A Study of Splashes Part 7

Polished serpentine sphere falling 14 cm. into water.

1 0003 sec.

2 0006 sec.

3 0008 sec.

4 0011 sec.

5 0013 sec.

6 0014 sec.]

It may here be observed that whether the sphere be rough or smooth, its size makes little or no difference in the character of the splash, within a range of diameter from 12 to 32 millimetres--i.e. from about 1/2 inch to about 1-1/3 inches. No doubt with a very large sphere, taking a long time to enter, the splash would be controlled more by gravity than by surface-tension, but so long as the sphere is within the limits mentioned this is not the case unless the height of fall be made very small indeed.

CHAPTER VIII

THE TRANSITION FROM THE SMOOTH OR "SHEATH" SPLASH TO THE ROUGH OR "BASKET" SPLASH

THE INFLUENCE OF VELOCITY.

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. (i.e. from 6 inches to 2 feet), the sphere being of polished ivory, we see that the enveloping sheath has in many places broken away from the surface before the summit has been covered.

It is well known that a sphere moving through a liquid pushes away the liquid in front of it, which flowing round closes in at the back of the sphere.

Although the surface round the column of Fig. 6 is still very flat, the liquid just below it must be streaming inwards,[G] as is indicated by the radial striae. To the meeting of these converging streams we must attribute the large access of liquid that is forced up into the column, whose subsequent toppling into drops is accompanied by the curious, characteristic, lop-sided curvature of the later figures.

[Ill.u.s.tration: SERIES XI

Polished ivory sphere, 19 centim. in diameter, falling 60 cm. into water mixed with milk.

1 2 T = 0 3 4 0002 sec.

5 6 0004 sec.

7 0031 sec.

8 0045 sec.

9 0062 sec.]

Series XII shows how even with a very highly polished metal sphere falling into water from the still greater height of 100 cm. the characteristic sheath of the "smooth" splash is no longer so closely fitting even at an early stage, but is beginning to resemble the earlier stages of the basket-shaped crater of the "rough" splash; yet no air was taken down at this height.

The transition was also watched by means of photographs taken below the water-line.

It may be well here to guard the reader against a possible misconception. The curved outline of the liquid in these photographs does not represent the path followed by the particles. Each particle must have travelled in a nearly straight line from the moment it left the surface of the sphere, and must still be moving upwards and outwards. Gravity has not had time to produce any sensible displacement.

This applies also to the curved outlines in many other early figures.

INFLUENCE OF THE CONDITION OF THE SURFACE.

By very careful rubbing of such a polished, steel sphere, it was found possible to increase the height of fall to 1625 cm. (well over 5 feet) and yet to secure a perfectly "airless," "smooth" splash. But the equilibrium of the splash, if I may use the phrase, is, at this high velocity of entry (564 cm. per sec., or about 18 feet per sec.), very unstable, and was found to depend on minute differences in the condition of the surface. How minute this difference may be, which yet makes the whole difference in the character of the splash, may be gathered from the following extract from the original paper:--

"A polished steel sphere 159 cm. in diameter was found (by naked-eye observation) to give an airless splash when falling into water from a height of 1325 cm.; at 1375 cm., there was much air taken down. This observation at 1375 cm. was repeated three times, observer C. doing the polishing. Then observer W. polished, and the splash was first _nearly_ airless and then _quite_ airless. Then, by persevering in the rubbing, the height of fall was gradually raised to 1625 cm., and a perfectly airless splash was secured, and even at 1725 cm. the record was 'very little air indeed.'

"Again, a polished marble sphere 257 cm. in diameter falling into water from a height of 112 cm. was found to take down 'much air' when rubbed with a certain clean handkerchief A, and 'none at all, or only very little,' when rubbed with clean handkerchief B. This result was confirmed four times with B and five with A. These handkerchiefs were subsequently examined under the microscope, but were found to be extremely similar, and the cause of the difference remained for the time beyond conjecture.

"On another occasion, of two similar nickel-plated steel spheres, each 19 millimetres in diameter, and each treated in exactly the same way, falling 22 cm. into paraffin oil, one would always take down much air and the other little or none, and again microscopic examination showed only a very slight difference in the surfaces."

[Ill.u.s.tration: SERIES XII

Smooth sphere of polished serpentine falling 100 centim. into water.

Scale 3/4.

1 T = 0 2 0001 sec.

3 0002 sec.]

By wetting the surface of a smooth sphere we can always convert a smooth or "sheath" splash into a rough or "basket" splash. Thus when the ivory sphere (which when dry and well-polished gave, with a fall of 60 cm., the splash of Series XI, p. 97), was allowed to fall _wet_ into the liquid, all other circ.u.mstances remaining the same, the splash of Series XIII, p. 103, was obtained, which is entirely different from the first.

The wetting was effected by dipping the sphere into the bowl of milky water into which it was to fall, and then shaking off as much as possible of the adherent liquid, but in all cases the splash quickly became unsymmetrical, probably through the liquid, during the fall, drifting to one side of the sphere.

INFLUENCE OF THE NATURE OF THE LIQUID.

The nature of the liquid employed has a great influence in determining whether at a given height the splash shall be "rough" or "smooth."

Thus with paraffin oil the maximum height that could be reached with an airless splash with highly polished nickel-plated spheres, well rubbed on a selvyt cloth, was found to be only 247 cm. (about 10 inches), but, with water, a fall of 160 cm. (over 5 feet) could be reached. The paraffin oil used in these experiments had, at a temperature of 125 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 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. An admixture of two parts of glycerine to fifty-one of water produced no perceptible change in the splashes observed. When the glycerine was increased to six volumes in fifty-one of water, though this made the viscosity half as great again, the change was noticeable but still slight, the chief difference being, with a smooth sphere, the greater salience of the ribs or flutings in some of the earlier stages of the glycerine splash, and the much greater reluctance of the subsequent jets to topple into droplets. This latter feature is well seen in the first figure on page 105, showing the entry of a smooth sphere of polished serpentine stone into this glycerine mixture from a height of 50 cm.

[Ill.u.s.tration: SERIES XIII

Splash of a smooth wet sphere.

1 T = 0 2 0003 sec.

3 0015 sec.

4 0037 sec.]

With pure glycerine, which is much more viscous, the splash of the same polished serpentine sphere falling from 75 cm. (about 2-1/2 feet), is shown in Series XIV. In the original photographs the radial furrows on the right-hand side of Fig. 2 are very p.r.o.nounced, and even in Fig. 1 the fluting of the film is seen to be already well developed on the left-hand side; but these details have proved rather too delicate for reproduction in the plate. Two photographs taken of stage 2 had each of them an isolated jet, owing probably to the fact that when working with so sticky a liquid it was difficult to avoid contaminating the cloth on which the sphere was each time repolished after washing in water, with the result that the spheres behaved as if locally rough. The relatively great length and height of this jet brings out well the part played by viscosity, both in delaying segmentation into droplets and also in hindering the flow of the rest of the liquid sheath which has remained in contact with the sphere.

With a rough sphere falling into pure glycerine from the same height of 75 cm., except for an occasional jet that may escape as in Fig. 4 of Series XV, the proceedings are uneventful, as a glance at the series will show. With the same height of fall into water we should have had an exquisite crater fringed with a mult.i.tude of fine jets, and ultimately closing to form a bubble. We thus see how little play is given to the action of the surface-tension in a very viscous liquid.

[Ill.u.s.tration: Polished stone sphere falling 15 centim. into water mixed with glycerine.]

[Ill.u.s.tration: SERIES XIV

Polished stone sphere falling 75 centim. into pure glycerine. Scale 9/10.

1 2 3]

[Ill.u.s.tration: SERIES XV

Rough sphere falling 75 centim. into pure glycerine. Scale 1/1.