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.
[Illustration: SERIES XI
Polished ivory sphere, 1.9 centim. in diameter, falling 60 cm. into
water mixed with milk.
1
2 T = 0
3
4 0.002 sec.
5
6 0.004 sec.
7 0.031 sec.
8 0.045 sec.
9 0.062 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 162.5 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 15.9 cm. in diameter was found (by naked-eye
observation) to give an airless splash when falling into water from a
height of 132.5 cm.; at 137.5 cm., there was much air taken down. This
observation at 137.5 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 162.5 cm., and a perfectly
airless splash was secured, and even at 172.5 cm. the record was 'very
little air indeed.'
"Again, a polished marble sphere 2.57 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."
[Illustration: SERIES XII
Smooth sphere of polished serpentine falling 100 centim. into water.
Scale 3/4.
1 T = 0
2 0.001 sec.
3 0.002 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 circumstances 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 24.7 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 12 deg..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 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.
[Illustration: SERIES XIII
Splash of a smooth wet sphere.
1 T = 0
2 0.003 sec.
3 0.015 sec.
4 0.037 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 pronounced, 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 multitude 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.
[Illustration: Polished stone sphere falling 15 centim. into water mixed
with glycerine.]
[Illustration: SERIES XIV
Polished stone sphere falling 75 centim. into pure glycerine. Scale
9/10.
1 2 3]
[Illustration: SERIES XV
Rough sphere falling 75 centim. into pure glycerine. Scale 1/1.
1 T = 0
2 0.001 sec.
3 0.002 sec.
4 0.003 sec.]
THE INFLUENCE OF TEMPERATURE.
It was found that if a polished sphere was heated in boiling water,
quickly rubbed dry, and let fall while still hot, a very marked
difference was produced. With the sphere hot, the height of fall can be
much increased before the splash becomes "rough." Thus with paraffin
oil, the height with a nickel-plated sphere rose from 22.2 cm. to 29.3
cm., and with water from 157 cm. to 234 cm.
THE REMARKABLE INFLUENCE OF A FLAME HELD NEAR THE LIQUID, AND TRAVERSED
BY THE SPHERE IN ITS FALL.
In our search for the explanation of the difference between the rough
and the smooth splash, it occurred to us to let the smooth sphere drop
through a flame held near the liquid, and the result was very
remarkable. With paraffin oil (and the sphere hot) the airless height
now rose from 29.3 cm. to 45.3 cm., and with water and a cold sphere, it
rose from 157 cm. to over 258 cm., which was the greatest height that
the laboratory would permit. Either the luminous flame of a bat's-wing
burner or the flame of a Bunsen burner held nearly horizontal produces
the effect, provided the flame is held near enough to the surface of the
liquid, and it is a very striking experiment to let the polished sphere
fall several times from a height which gives a large volume of bubbles
rising with much noise to the surface, and then to let it fall through
the flame, and to observe the complete change in the phenomenon. On a
sphere already roughened the flame has no observable effect.
THE SUPPOSITION OF ELECTRIFICATION TESTED AND REJECTED.
The behaviour with a flame led at first to the supposition that we had
to deal with an electrical phenomenon, for a flame would certainly
discharge completely any electrified sphere passing through it, and it
appeared reasonable to suppose that the sphere might become electrified
by friction with the air through which it fell.
It required a long series of experiments, into the details of which I
need not now ask my readers to enter, to prove that this tempting
explanation was untenable, and that there was no reason to believe that
electrification had anything to do with the matter.
EXPERIMENTS IN VACUO.
It remained to examine what part was played by the air in the whole
transaction. This could only be settled by removing the air and letting
the spheres, whether rough or smooth, fall through a vacuum into the
liquid, or rather through a space occupied only by the vapour of the
liquid in use.
Instantaneous photographs obtained under these conditions showed that
the presence of the air has no material influence on the early course of
the splash, and that a sphere which gives a "smooth" splash in air will
give a "smooth" splash in vacuo, while if the splash is "rough" in air,
it will also be "rough" in vacuo.
FOOTNOTES:
[G] Some useful information about the internal flow of the liquid was
obtained by the device of letting the sphere descend between two slowly
ascending streams of very minute bubbles liberated by electrolysis at
two electrodes placed in the liquid. These streams, initially straight
and vertical, were displaced and distorted as the sphere passed near
them and afforded a measure of the displacement of the fluid at
different points. For details see _Phil. Trans. Roy. Soc._, Vol. 194, p.
178 (1900).
[H] Glycerine was found to be a rather treacherous liquid, requiring
special precautions for which the reader who desires details is referred
to the original memoir. _Phil. Trans. Roy. Soc._, Series A, 1900. Vol.
194, p. 198.