Text: THE FORMATION OF ROTATING RINGS (VORTEX RINGS) OF AIR AND LIQUIDS UNDER CERTAIN CONDITIONS OF DISCHARGE PROF. WILLIAM B. ROGERS NEW HAVEN PRINTED BY E. HAYES 1858 ON ROTATING RINGS OF AIR AND LIQUIDS It has long been a familiar fact that the bubbles of phosphuretted hydrogen gas consisting of PH3 with an admixture of PH2, give rise by their explosive combustion in the air to a ring of white vapor-like phosphoric acid, which dilating as it ascends exhibits a rotation of each vertical element around the curved axis of the figure. A similar motion is sometimes discernible in the smoke from a cannon, and in the steam which escapes by momentary puffs from a steam-pipe, and as expert smokers know, such revolving rings are readily produced by ejecting the smoky breath in a peculiar manner from the rounded opening of the lips. In studying recently the phenomena of air-jets, I have been led to a somewhat critical examination of the conditions under which these ring-discharges are produced. By the use of suitable arrangements I have been able not only to trace the development of the rings produced in air projected from apertures, but to detect similar movements in that which is released by the bursting of an ordinary bubble. I have, moreover, by a modified contrivance succeeded in forming at will similarly constituted rings from water and other liquids, and in tracing them to the same mechanical causes which give origin to the rings of air. As the methods of experimenting which I have adopted, as well as most of the observations, appear to be new, and as the mechanism of these beautiful effects has not, that I am aware, been specially treated of before, I trust that the following details may be regarded as a not uninteresting addition to our knowledge in this department of inquiry. I. Of the air-rings formed by momentary discharges from an aperture. 1. Mode of producing the air-rings.- To render the form and internal movements of the escaping air in such cases distinctly visible, I use a large glass reservoir, (fig. 1) in which the air is kept opaque by a continual supply of chloride of ammonium generated within. To the top of the jar is adapted, by grinding and an unctuous cement, a zinc or glass cover pierced with three holes, viz.: a central round aperture one inch in diameter, and two others of much smaller size, each furnished with a short socket-tube rising above the plate. Of these, one is intended for connecting with tubes of discharge, and is kept closed when the central orifice is in use. The other receives a slender glass tube, entering above by a rectangular bend and descending to within two inches of the bottom of the jar. At its outer end this is connected with a flexible pipe through which the operator, impelling the air in successive puffs into the lower part of the vessel, can at will eject corresponding volumes of the cloudy air through either of the apertures. For this purpose he may either use the mouth, or a gum-elastic bag attached to the end of the tube - the former being in most cases the preferable instrument. At equal distances on opposite sides of the central hole, two hooks are affixed to the lower surface of the plate, from which are suspended long slips of thick cotton cloth. To prepare the apparatus for experiment, we remove the cover and pour into the jar common hydrochloric acid to the depth of half an inch, adding to it one or two cubic inches of nitric acid. The slips of cotton cloth, after being dipped in strong water of ammonia, are replaced on the hooks, and the cover restored to its position with a slight pressure to render the junction firm and air-tight. The included air quickly becomes opaque with the dense cloud of chloride, and by applying the lips to the free end of the flexible tube may be expelled from the aperture which is left unclosed, either in the form of successive puffs or of a continuous jet. It is almost needless to say that in making the experiment the surrounding air should be as little moved as possible, the slightest agitation near the aperture sufficing to mar the symmetry of the effect. 2. Stages of the ring-formation.- When by a moderately strong impulse the cloudy air of the jar is to issue in a succession of quick but not violent puffs, each little cloud assumes near the aperture the form of a ring, which gradually dilating as it rises retains its symmetry until it has reached the height of two or sometimes even of three feet above the opening. Using a gentler and less sudden impulse we cause the ring as it ascends to carry with it a train of cloudy air which forms the downward continuation of the inner portion of the coil. With a still lighter breathing at the mouth-piece we may expel the air in so gentle a wave as to be able to mark the escaping cloud rolling slowly over on each side of the aperture without breaking its connection with the central mass - the whole thus assuming the appearance of the top of a column adorned with volutes. In these experiment no actual ring is generated, but we have the opportunity of watching the beginning of such a form and tracing the mechanical movements to which it owes its development. In fig. 2 the earliest stage is indicated by a, and the imperfectly formed ring with part of the attached train by b, the lateral sections of the ring only being represented. When the discharge is produced by a stronger impulse than in the case first mentioned, the resulting ring darts upward so rapidly as to break away from its train, leaving the latter either to lag behind as a formless mass, or, when retaining sufficient velocity, to evolve from its own substance a second and smaller ring which is seen quickly pursuing the first. By applying a yet more energetic force, we may cause the ejected air to form three, four, or even a greater number of such successively developed rings. The size of the ring when first formed is dependent chiefly on the width of the aperture, and in some degree also on the strength of the blast. With a hole one and a half inch in diameter, and a proportionally large injecting tube, it is easy, by a suitable impulse of the breath, to generate rings of from two to three inches in diameter of the most perfect symmetry, and having force enough to ascend unbroken to a height of six or eight feet. In this way we may render these beautiful phenomena visible over a large apartment, causing the smoky wreaths to chase each other until flattened against the ceiling. If instead of the mouth we use the elastic bag as a means of impelling the cloudy air, we find that a quick pressure and subsequent withdrawal of the hand give rise to rings of great symmetry, and that these are usually unaccompanied by any train. The latter result is evidently due to the sudden recoil of the bag, and the consequent retraction of the latter part of the cloudy mass back into the reservoir. By continuing the pressure so as to prevent the recoil we may produce the same phases of the phenomena as when the impulse is given by the breath. 3. Rotation and structure of the air-rings.- To obtain a distinct view of the motion and internal structure of the ring, it should be viewed in a nearly horizontal direction, and by a strong transmitted light. This is conveniently done by placing the apparatus on a table a little below the level of a gas lamp, but at a considerable distance from it. It will then be seen that the rotation of the ring, either in its incipient stage, or with the attached train, or when entire and separate, has always one direction, the inner circumference being carried forward or in the ordinary mode of experiment upward, and the outer in the reverse direction, as shown in fig. 3. In order that the eye may readily follow this motion in the interior of the ring while it retains its perfect form and rapid rotation, the air of the reservoir should be only moderately cloudy, and the impelling force quick without being violent. Under these circumstances we observe the ring to be made up of a coil of cloudy air - between the folds of which is rolled up a similar coil of transparent atmosphere. When the ring carries a train it is easy to discern that the cloudy spiral is continuous with this attendant mass, and really issues from it near the inner circumference of the ring. In a yet earlier stage of the action we are able to mark the beginning of this two-fold spiral by observing how each volute as it draws its supply from the central mass gathers in a portion of the clear external air to be enfolded between its turns. 4. Origin of the rotation.- This is obviously preferable to the combined agency of the outward impulse and the resistance which the sides of the issuing mass encounter from the edge of the opening, and from the air into which it is impelled. The former of these forces, due to the tension propagated through the reservoir, must to some extent operate in diverging directions, while the resistance acts in nearly opposite lines. Thus, at the outset, there would be produced a reversion or curling of the issuing cloud around the aperture, which, as the action continued, would be developed into the spreading volutes before described, and at length into the perfect and rapidly revolving ring. The dilation of the ring in its ascent would seem to be the natural result of the divergent character of the impulse impressed upon the air as it passes from the orifice. 5. Horizontal bands of the ring.- On examining a ring in which the clear and cloudy spirals are plainly distinguished, it will be found to have the appearance of alternating layers or bands of cloudy and comparatively clear air arranged horizontally, but which are most strongly marked towards the top and bottom of the ring, and cease to be discerned near the middle. When the air employed is only moderately cloudy, and the rings are large and perfectly developed, this banded appearance is admirably brought out by a mild transmitted light, and adds not a little to the beauty of the revolving and expanding wreath. It is easy to see that this apparent structure is an optical illusion due to the passage of the light alternately through a greater and a less thickness of the cloudy lamina of the composite ring. Thus it will be observed (fig. 3) that the rays coming to the eye in the horizontal plane which passes through the upper part of the cloudy spiral will be much more obscured than those which pass in a parallel plane through the clear space immediately beneath, the former having to pass lengthwise through a considerable distance in the cloudy layer, while the latter traverse little more than twice its thickness. The same relations must hold for the next inner turns of the spiral, but as its circuit grows narrower the difference between the aggregate of clear and cloudy portions passed through must continually grow less, and near the equator of the ring become quite insensible; hence the bands which are so distinctly marked towards the top and bottom of the ring disappear as we approach its midway line. 6. On the effects produced by a continuous blast.- By slightly prolonging the impulse either from the mouth or the bag so as to expel a comparatively large amount of the cloudy material at a moderate velocity we are able to mark the partial formation of a second ring in the swollen part of the train which still adheres to the first, and even of a third yet more imperfect one in the train prolonged below the second, the whole still forming a united mass. With a continuous and uniform blast of moderate force the appearances are even more curious and instructive. The column in this case retaining its smooth cylindrical outline for only a short distance above the aperture, presents higher up along its sides, and at nearly equal intervals, a succession of whorls or volutes, more and more developed as we ascend, and which not unfrequently terminate at the top in a nearly perfect and separate ring, (fig. 4). On urging the blast with a much increased velocity these lateral markings of the column become less conspicuous, and assume throughout, nearly to the summit, the aspect of a series of short projections curving steeply downwards, like the lowest and least developed volutes in the preceding experiment. On examining these lateral gyrations as shown in the figure it will be seen that each is formed at the expense of the adjacent parts of the column both above and below it. The central arrows pointing divergingly upward indicate the direction in which the inner portions of the stream are deflected to unite with the wider part of the spiral; the exterior arrows directed downwards mark the relatively retreating motion impressed by the resistance acting at the sides, and show the course of the particles passing into the spiral from above. It would seem that these movements must have the effect, superficially at least, of dividing the column into alternate tracts of rarefied and condensed air, the former situated about midway between the successive coils, and the latter directly above where the coils unite with the main mass. These regular alternations, virtually equivalent to a system of waves or vibrations generated in the effluent stream, indicate the analogy in condition of large streams of gaseous matter, and the slender jet in which such vibratory movement has already been demonstrated, and point to one of the agencies which may be concerned in the latter phenomena. They at least furnish conclusive proof that even a large stream of gas discharged under a steady pressure does not flow with continuous uniformity, but become the seat of periodical movements at equally recurring intervals. II. Of the motion of the air produced by the rupture and by the explosion of bubbles. As the beautiful rings developed by the explosive combustion of phosphuretted hydrogen gas are formed under the influence of far more energetic forces than are brought into play by the rupture of a bubble of common air, it becomes important to determine what kind and amount of effect is due to the simple bursting of the bubble independent of any explosive action. I have, therefore, made numerous experiments on bubbles of common air rendered cloudy as in the previous experiments, and have been much interested by discovering that in all such cases a distinct rotary motion is produced corresponding with that of the air rings already described. 7. Mode of experimenting with floating bubbles of air.- In order to observe the movement of the air occasioned by the bursting of the bubble I use a deep glass bowl, into which is poured a layer of water containing soap enough to give durability to the bubbles when formed on its surface. A finger bowl of the largest size answers for this purpose. Placing this on the table near the ring apparatus (fig. 1) previously charged with very opaque air, I attach to the tubulated aperture of the jar a flexible pipe terminating in a glass tube of about one-tenth inch in diameter. Dipping the end of the tube into the soapy water so that it may take up a short column of the liquid, I hold it centrally over the water and close to the surface. Then breathing carefully into the mouthpiece, provided for this purpose with a narrow opening, I form a floating bubble of any size from a half inch to three inches in diameter. This being done the glass beak is to be gently lifted away, and the bowl covered with a glass plate, brought over it with a sliding motion. The bubble must now be left undisturbed for fifteen or twenty seconds, to allow its contents and the air of the bowl to come to rest, at which time the suspended cloud will be seen to have subsided a little from the apex, showing a level surface above. As it is necessary for a satisfactory observation that the rupture of the bubble should begin exactly at the top and extend symmetrically around that point, and as in the spontaneous bursting this only occasionally occurs, it is expedient not to wait for the rupture but to force it by means of a wire inserted vertically through the apex and quickly withdrawn, the glass cover having first been removed by a gentle sliding motion. When this has been done so as to avoid agitation we see a cloudy column rising some inches above the liquid, and rolling over in delicate volutes at the top. With a bubble of from one to one and a half inches in diameter the symmetry of the resulting column is quite striking and its correspondence in motion and shape with that already described as an early stage of the ring formation is not to be mistaken. In many cases a perfect and almost separate ring is developed at the top, and when the air is not too opaque the alternate coils and the resulting horizontal bands are perfectly distinct. But from the feebleness of the rotation these appearances are only momentary. When the bubble is two or three inches in diameter, the outward and downward curling at the top of the cloudy mass is still quite observable, although much less marked than in the preceding case. When very small bubbles are broken, the motion is too quick and the cloud too small for satisfactory observation.

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