Popular Science Monthly/Volume 20/December 1881/Studies of Vortex-Rings
| STUDIES OF VORTEX-RINGS. |
By ADRIEN GUÉBHARD.
A FAKING skip-rings in the water, and gazing at the vapors in the air, furnish common expressions for complete inactivity and vacuity. Yet, in these occupations may be found subjects of profound and worthy studies. Nothing is vulgar to one who knows how to see, nothing indifferent to one who knows how to observe; and the fall of a drop of water, insignificant as we may regard it, may bring us into the neighborhood of the ultimate mysteries of those regions to which the fall of an apple once transported the immortal genius of Newton. As profitable subjects for study may be found in those common rings, simple wrinkles on the surface of the water, in which the physicist sees many things and the clown few; or, in those turbid clouds of smoke which every day float toward the sky from our fires here below. Everybody has seen some adroit smoker throw from his mouth or his pipe pretty, white wreaths, whose whirling vapors it was a pleasure to follow in the air.[1] It is a fact of daily observation that a drop of soap and water dropping from the end of the fingers spreads out in the basin into the form of a perfect ring that gradually increases as it descends toward the bottom.
Why do the light particles, instead of scattering promiscuously in the liquid or gaseous medium, take this special state of mobile equilibrium and regular grouping? Why this form so fragile in appearance, instead of any other more simple and possibly more stable? Is it by pure chance or by pure direction? And, if the latter is the case, what is the secret of it? It will not be difficult to detect the secret in a short time, and a few words will show that we have here, not an exceptional and rare case, but a general law of nature, common examples of which exist under our eyes.
Fig. 1. Wreaths of Tobacco-Smoke. (From Brauwer's picture in the Lacaze Gallery, Louvre.)
Wreaths of the same shape are often seen to issue from the mouths of cannon when they are fired off; I have seen them following the locomotive of an express-train. Any one who has pursued a course in chemistry may remember the beautiful experiments in which bubbles of phosphoretted hydrogen take fire spontaneously as they rise to the surface of the basin, and develop superb wreaths of white fumes.
Nature herself sometimes produces this phenomenon without any human intervention, and shows us the vortices of the ignis fatuus, to which the middle ages attached so many poetical legends, rising on summer evenings from the stagnant waters of marshes. The craters of volcanoes also frequently give off smoke in the form of magnificent ring-clouds.
Huygens observed, with one of the first telescopes, the annular form of those curious satellites of Saturn, the singular equilibrium of which is still a subject of discussion. The periodical November meteors form a real ring of planetary fragments around the earth; everything seems to prove that the milky way is nothing but a gigantic ring of cosmic dust, of which our sun and its satellites are only a few grains; the question of the form of the zodiacal light is hardly doubtful; and, finally, among the infant worlds that we call nebula?, the annular figure recurs with such frequency that it can no longer be considered exceptional; and the inspiration of genius which caused Laplace to see in the fracture of such a ring the whole origin of our solar system is reflected in the broken rings which are found among some of these nebulæ.
The laws of nature, however, frequently reveal themselves best in the infinitely little; and I have made my first observations toward a new study in watching the filiform currents produced during the osmotic interchange of two liquids through the pores of a membrane.[2]
While intimately regarding the curious phenomena with which Ducrochet sought to connect all the laws of life, I devised a way to observe the current of osmose, if I may so speak, in the act. This is not easily done with alcohol or water, but, by carefully taking advantage of the refracting and magnifying properties of cylindrical glasses, I succeeded, at last, in distinguishing before either very dark or very light grounds, slight, thin trains indicative of movement; and it was really a curious phenomenon to see two liquids of so strong affinities for each other, brought into intimate contact through a permeable membrane, obeying the laws of gravity almost without mixing, and taking their course across each other in the form of distinct threads, which presented at the same time the sharpness and the apparent fixity of a fiber of pure glass. The figure of these threads is not constantly stationary, but is subject to a regular movement, in which periodically, while still preserving its individuality, it seems to undergo alternate swellings and attenuations that give it the appearance from a certain distance of shafts of columns put one upon the other, of larger and larger capitals, or of pointed parasols, or Chinese hats with several crowns. If we look at them from above, we may perceive, in these spirals and expansions, the profiles of real circular rings, slightly attached by an invisible cord to a central stalk which bears them in groups of two or three, and animated by special movements. A section of the chain along its axis of revolution gives the forms represented in Fig. 2, A. The superposed forms of the figure, A, are evidently only the successive phases of a single drop as emitted at each pulsation; and all our efforts should be directed to isolating the drops and retarding their descent, so as to make them
Fig. 2.—Forms of a Colored Drop penetrating a Colorless Liquid.
more visible under their different aspects. This is easily done. A variety of colored liquids are at our disposal, and, with a little alcohol, or a trace of glycerine or sugar, we may modify insensibly the density of the liquids, reduce the action of gravity to a minimum, and have at will ascending or descending currents. The last are generally easiest to obtain. Fig. 3 represents a simple apparatus for the experiment, the operation of which is dependent on the familiar principle of the siphon: we have only to raise the level of the colored liquid in the glass to change the rate of flow as we may wish. Certain manual difficulties in handling this apparatus may be obviated by using a system of communicating vessels, such as may be made by taking a common lamp-chimney, corking up the lower part and putting it in communication, by means of a pipe inserted in the cork and an India-rubber tube, with the bottom of a similar vessel or the nozzle of a vertical funnel. A string around the tube, or a pair of nippers, may serve to regulate the flow of the colored liquid, which should be only a little less dense than the other; and by inclosing a bubble of air above this Liquid and covering the. top of the chimney with a membrane, we may vary the pressure without changing the level of the liquid. If we have not a glass tube at hand, we may make the communication by means of a tine bird's-quill, or a thin straw of grass, or even by a pinhole pierced in a piece of membrane. Having brought the orifice and the surface of separation of the two liquids to the same level, if we give a gentle push, we may see issue a kind of swelled fungus with a short
Fig. 3.—Arrangement of an Apparatus for the Study of Vortical Veins in Liquids.
stem (Fig. 2, C 1), on the edges of which a backward rotation is immediately manifested, an evident sign of the resistance and friction of the ambient mass. Hardly is the drop detached from the tube before we see it widening on its stem and becoming hollow below (Fig. 2, C 2); the edges fold back and soon take the motion of a winding scroll, which seems to attract to itself the lingering part of the colored filament (Fig. 2, C 3). Once begun, this whirling motion is continually kept up by the friction, which, upon the exterior contours, exhausts a little of the acquired velocity. The whole substance of the drop will pass into it, and with it numerous molecules of the uncolored liquid, the interposed layers of which will assist in supporting the geometrical rolling up of the steadily growing spirals. It is really an endless reeling, a stretching out into a surface of the whole of a little liquid mass; so that finally (Fig. 2, C 4) the line of the front appears as only a minutely fine thread, which is destined to burst under the strain of the tension of the whole contour. At length (Fig. 2, C 5) we find ourselves in the face of that curious form of mobile equilibrium of fluids of which we have noticed so many examples, and of which we have in a manner just studied the genesis and the anatomy. These singular wreaths have a still more singular constitution than we conceive; they are not full rings, nor even such simple hollow rings as we might make by bringing together the ends of an India-rubber tube. We have to
imagine a continuous necklace of watch-springs locked one to another along a circle, by which all their ends are joined; or, to speak geometrically, the figure of revolution which would be produced by a plane spiral turning round an asymptotic axis. Observation shows, together with a delicacy of design in the shaft, and a transparency which nothing can excel, fine horizontal striæ passing from one volute to another, and marking with exceeding neatness the number and divergence of the rollings. In water, effects of exquisite beauty may be produced directly without passing through the intermediate phases, by means of taps on the membrane of the apparatus. The experiment may again be simplified by forming with the membrane itself the bottom of the vessel, and using for an orifice a hole pierced in a disk which has been forced down tight into the middle of the tube. This instrument gives at each expulsion of the colored ring a corresponding return ring, a kind of negative ring, that descends clear in the interior of the colored liquid, or vice versa, if it is the liquid in the upper part that has been colored. The same phenomena appear when smoke is used, as in Fig. 4. We may dispense with all apparatus and Let fall from the height of about an inch a lightly tinted drop into a still colorless mass. From this experiment chemists learned, even before Trowbridge explained the theoretical reason for it, that it was best to employ liquids differing but little from each other, or at least such as were easily diffusible in each other. Reusch, however, has described some very unstable rings of oil in water that may be produced with an apparatus similar to ours. It is interesting, in view of the cosmic examples to which we have referred, that after the oil of the upper compartment has been replaced with water, each jet carries along from the borders of the tubing myriads of little oily drops, the drift of which renders visible in the interior of the clear water the annular constitution of the vortex formed by the irruption of a mass of absolutely identical liquid. The generality of the fact may be verified with an emulsion of ginger, or simply with superficial dust on the brightly lighted bottom of a white porcelain plate.
Imperceptible grains of coloring substance, put upon the surface of the water, immediately give rise to fine descending trains, which permit us to detect in the phenomena of solution the same character of intermittence and discontinuity that marks that of osmose. A penful of ink, a bit of sugar, a thousand simple means of observing the development of vortices, may be suggested. A piece of thread, hanging from a glass filled to the brim, makes an excellent capillary siphon, and furnishes perfect continuous movements, so that, unless the liquid is superficially stirred, or the lower glass is shaken, we obtain trains of provoking fixity, that follow their determined route without giving a pulsation to betray their interior motion. Of this character are the upright columns of mist that rise from the calm plain of the desert. So a flexible thread, carried by a balloon, revolves in the breath of the wind without breaking. The direction of a straight line is not an essential one; and, if the density of the liquid happens to be variable, the thread takes the form of an elongated spiral, the curves of which are alternately narrower and wider, and end in scrolls resembling foliage or florescence. These phenomena are not transient, but may last for days, although the rings we have been considering continue only for a few moments, and, while they present a real elasticity of form as long as they are in motion, never survive the loss of the impulse that produced them. Most frequently denser nuclei appear in their interior, which take the lead, and descend as if suspended from elastic arches, of which they draw out long branches (Fig. 2, B). Each of these nuclei appears to undergo, in its interior, the different transformations of Fig. 2, C, till a little secondary ring is formed, which sometimes remains attached, is at other times separated and divided into several others, that will, if they are small enough, continue for a long time suspended in the liquid.
All of these little rings, with the curved filaments supporting them, form in the water a very marked figure—a kind of diadem, a fantastic hydra, or a diaphanous cup (Fig. 2, B)—the singular figure of which causes us to neglect at first certain less visible details in which the real mechanism of the phenomenon is revealed; and a very light or a very dark ground, according to the character of the colored liquid, is required in order to discover the frame-work and the processes of the formation.
Rings of vapor are capable of attaining considerable dimensions without breaking. If we take a box, make a hole in it, substitute a stretched cloth or plate of metal for one of its sides, and develop in it vapors of phosphoric acid or muriate of ammonia, we can easily by
Fig. 5.—The same experiment, performed with a box made of playing-cards. The box is filled from the mouth at the hole in the upper side.
means of a slight blow cause wreaths several inches in diameter, exhibiting the structural details of the liquid rings, to shoot out to a considerable distance. A soap-bubble filled with smoke produces similar effects when it bursts; and a cubic box made of playing-cards (Fig. 5) will enable us to study, with the help of tobacco-smoke, how little influence the shape of the opening has upon the rings which we drive out through the hole at which we have tilled the box. We may make the hole square or rectangular; or, if we cut certain combinations of long slits or several holes, those composite forms which Thomson has described as vibrating rings will be produced.
If two rings are sprung in succession, they will constantly tend to overtake each other and cross each other alternately in a curious play of approaches and withdrawals, but always with some damage to each other if they are large; and this property is best studied in liquids. Two equal vortices shot from, different boxes will play with each other indefinitely, and the same happens when they strike the Avail. But, if they pass each other, only grazing their edges, they will merely change shape without breaking and without getting out of the way, and then immediately bound back to their original form like an India rubber spring. This power of resistance, or power of annular elasticity, is the most striking characteristic of these singular forms, real magazines of energy, in which all the living primitive force collects itself under the influence of external friction. Theoretically, the vortical movement, in a perfect fluid, can neither be created nor destroyed; eternal as matter itself, it has neither beginning nor end. The vortex-ring is indivisible. Attack it as quickly as you will, says Professor Tait, cut at it with the sharpest knife, you can never sever it or mar it; but, flying away or enveloping the material object, it remains whole, always itself; and, when we consider its wonderful properties, we need hardly be surprised that philosophers have aspired to build up upon it theories of the constitution of matter, and of the origin of all the physical forces, from gravitation to electricity.
We conclude with the citation of an extremely simple experiment described by Helmholtz: If we draw the rounded end of a spoon or a knife over the surface of a liquid, we may produce all around a vortical agitation giving the form of a vertical half-ring, the internal contour of which corresponds with the semicircular edge of the solid object, while on the right and left, on the surface of the liquid, appear two portions of the same diametrical section, which should reproduce the schemes of Fig. 2, C. Quite plain, in effect, are the scrolls designed on the dark surface of a cup of coffee by the white trains of the cream; and it is very easy to study thus all the mutual reactions of these vortices, similar as they are to those which the waterman sees running along the edge of his oar, and which can be reproduced of satisfactory dimensions on the surface of a bath-tub. Such experiments are within the reach of every one.—La Nature.
- ↑ Fig. 1 has been designed after the celebrated picture of Brauwer in the Lacaze Gallery of the Louvre. In the original, the picture only represents a spiral of smoke. But the form of the mouth and the convergence of the eyes sufficiently indicate the helpless effort of the drunken man. The subject seems to have been a favorite one with the old Flemish painters, for it recurs under all sorts of forms, either as a detail or as the principal motive in ten, at least, of Teniers's pieces, and in another Brauwer in the gallery at Madrid.
- ↑ "Études sur l'osmose de l'alcool à travers la gutta-percha" (C. R. de l'Assoc. France, Montpellier, 1879).