A Study of Splashes Part 4

20 0311 sec.

21 0321 sec.]

CHAPTER V

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, 736 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 161 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.

[Ill.u.s.tration: SERIES II

Milk into water (100 cm. fall).

1 0002 sec.

2-a 2 0002 sec.

3 0002 sec.

4 0009 sec.

5 0018 sec.

6 0018 sec.

7 0039 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 ill.u.s.trate 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.

[Ill.u.s.tration: SERIES II--(_continued_)

8 0054 sec.

9 0085 sec.

10 0105 sec.

10-a 0103 sec.

10-b 0111 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.

[Ill.u.s.tration: SERIES II--(_continued_)

11 0105 sec.

12 0095 sec.

13 0113 sec.

14 0132 sec.

15 0194 sec.]

[Ill.u.s.tration: SERIES II--(_continued_)

16 0217 sec.

17 0240 sec.

18 0272 sec.

19 0311 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.

[Ill.u.s.tration: SERIES III

Water-drop weighing 04 grams falling 137 cm. (4-1/2 feet) into milk mixed with water. Scale 1/2.

1 T = 0 2 0005 sec.

3 0016 sec.

4 0019 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.

[Ill.u.s.tration: SERIES III--(_continued_)

5 0017 sec.

6 0020 sec.

7 0036 sec.

8 0053 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 04 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.

[Ill.u.s.tration: SERIES III--(_continued_)

9 0040 sec.

10 0046 sec.

11 0070 sec.]

[Ill.u.s.tration: FIG. 16

Arrangement for taking photographs below the surface of the liquid.]