Fig. 3) completely envelops the sphere even before its
summit has reached the water-level. Figs. 4 and 5 show the comparatively
insignificant column that remains to mark the spot where the sphere has
entered. Fig. 6 was the result of a lucky accident, which left the
sphere rough on the right-hand side, smooth on the left. Nothing could
show better than this photograph the essential difference between the
two splashes.
[Illustration: SERIES VIII
Rough sphere. Splashes viewed below the surface.
The bursting of the bubble.
1 0.055 sec.
From a splash into Petroleum
24.5 cm. fall.
2 0.060 sec.
3 0.064 sec.
From a splash into Petroleum
32 cm. fall.
4 0.070 sec.
5 0.082 sec.]
The reader's attention is directed to the remarkably deep furrows which
characterize the whole sheath in Fig. 3 and the left-hand (smooth
splash) part in Fig. 5. About these furrows we shall have something to
say later.
A better idea of the extreme thinness of the enveloping sheath is
obtained when the illumination is from behind as in Series X, in which
the sphere was of highly polished serpentine stone 2.57 cm. (or just
over 1 inch) in diameter, the fall being 14 cm. (or not quite 6 inches).
[Illustration: SERIES IX
The "sheath" splash of a smooth sphere.
1 T = 0
2 0.002 sec.
3 0.013 sec.
4 0.024 sec.
5 0.039 sec.
6]
Examination of either Series IX or Series X shows that with the smooth
sphere as with the rough the amount of water lifted above the surface in
the immediate neighbourhood of the splash is much less than the whole
volume displaced, so that we are again driven to the conclusion that the
surface at even a considerable distance must be bodily lifted without
its flatness being sensibly disturbed. This conclusion was confirmed by
a direct experiment. The not very wide vessel of Fig. A was taken and
filled brimful with milk, and the lower edge of a card millimetre scale
was placed just in contact with the liquid surface at one side. The
reader should notice that the liquid is not quite up to the level of the
spout on the right-hand side of this figure. Then the sphere was dropped
in and the photograph of Fig. B was taken when the sphere was about
two-thirds immersed. The rise at the edge of the scale is about 3
millimetres, and there is an apparently equal rise at the spout, where,
however, the surface appears quite flat.
[Illustration: FIG. A]
[Illustration: FIG. B]
It seems probable, then, that whenever a stone is thrown into a lake the
impulse accompanying its entry travels with the velocity of a
compressional wave (i.e. with the velocity of sound) through the
liquid, and is therefore almost instantly felt and produces a minute
rise of level even in remote parts of the lake long before the arrival
of any ripple or surface disturbance.
[Illustration: SERIES X
Polished serpentine sphere falling 14 cm. into water.
1 0.003 sec.
2 0.006 sec.
3 0.008 sec.
4 0.011 sec.
5 0.013 sec.
6 0.014 sec.]
It may here be observed that whether the sphere be rough or smooth, its
size makes little or no difference in the character of the splash,
within a range of diameter from 12 to 32 millimetres--i.e. from about
1/2 inch to about 1-1/3 inches. No doubt with a very large sphere,
taking a long time to enter, the splash would be controlled more by
gravity than by surface-tension, but so long as the sphere is within the
limits mentioned this is not the case unless the height of fall be made
very small indeed.