A. M. Worthington

“ The splash of a drop is a transaction which is accomplished in the twinkling of an eye, and it may seem to some that a man who proposes to discourse on the matter for an hour must have lost all sense of proportion. ”

“ 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. ”

“ The reason that with ordinary continuous light nothing can be satisfactorily seen of the splash, is not that the phenomenon is of such short duration, but because the changes are so rapid that before the image of one stage has faded from the eye the image of a later and quite different stage is superposed upon it. ”

“ If we gradually increase the velocity with which a well-polished sphere enters the liquid we find that there is a gradual transition from the silent "smooth" or "sheath" splash taking down no air and giving rise to only an insignificant column, to the noisy, "rough," "basket" splash taking down much air and throwing up a tall and conspicuous jet. Thus in the fourth figure of Series XI, in which the height of fall has been increased from 15 to 60 cm. ”

“ It is not difficult to recognize some features of this splash without any apparatus beyond a cup of tea and a spoonful of milk. Any drinker of afternoon tea, after the tea is poured out and before the milk is put in, may let the milk fall into it drop by drop from one or two inches above it. The rebounding column will be seen to consist almost entirely of milk, and to break up into drops in the manner described, while the vortex ring, whose core is of milk, may be seen to shoot down into the liquid. ”

“ The two principles that I have now explained, viz. the principle of the skin-tension, and the principle of the instability and spontaneous segmentation of a liquid cylinder, jet, or annulus, will go far to explain much that we shall see in any splash, but it is well that the reader should realize how much has been left unexplained. Why, for example, should the crater rise so suddenly and vertically immediately round the drop as it enters? ”

“ It remains only to speak of the greater irregularity in the arms and rays as shown by the photographs. The point is a curious and interesting one. In the first place I have to confess that in looking over my original drawings I find records of many irregular or unsymmetrical figures, yet in compiling the history it has been inevitable that these should be rejected, if only because identical irregularities never recur. Thus the mind of the observer is filled with an ideal splash—an "Auto-Splash"—whose perfection may never be actually realized. ”

“ If, for example, a particular stage of the splash is photographed when the timing sphere falls just four feet to the gap, then by raising its releasing-lever about two-fifths of an inch, the laws of falling bodies tell us that we shall postpone the flash by just one-thousandth of a second, and the next photograph will accordingly reveal a stage just so much later. ”

“ Now this tendency to segment or topple into drops, whether of a straight cylinder or of an annulus, is the key to the formation of the arms and satellites, and indeed to much that happens in all the splashes that we shall examine. Thus in Fig. 12 we have an annular rim, which in Figs. 13 and 14 is seen to topple into lobes by which the rays are united in pairs, and even the special rays that are seen in Fig. 9 owe their origin to the segmentation of the rim of the thin disc into which the liquid has spread. ”

“ With a drop weighing only 0·4 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 Ia. 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 ”

“ Now this argument from analogy with a solid is rather misleading, for the forces that operate in the case of a solid sphere that flattens itself and rebounds, are due to the bodily elasticity which enables it not only to resist, but also to recover from any distortion of shape or shearing of its internal parts past each other. ”

“ Finally, in confirmation of our explanation, we have the fact that with a liquid of small density and surface-tension, such as paraffin oil, a much smaller velocity of impact with a highly polished sphere suffices to give a "rough" splash than with water, a liquid of greater density and surface-tension, the reason being without doubt that the tangential velocity given by the impact is greater with the lighter liquid, as, indeed, is proved to be the case by the greater height to which the surrounding sheath is thrown up. ”

“ But a liquid has no power of recovering from such internal shear, and the only force that checks the spread, and ultimately causes the recovery of shape, is the surface tension, which arises from the fact that the surface layers are always in a state of extension and always endeavouring to contract. ”

“ A liquid sphere makes a "rough" splash, and the photographs obtained show that the lower part of the in-falling drop is swept away by the tangential flow, while the upper part is still undistorted. Here we have cohesion but no rigidity.
Also we find that the "rough" splash is obtained by any process which gives a non-rigid surface to the sphere. Thus the splash made by a marble freshly roughened by sand-papering, or by grinding between two files and let fall from the very small height of 7·5 cm., can be practically controlled by attending to the condition of the surface. ”

“ It would be an immense convenience, as was suggested in the first chapter, if we could use a kinematograph and watch such a splash in broad daylight, without the troublesome necessity of providing darkness and an electric spark. But the difficulties of contriving an exposure of the whole lens short enough [pg 119] to prevent blurring, either from the motion of the object, or from that of the rapidly-shifting sensitive film, are very great, and any one who may be able to overcome them satisfactorily, will find a multitude of applications awaiting his invention. ”

“ Specimens of such patterns, obtained by letting drops of mercury, alcohol, and water fall on to smoked glass, are thrown on the screen, and the main characteristics are easily recognized. Such a pattern corresponds to the footprints of the dance that has been performed on the surface, and though the drop may be lying unbroken on the plate, it has evidently been taking violent exercise, and were our vision acute enough we might observe that it was still palpitating after its exertions. ”

“ When a sphere, either rough or smooth, first strikes the liquid, there is an impulsive pressure between the two, and the column of liquid lying vertically below the elementary area of first contact is compressed. For very rapid displacements the liquid on account of its viscosity behaves like a solid. ”

“ The splash is insignificantly small and of very short duration. [3] If the drying and polishing be not so perfect, the configurations of Series VII. are produced; while if the sphere be roughened with sandpaper, or left wet, Series VIII. is obtained, in which it will be perceived that, as was the case with the liquid drop, the water is driven away laterally, forming the ribbed basket-shaped hollow, which, however, is now prolonged to a great depth, the drop being followed by a cone of air, while the water seems to find great difficulty in wetting the surface completely. ”

“ The fact thus established experimentally, that the surface of a smooth sphere must be rigid if the film is to envelop it closely, suggests also a satisfactory explanation of the flutings. For we know from other researches on the motion of liquids, [J] that a layer of liquid actually in contact with a solid can have no motion relative to the solid, but must move with it. Thus in the film or sheath which rises over and envelops the sphere, the layer of liquid next to the solid must be moving downwards with it, while the outermost layers at least are moving upwards ”

“ The modus operandi is consequently as follows:—The observer, sitting in comparative but by no means complete darkness, faces the apparatus as it appears in Fig. 2, presses down the ends A ́B ́ of the levers first described, so that they are held by the electro-magnet C (Fig. 1) ; then he presses the lever NP down on the electro-magnet F, sets the timing sphere and drop in place, and then by means of a bridge between two mercury cups, short-circuits and thus cuts off the current of the electro-magnet C. This lets off drop and sphere, and produces the flash. ”

“ If we keep to the same size of drop and increase the fall to something over a yard, no great change occurs in the nature of the splash, but the emergent column is rather higher and thinner and shows a tendency to split into drops. ”

“ No one has yet examined what happens when a rough sphere enters a liquid with a very high velocity. That the motion set up must differ from that at a low velocity is apparent to any one who has thrown stones from a low bridge into deep water below. ”

“ For this purpose I have reduplicated the apparatus which you have seen, and have it here so arranged that I can let the drop fall on to the horizontal condenser plate of the lantern, through which the light passes upwards, to be afterwards thrown upon this screen. The illuminating flash will be made inside the lantern, where the arc light would ordinarily be placed. I have now set a drop of mercury in readiness and put the timing sphere in place, and now if you will look intently at the middle of the screen I will darken the room and let off the splash. ”

“ 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 [pg 33] hand, if the surface is concave outwards, then the surface-tension tends to pull the interior liquid forward, and so to diminish the concavity. ”

“ Very beautiful forms of the same type indeed, but different in detail, are those produced by a drop of water falling into the lighter and more mobile liquid, petroleum.
It will now be interesting to turn to the splash that is produced when a solid sphere, such as a child's marble, falls into water. ”

“ On cutting off the current from the electro-magnet the spring, acting as a catapult, tosses up the longer arm of the lever and thus removes the watch-glass from below the drop (D) , which is left unsupported in mid-air, so that it falls from a definite fixed distance into a bowl of water placed below it, towards the surface of which the camera (C) is directed. This solves problem number one. Of course, if we wish to observe the splash of a solid sphere, there is no need to smoke the surface of the watch-glass. Indeed, the sphere may be more conveniently supported on a small ring. ”

“ The flash must be bright enough for the image of what is seen to remain long enough on the eye for the observer to be able to attend to it, and even to shift his attention from one part to another, and thus to make a drawing of what is seen. If necessary the experiment must be capable of repetition, with an exactly similar drop falling from exactly the same height, and illuminated at exactly the same stage. ”

“ That the jet we now see should be directed downwards rather than upwards may, I think, be explained in a general way as follows:—The great initial momentum of the sphere causes it to continue in rapid motion after the bubble has closed, thus the sphere acts as a sort of piston, which by increasing the length of the air-tube diminishes the pressure in it and so sucks in the bubble, which is driven down by the greater atmospheric pressure above. ”

“ The paraffin oil used in these experiments had, at a temperature of 12°·5 centigrade, a specific gravity ·840 and a surface-tension about ·39 of that of water. Since only a small increase of height was required with this liquid to make a smooth sphere give [pg 102] the same splash as a rough one, this liquid was found much more convenient than water in investigating the transition.
When water is made more viscid by the gradual addition of glycerine, [H] the surface-tension and the specific gravity are but little altered though the viscosity is steadily and sensibly increased. ”

“ As the drop descends the hollow becomes wider and deeper, and finally closes over the drop (Fig. 3) , which, however, soon again emerges as the hollow flattens out, appearing first near, but still below the surface (Fig. 4) , in a flattened, lobed form, afterwards rising as a column somewhat mixed with adherent water, in which traces of the lobes are at first very visible.
The rising column, which is nearly cylindrical, breaks up into drops before or during its subsequent descent into the liquid. ”

“ 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. ”

“ As it disappears below the surface the outward and downward flow causes a hollow to be again formed, up the sides of which an annulus of milk is carried, while the remainder descends to be torn again a second time into a vortex ring, which, however, is liable to disturbance from the falling in of the drops which once formed the upper part of the rebounding column. ”

“ If the present volume is so fortunate as to find many readers among the general public, as the author hopes it may, especially among the young whose eyes are still quick to observe, and whose minds are eager, it will be on account of admiration for the exquisite beauty of some of the forms assumed, of surprise at the revelation of so much where so little was expected, and because of the peculiar fascination that is always felt in following any gradually changing natural phenomenon, in which the sequence of events can, partly at any rate, be anticipated and understood. ”

“ In an attempt made eighteen years ago to photograph the splash of a drop of mercury, I was unable to procure plates sufficiently sensitive to respond to the very short exposures that were required, and consequently abandoned the endeavour. But in recent years plates of exquisite sensitiveness have been produced, and such photographs as those taken by Mr. Boys of a flying rifle bullet have shown that difficulties on the score of sensitiveness have been practically overcome. ”