Chapter 2 THE SPLASH OF A DROP-LOW FALL

We will now turn to the photographic record itself. The first series shows the splash of a drop of water weighing ·2 of a gram, and therefore 7·36 millimetres (or rather less than one-third of an inch) in diameter, falling 40 cm. (about 16 inches) into milk mixed with water. The object of adding milk to the water was to make it more visible. The addition of milk makes, as we shall see, a little but not much difference in the general character of the splash. The scale of the figures is three-quarters of the actual size.

The number written against any figure gives, on the assumption that no unobserved error has crept in, the time in decimal parts of a second that has elapsed since the stage marked "T = 0," which is nearest to the first instant of contact. The reader will understand from what has been said that the error in any of these times may be as much as two-thousandths of a second, but is not likely to be more than that, when all precautions were taken.

It will be observed that as the drop descends into the liquid the upper portion is at first not appreciably distorted, but that a little cup or crater of liquid is thrown up round it. As the drop descends further, this crater grows wider and higher and thicker in the wall, and jets are shot out from its edge or rim. These jets are visible even in the second figure. The black marks on the inside wall of the crater are due to the lamp-black carried down with the drop from the smoked surface of the supporting cup: though in one sense a disfigurement, they serve to show by their presence that the interior of the crater is lined by the original liquid which formed the drop, and thus afford useful information as to the nature of the flow.

The crater rises with great rapidity up to Fig. 4. In Fig. 5 the walls are beginning to grow thicker, while the next three figures show the crater subsiding and widening, till in Fig. 9 it lies as a mere ring of lobes on the surface, surrounding a central hollow.

SERIES I

Milk into water (40 cm.). Scale 3/4.

1

2

T = 0

3

0·002 sec.

4

0·007 sec.

5

0·018 sec.

6

0·031 sec.

7

0·040 sec.

8

0·050 sec.

9

0·056 sec.

Fig. 10 shows the beginning of the rebound, in the rising of a central column. It will be seen that the lamp-black is now all swept to the middle, indicating that the liquid of the original drop emerges at the head of the central column. Full confirmation of this is obtained from Fig. 12, which represents the emergent column obtained when the circumstances are all the same, except that we have a drop of milk falling into water instead of water falling into milk. It will be observed that the upper part only of the column is visible, precisely because it contains nearly all the milk of the drop, while the lower part, consisting chiefly of transparent water, remains invisible.

SERIES I-(continued)

10

0·064 sec.

11

0·073 sec. 12

13

0·093 sec.

No. 15 shows the column at its greatest height, and it should be noticed that Figs. 16 and 17 show a tendency on the part of the head of this column to split off as a separate drop.

SERIES I-(continued)

14

0·103 sec.

15

0·116 sec.

16

0·129 sec.

The column in subsiding forms a "cake" of liquid round the base. The edge of this circular cake (see Figs. 17, 18, and 19) is the first well-marked ripple spreading outwards in an ever-widening circle.

SERIES I-(continued)

17

0·153 sec.

18

0·197 sec.

19

0·217 sec.

If Fig. 19 is reached without the top of the column having separated, then the splash follows the course shown in Figs. 20a to 23a, in which it will be observed that the disappearance of the first column is very quickly followed by the rise of a secondary column very different in shape, which itself subsides again, but has not yet (in 23a) formed, as it ultimately will, a second "cake" on the top of the first. Thus the second ripple follows late after the first.

SERIES I-(continued)

Alternative (a).

20a

0·240 sec.

21a

0·242 sec.

22a

0·248 sec.

23a

0·253 sec.

If, however, the summit of the primary column succeeds in breaking off (as in Fig. 18b), or even in very nearly breaking off, then the impact of this newly-formed drop forms a second slight crater on the top of the first cake, and we have the series (18b to 24b), in which it will be observed that the rim of the secondary crater spreads rapidly outwards, so that a second well-marked circular ripple in this case quickly follows the first. The secondary column that is thrown up in Fig. 23b is very like that which emerged at a much earlier stage in the (a) series.

The photographs of this (b) series show very beautifully the manner in which the advancing edge of the ripple degenerates into smaller ripples travelling with greater speed.

SERIES I-(continued)

Alternative (b).

18b

0·214 sec.

19b

0·237 sec.

20b

0·242 sec.

21b

0·244 sec.

SERIES I-(continued)

Alternative (b).

22b

0·261 sec.

23b

0·257 sec.

24b

0·311 sec.

It will be readily understood that if the splitting off of the head of the primary column happens to take place a little earlier, or on the other hand is nearly, but not quite, complete when it descends below the surface, then subsequent configurations will differ somewhat from either of the sub-series here shown.

Since any figure photographed might belong to either sequence, the disentanglement of the two series required careful consideration and long experimenting.

The reappearance of the original drop at the head of the rebounding column, of which the explanation has been given in this chapter, is easily verified by naked-eye observation.

Let the reader when he next receives a cup of tea or coffee to which no milk has yet been added, make the simple experiment of dropping into it from a spoon, at the height of fifteen or sixteen inches above the surface, a single drop of milk. He will have no difficulty in recognizing that the column which emerges carries the white milk-drop at the top only slightly stained by the liquid into which it has fallen.

In the same way naked-eye observation reveals the crater thrown up by the entry of a big rain-drop into a pool of water. In either case what we are able to glimpse is a "stationary" stage. The rebounding column reaches a maximum height, remains poised for an instant, and then descends. The same is true of the crater. It is the relatively long duration of the moment of poise that produces on the eye a clear impression where all else is blurred by rapid change.

But there is frequently a curious illusion. We often seem to see the crater with the column standing erect in the middle of it. We know now that in reality the crater has vanished before the column appears. But the image of the crater has not time to fade before that of the column is superposed on it.

Those who are accustomed "to believe nothing that they hear and only half of what they see" may be glad to find at least the latter part of their maxim so completely justified.

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