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.
[Illustration: 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.
[Illustration: 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).