HIGHER FALLS--BUBBLE-BUILDING
It might well be expected that the effect of increasing the height of
fall of our drop to 100 cm. would be simply to emphasize the phenomena
already observed, and to obtain a higher crater and a taller rebounding
column. Such an expectation would be mistaken. A new phenomenon makes
its appearance. The crater does indeed rise to a greater height, but its
mouth closes so as to form a bubble on the surface of the liquid. If the
height be not too great the closing is either incomplete or at any rate
only temporary, and the bubble reopens at the top to make way for the
column which rises as before from the base, but is now much thicker and
hardly so high as before.
In the Series II, which is now given, the drop was of milk, 7.36 mm. in
diameter, and fell 100 cm. into water.
Photographs 1 and 2--to which is added 2-a, though taken under slightly
different conditions--show that the drop on entering punches a
sheer-walled hole, for the fine line of light seen above the level of
the top of the drop in Figs. 2 and 2-a marks the circular cliff-like
edge of the as yet undisturbed liquid. Up the vertical sides of this
circular pit the liquid of the drop is streaming. This cliff is highest
and perhaps clearest in Fig. 2-a.
The closing of the mouth of the crater, which is just beginning in Fig.
5, is to be explained as follows. If the crater were a simple
thin-walled cylinder of liquid, it would contract under the influence of
the surface-tension just as does a soap-bubble, but not so fast, since
the walls have only a horizontal curvature. If the wall is thinner above
than below, then the upper part will contract faster than the lower,
through there being less liquid to accelerate. Now the supply of liquid
is from below, and will thicken the lower part of the walls first, and
thus account for the faster closing of the mouth. On the other hand, the
uppermost edge of the crater is the place where the checking influence
of the surface-tension on the upward flow is first felt, with the result
that the edge of the rim is thickened by the influx from below, so that
a more or less regular rope-like annulus is formed round the edge. Now
calculation shows that such an annulus, so long as its thickness is not
more than 1.61 times the thickness of the wall below, will contract
quicker than the wall, and this will tend to close the crater, somewhat
as a bag would be closed by the contraction of an elastic cord round the
mouth. This rope-like thickening of the edge is to be seen in Figs. 5
and 7, and especially in Figs. 3 and 4 of Series III on page 63.
[Illustration: SERIES II
Milk into water (100 cm. fall).
1 0.002 sec.
2-a
2 0.002 sec.
3 0.002 sec.
4 0.009 sec.
5 0.018 sec.
6 0.018 sec.
7 0.039 sec.]
The photographs 9, 10, and 11 (obtained after adding a little milk to
the water in order to render it more visible) were at first very
puzzling. What happens is that the bubble sometimes reopens very soon
(or perhaps does not quite close) as in Fig. 9, and makes way for the
column which rises from the base exactly as in the previous series. This
column may be dimly seen through the walls of the bubble in Fig. 9, and
No. 10 shows the column alone, the bubble having opened early and
receded with great velocity, a few drops round the base being all that
is left of it. Nos. 10-a and 10-b illustrate this reopening. In 10-a the
milk-drop was allowed to fall again into quite pure water, and the
photograph shows very beautifully the summit of the column, with the
original milk-drop at the top, emerging through the reopening mouth of
the bubble; and Fig. 10-b shows the same at a very slightly later stage
when the bubble has completely retreated.
[Illustration: SERIES II--(_continued_)
8 0.054 sec.
9 0.085 sec.
10 0.105 sec.
10-a 0.103 sec.
10-b 0.111 sec.]
In Fig. 11 the bubble has been too firmly closed to reopen, and the
summit has been struck by the column within. The next figure (No. 12)
shows how in such a case the emergent column becomes entangled in the
liquid of the bubble when it bursts. Under the influence, however, of
the surface-tension, which pushes back the protuberances and pulls out
the hollows, regularity of form is soon regained. Thus Fig. 13 shows the
emergent columns at a later stage after such an encounter, already much
more symmetrical; and the subsequent photographs (for which a good deal
of milk was added for the sake of greater visibility) show a column of
uniformly sedate and respectable rotundity, betraying no traces of any
youthful irregularities.
[Illustration: SERIES II--(_continued_)
11 0.105 sec.
12 0.095 sec.
13 0.113 sec.
14 0.132 sec.
15 0.194 sec.]
[Illustration: SERIES II--(_continued_)
16 0.217 sec.
17 0.240 sec.
18 0.272 sec.
19 0.311 sec.]
Series III shows the effect of still further increasing the height of
fall of the water-drop (to 137 cm., or about 4 ft. 6 in.), and at the
same time doubling its volume so that it now weighs .4 gram. The crater
now closes in about 18/1000 of a second, and forms a comparatively
permanent bubble. The rope-like thickening of the edge, already alluded
to, is well seen in Figs. 3 and 4. In its earlier stages the bubble is
thick-walled, rough, and furrowed, but becomes smoother and thinner the
longer it lasts, both because the liquid drains down the sides and
because it becomes more uniformly distributed under the equalizing
influence of the surface-tension.
[Illustration: SERIES III
Water-drop weighing 0.4 grams falling 137 cm. (4-1/2 feet) into milk
mixed with water. Scale 1/2.
1 T = 0
2 0.005 sec.
3 0.016 sec.
4 0.019 sec.]
Such a bubble may remain long closed, as in Fig. 8, becoming every
moment more delicate and exquisite, or it may open at an even earlier
stage, as in Fig. 9.
There is a characteristic difference between the arms of a closing and
of an opening bubble. It will be noticed that up to the moment of
closing the arms slope outwards. The upper portions have been projected
at an earlier stage when the mouth of the crater was wider open and the
flow was either actually outwards or more nearly vertical; then as the
mouth contracts the arms are left behind in the upper parts.
[Illustration: SERIES III--(_continued_)
5 0.017 sec.
6 0.020 sec.
7 0.036 sec.
8 0.053 sec.]
In an opening bubble, on the other hand, the arms are at first vertical,
and later have the very characteristic inward slope of the last figure,
which is also well seen in Fig. 10-a of the last series. Here the edge
of the opened bubble retreats outwards and downwards, leaving the arms
behind.
Such is the origin of the bubbles raised by the big drops of a thunder
shower on the surface of a pool. The building of each fairy dome is
accomplished in less than two-hundredths of a second, and before
one-tenth of a second has elapsed the whole construction may have
vanished. One can almost regret that so beautiful a process should have
been so long unwatched.
To build these bubbles a large drop is essential. With a drop weighing
only 0.4 of a gram, even though it fall from a height of 177 cm., there
is no bubble, and the splash is almost exactly that of Series I-a. The
exact time required for the closing of the bubble probably depends a
good deal on the phase of oscillation of the drop at the moment of
entry, and, as already observed, a big drop, which lies very flat in
the dropping cup, is set vibrating more strongly on liberation than a
small one.
We shall see in Chapter VII that the impact of a rough solid sphere, if
falling from a sufficient height, produces a very exquisite bubble; in
this case irregularities due to oscillation are absent, and the closing
can be timed with greater precision.
[Illustration: SERIES III--(_continued_)
9 0.040 sec.
10 0.046 sec.
11 0.070 sec.]
[Illustration: FIG. 16
Arrangement for taking photographs below the surface of the liquid.]