A Study of Splashes Part 2

17 0153 sec.

18 0197 sec.

19 0217 sec.]

If Fig. 19 is reached without the top of the column having separated, then the splash follows the course shown in Figs. 20-a to 23-a, 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 23-a) formed, as it ultimately will, a second "cake" on the top of the first. Thus the second ripple follows late after the first.

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

Alternative (_a_).

20-a 0240 sec.

21-a 0242 sec.

22-a 0248 sec.

23-a 0253 sec.]

If, however, the summit of the primary column succeeds in breaking off (as in Fig. 18-b), 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 (18-b to 24-b), 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. 23-b 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.

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

Alternative (_b_).

18-b 0214 sec.

19-b 0237 sec.

20-b 0242 sec.

21-b 0244 sec.]

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

Alternative (_b_).

22-b 0261 sec.

23-b 0257 sec.

24-b 0311 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.

CHAPTER III

PRINCIPLES INVOLVED

The reader's attention has now been directed to various features which, with certain modifications, will be found in many of the splashes that we shall examine; but so far the language used has been simply descriptive and in no way explanatory. Instead of going on to describe other splashes in the same way, and thus to acc.u.mulate a great ma.s.s of uncoordinated descriptive detail, it will be better to pause for a moment in order to become acquainted with certain principles connected with the behaviour of liquids, the application of which will go a long way towards explaining what we see going on in any splash.

The first principle to be understood is that the surface layers of any liquid behave like a uniformly stretched skin or membrane, which is always endeavouring to contract and to diminish its area. If the surface is flat, like the surface of still liquid in a bowl, this surface-tension has only the effect of exerting a small inward pull on the walls of the bowl. But if the surface is curved, with a convexity outwards, then the surface layers, on account of their tension, press the interior liquid back, and thus tend to check the growth of any protuberance; while, on the other hand, if the surface is concave outwards, then the surface-tension tends to pull the interior liquid forward, and so to diminish the concavity.

Direct evidence of this surface-tension is easy to cite. We have it in any pendent drop, such as any of those shown in the accompanying figures.

[Ill.u.s.tration: WATER.

TURPENTINE.

Pendent drops (magnified 2-1/4 times).]

If we ask ourselves how it is that the liquid in the interior of one of these drops does not flow out, pressed as it is by the liquid above it, the answer is that everywhere the stretched skin presses it back. A soap-bubble too presses on the air in its interior, both the outside layers and the inside layers of the thin film being curved over the interior s.p.a.ce. This is the reason that a soap-bubble blown on the bowl of a pipe will slowly collapse again if we remove the stem of the pipe from our mouth. The bubble drives the interior air back through the pipe. And it is easy to show that if two soap-bubbles be blown on the ends of two tubes which can be connected together by opening a tap between them, then the smaller will collapse and blow out the larger.

The reason of this is that in the bubble of smaller radius the surface layers are more sharply curved, and therefore exert a greater pressure on the air within. Thus if a strap be pulled at each end with a total tension T and bent over a solid cylinder of small radius, as in Fig. 6, it is easy to see that the pressure on the surface of the part of the cylinder touched by the strap is less than if the strap be bent over an equal area on a cylinder of larger radius (Fig. 7). The tension of the surface layers of a liquid causes them to act on the liquid within, exactly as does the stretched strap on the solid in these figures. If at any place the liquid presents, as it generally does, not a cylindrical surface, but one with curvature in two directions, then the pressure corresponds to what would be produced by two straps crossing at right angles, laid one over the other, each with the curvature of the surface in its direction (Fig. 8).

[Ill.u.s.tration: FIG. 6]

[Ill.u.s.tration: FIG. 7]

[Ill.u.s.tration: FIG. 8]

[Ill.u.s.tration: FIG. 9]

We can now understand why the drop that has been lying on the watch-gla.s.s should oscillate in its descent. The sharp curvature of the edge AA of the drop (see Fig. 9) tells us that the liquid there is pushed back by the pressure of the stretched surface layers, and when the supporting gla.s.s is removed the sides of the drop move inwards, driving the liquid into the lower part, the tendency being to make the drop spherical, and so to equalize the pressure of the surface at all points. But in the process the liquid overshoots the mark, and the drop becomes elongated vertically and flattened at the sides. This causes the curvature at top and bottom to be sharper than at the sides, and on this account the back-pressure of the ends soon checks the elongation and finally reverses the flow of liquid, and the drop flattens again. As an example of the way in which a _concavity_ of the surface is pulled out by the surface-tension may be cited the dimples made by the weight of an aquatic insect, where its feet rest on the surface without penetrating it.

This same surface-tension checks the rise of the crater, and would cause it to subside again even without the action of gravity. Thus the pressures of the sharply curved crater-edge on the liquid between the crater walls are indicated by the dotted arrows in Fig. 10, and arise from the surface-tension indicated by the full arrows. During the early part of the splash the surface-tension is more important than gravity in checking the rise of the walls. For, as the numbers show, the crater of Series I is already at about its maximum height in No. 4, i.e. about seven-thousandths of a second after first contact. In this time the fall due to gravity would be only about 1/100 of an inch. Thus if gravity had not acted the crater would only have risen about 1/100 of an inch higher. The same reasoning applies to the rise of the central column, but here the curvature at the summit is much less sharp. The numbers show that the column reaches its maximum height in about 5/100 of a second after its start in No. 10, and in this time the fall due to gravity is about half an inch, so that gravity has reduced the height by this amount.

[Ill.u.s.tration: FIG. 10]

The second principle which I will now mention enables us to explain the occurrence of the jets and rays at the edge of the crater and their splitting into drops.

It was shown in 1873 by the blind Belgian philosopher, Plateau,[D] that a cylinder of liquid is not a figure of stable equilibrium if its length exceeds about 3-1/7 times its diameter. Thus a long cylindrical rod of liquid, such as Fig. 11, if it could be obtained and left for a moment to itself, would at once topple into a row of sensibly equal, equidistant drops, the number of which is expressed by a very simple law, viz. that for every 3-1/7 times the diameter there is a drop, or that the distance between the centres of the drops is equal to the circ.u.mference of the cylinder.

[Ill.u.s.tration: FIG. 11]

The cause of this instability is the action of the same skin-tension that we have already spoken of. Calculation shows, and Plateau was able to confirm the calculation by experiment, that if through chance agitations lobes are formed at a nearer distance apart than 3-1/7 times the radius, with hollows between as in the accompanying Fig. 12, then the curvatures will be such as to make the skin-tension push the protuberances back and pull the hollows out. But if the protuberances occur at any greater distances apart than the length of the perimeter, then the sharper curvature of the narrower parts will drive the liquid there into the parts already wider, thus any such an initial accidental inequality of diameter will go on increasing, or the whole will topple into drops.

[Ill.u.s.tration: FIG. 12]

At the last moment the drops are joined by narrow necks of liquid (Fig.

13), which themselves split up into secondary droplets (Fig. 14).