A Study of Splashes Part 5

CHAPTER VI

BELOW THE SURFACE[F]

Our investigation has so far been limited to what we can see from above the surface of the liquid; nor perhaps would it occur to any one acquainted only with so much as we have yet examined that it might be worth while to look below the general level of the surface. The discovery, however, that when the splash is made by a solid sphere very remarkable phenomena, which will be described in the next chapter, take place below the surface, led at a much later date to a similar examination in the case of a liquid drop.

A suitable arrangement of the apparatus in the dark room is shown in the accompanying diagram (Fig. 16).

The water into which the drop is to fall is placed in a thin gla.s.s vessel AB, with parallel sides. (An inverted clock-shade makes a very convenient vessel.) The water fills the vessel to the brim, and is allowed to overflow it in a steady stream, thus presenting a surface which, being perpetually renewed, is maintained perfectly clean. Close behind the vessel is a plate P of finely roughened gla.s.s, on which the light from the spark-gap F, in front of its concave reflector M, is thrown by means of the condenser lens L taken from an optical lantern.

This provides a very uniformly illuminated background against which the splash is viewed by means of the camera C, whose optic axis is horizontal, either a little below the level of the liquid surface or at that level. By having it just at the level of the surface we secure simultaneous pictures of what is going on both above and below the surface. There is, to be sure, a narrow band or region of confusion stretching across the photographs in which the images obtained by reflection, both external and internal, overlap the direct images, and it should also be mentioned that the two pictures will not be quite in focus together, for the optical effect of the water, through which the part below the surface is viewed, is to bring the image forward.

The photographs of Series IV were obtained in this way from the splash of a drop of water weighing 0176 grams falling 40 cm. into water. (The same splash as that of Series I-a.) The perfectly spherical form presented by the cavity below the surface is very remarkable. In the present case, this spherical cavity when at its deepest, as in Fig. 5, would contain about fifty of the original drops, and in other cases--e.g. with a drop of 1/4 the volume, falling from 177 cm.--the cavity would contain as many as 360 of the original drops.

In Figs. 5, 6, and 7 the depth of the cavity is nearly constant, but the diameter is steadily increasing. The spherical form, however, is still maintained. The last figure shows the central column just beginning to rise.

[Ill.u.s.tration: SERIES IV

The splash of Series I-a viewed below the surface.

1 2 T = 0 3 0009 sec.

4 0012 sec.

5 0016 sec.

6 0023 sec.

7 0039 sec.

8 0055 sec.

9 0070 sec.]

There can be no doubt that the liquid of the original drop is spread out in an excessively thin lining over the interior of this sphere. The reader has seen for himself part of the evidence in the streaks of milk that are carried up the inner walls of the crater when a milk-drop falls into water (Series II); in the streaks of lamp-black that are carried there when the drop is of milk, and it may here be mentioned that other photographs that cannot be reproduced here have enabled me to trace the gradual deformation of the drop into this thin layer and show that it pa.s.ses through configurations like Figs. 17, 18, and 19.

[Ill.u.s.tration: FIG. 17]

[Ill.u.s.tration: FIG. 18]

[Ill.u.s.tration: FIG. 19]

It appears possible that the study of this remarkable spherical excavation may afford a clue that will lead to a solution of the very difficult hydro-dynamical questions involved, and the matter is still being investigated.

FOOTNOTES:

[F] The information conveyed in this chapter was first published in a communication to the Mathematical and Physical Section of the British a.s.sociation at Leicester in 1907.

CHAPTER VII

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 gla.s.s "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 15 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.

[Ill.u.s.tration: SERIES V

Rough sphere. "Basket splash."

Diameter of sphere, 15 centim. Height of fall, 15 centim.

1 T = 0 2 0003 sec.

3 0006 sec.

4 5 6]

[Ill.u.s.tration: SERIES V

Rough sphere--(_continued_).

7 0024 sec.

8 0032 sec.

9 0042 sec.

10 0060 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.

[Ill.u.s.tration: SERIES V

Rough sphere--(_continued_).

11 0068 sec.

12 0076 sec.

13 0088 sec.

14 0100 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.

[Ill.u.s.tration: SERIES VI

The splash of a rough sphere as seen below the surface.