Chapter 9 THE EXPLANATION OF THE CAUSE OF DIFFERENCE BETWEEN THE TWO SPLASHES

I have some hope that, by the enumeration of the many surprising and puzzling facts mentioned in the last chapter, I may have succeeded in producing in the mind of my reader some sympathy with the state of perplexity of Mr. Cole and myself when, after four years of experimenting, we found ourselves still unable to answer the question, "Why does the rough sphere make one kind of splash, the smooth sphere another kind?"

By reflecting, however, on all the facts at our disposal, we were at last led to what seems to be an entirely satisfactory explanation, and one moreover which we were able to test by further experiment.

This explanation may be stated as follows:-

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. In the case of a solid rod we know that the head would be somewhat flattened out by a similar blow, and a wave of compression would travel down it; to this flattening or broadening out of the head of the column corresponds the great outward radial velocity, tangential to the surface, initiated in the liquid, of which we have abundant evidence in many of the photographs. (See pp. 75, 87, and 99.)

Into this outward-flowing sheath the sphere descends, and since each successive zone of surface which enters is more nearly parallel to the direction of motion of the sphere, the displacement of liquid is most rapid at the lowest point, from the neighbourhood of which fresh liquid is supplied to flow along the surface. Whether the rising sheath shall leave the surface of the sphere, or shall follow it, depends upon the efficiency of the adhesion to the sphere. If the sphere is smooth and clean, the molecular forces of cohesion will guide the nearest layers of the advancing edge of the sheath, and will thus cause the initial flow to be along the surface of the sphere.

To pull any portion of the advancing liquid out of its rectilinear path the sphere must have rigidity. If the advancing liquid meets loosely attached particles, e.g. of dust, these will constitute places of departure from the surface of the sphere; the dust will be swept away by the momentum of the liquid which, being no longer in contact with the sphere, perseveres in its rectilinear motion. If the dust particles are few and far between, the cohesion of the neighbouring liquid will bring back the deserting parts, but if the places of departure are many, then the momentum of the deserters will prevail. Thus at every instant there is a struggle between the momentum of the advancing edge of the sheath and the cohesion of the sphere; the greater the height of fall the greater will be the momentum of the rising liquid, and the less likely is the cohesion to prevail, and the presence or absence of dust particles may determine the issue of the struggle.

Roughness of the surface will be equally efficient in causing the liquid to leave the sphere. For the momentum will readily carry the liquid past the mouth of any cavities (see Fig. 20), into which it can only enter with a very sharp curvature of its path. It is to be observed that the surface-tension of the air-liquid surface of the sheath will act at all times in favour of the cohesion of the sphere, and even if the film has left the sphere the surface-tension will tend to make it close in again, but we should not be right in attributing much importance to this capillary pressure which, with finite curvatures, is a force of a lower order of magnitude than the cohesion, and, as the photographs now to be shown will clearly show, is incompetent to produce the effects observed.

Fig. 20

Having arrived at this general explanation, we proceeded to test it.

EXPERIMENTS ON THE INFLUENCE OF DUST.

In the first place, to test the influence of dust, the experiment was made of deliberately dusting the surface of the sphere. For this purpose a highly polished nickelled sphere was held in a pair of crucible tongs by an electrified person standing on an insulating stool, and by him presented to any dusty object that stood or could be brought within reach. Particles of dust soon settled on the electrified sphere, which was then carefully placed on the dropping ring with the dusty side lowest. The liquid used was paraffin oil, and the height of fall was 31·7 cm., at which this sphere when not dusted gave always a quite airless splash. When dusted an enormous bubble of air was carried down on each occasion. Although the sphere when laid on the dropping ring must have completely lost the electrical charge, yet it seemed worth while to go through the same electrifying process without dusting. The result showed that no change was produced. In order to see how far the influence of dust would go, the height of fall was now reduced, and it was found that with sphere (1) a fall of 17·1 cm. gave a perfectly rough splash when the surface was visibly dimmed with fine dust, and with a second similar sphere a fall of 16·7 cm. availed. If the surface was only slightly dusty, then at these low heights the splash remained "smooth."

It then occurred to us to try the effect of partial or local dusting, for we had already found by experimenting with a marked sphere that the method of dropping did not impart any appreciable rotation to the sphere, which reached the liquid in the attitude with which it started from the dropping ring. Accordingly, after dusting the sphere in the manner already described, the dust was carefully rubbed away from all but certain parts whose position was recorded. The experiments were very successful, and the results are shown on page 113. The liquid used was water, and the sphere was of polished serpentine, 2·57 centim. in diameter, falling 14 centim.

In Fig. 1 of Series XVI the sphere was dusted on the right-hand side, and a "sound of splash" was recorded. On the left side we see that there is no disturbance of the "smooth splash"; on the right is a "pocket" of air such as was obtained by accident in Series IX, Fig. 6 (see p. 91). The point of departure at which the liquid left the sphere is well marked, and a tangent from this point passes through the outermost conspicuous droplets that must have been projected from it.

In Fig. 2 the sphere was dusted at the top and on the right-hand side, but not much more than half-way down, and the configuration corresponds entirely to the facts. Here again a tangent from the well-marked drops on the right-hand side leads very nearly to the place of departure from the surface of the sphere.

In Fig. 3 the sphere was dusted near the bottom only. The appearance on the left-hand side seems to show that the liquid has, after leaving the sphere, again been brought within reach. This recovery at an early stage is explained by reference to photographs of Series VI (p. 81) of the splash of a rough sphere, which show that even the rough sphere is soon wetted for some distance up the sides, by the gradual passage of the sphere into the divergently flowing cone of liquid which surrounds the lower part. When the liquid again touches a polished part the film will be again guided up it in the manner already explained.

SERIES XVI

Spheres dusted at one side.

1 2

3

We observe that in Figs. 1 and 2 (as also in Fig. 6 of page 91) the continuous film or shell of liquid no longer reaches the outermost droplets that once have been at its edge. It must evidently have been pulled in by its own surface-tension, which of course will cease to exercise any inward pull on a drop that has once separated.

The influence of dust, thus incontestably proved, seems also to afford a satisfactory explanation of-

(1) The effect of a flame.

(2) The effect of heating.

(3) The variable and uncertain effects of electrification.

For, (1), we may suppose that the flame burns off minute particles of dust; (2), we know from Aitken's experiments[I] that dust from the atmosphere will not settle on a surface hotter than the air; (3) an electrified sphere descending through the air would attract dust to its surface unless it happened, as well might happen, that the air round about it, with its contained dust, had become itself similarly charged through the working of the electrical machine.

In further confirmation of our view that the leading clue to the explanation of the motion is the struggle between the adhesion of the rigid sphere and the tangential momentum of the liquid, we may cite the following points:-

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. If the surface is quite dry and still covered with the fine powder resulting from the process of roughening, the splash is "rough," and a great bubble of air is taken down. But if this coat of powder, which has neither cohesion nor shearing strength, be removed by rubbing, the splash (under this low velocity) is "smooth." Again, a marble freshly sand-papered and covered with the resulting powder, if let fall from 12 or 15 cm., gives a rough splash. The same marble picked out of the liquid and very quickly dropped in again from the same height, will give again a rough splash. Here the liquid film is thick and "shearable." But if the same sphere be allowed to drain or be lightly wiped, the splash will be smooth. We may conjecture that in this case enough fluid is left to fill up the interstices, but that the coat is not thick enough to shear easily. If, however, the sphere be thoroughly dried, the splash becomes "rough" again. This gives us the explanation of the facts already recorded in respect of the splash of a wet sphere. This splash was always irregular; the liquid drifted to one side where it would shear, while it disappeared from the other or became there too thin to shear, though sufficient to fill up crevices.

EXPLANATION OF THE RIBS OR FLUTINGS IN THE SPLASH OF A SMOOTH SPHERE.

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; thus there must be a strong viscous shear in the film impeding its rise. If by any fortuitous oscillation a radial rib arises, this will be a channel in which the liquid, being farther from the surface, will be less affected by the viscous drag; it will therefore be a channel of more rapid flow and diminished pressure, into which, therefore, the neighbouring liquid will be forced from either side. Thus a rib once formed is in stable equilibrium, and will correspond to a jet at the edge of the rim. This explains the persistence of the ribs when once established, and we may attribute their regular distribution to the fact that they first originate in the spontaneous segmentation of the annular rim at the edge of the advancing sheath. This explanation quite accords with the appearance of such figures as Fig. 6 of page 91 and Figs. 1 and 2 of page 113, in which, firstly, we see that the flutings are absent from that part of the sheath which has left the sphere, and, secondly, we see how much higher in every case the continuous film has risen in that part which has left the sphere than in the part which has clung to it, and has been hindered by the viscous drag. Especially is this the case in Fig. 2, Series XIV (p. 105), where the liquid was pure glycerine. The effect of the viscous drag is, in fact, most marked in the most viscous liquid, and it is also in the viscous liquid that the ribs are most strongly marked.

INFLUENCE OF THE NATURE OF THE LIQUID EXPLAINED.

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. The surface-tension also being smaller, the less is the abatement of velocity on account of work done in extending the surface.

FOOTNOTES:

[I] See Nature, vol. xxix., January 31, 1884.

[J] See Whetham on "The Alleged Slipping at the Boundary of a Liquid in Motion." Phil. Trans. Roy. Soc., Vol. 181 (1890).

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