Chapter 7 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.

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

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.

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.

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.

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.

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.

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.

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).

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.

Fig. A

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.

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.

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