Part 3

Slow as was the formation of this drop, it was still too rapid to enable you to trace the origin of the droplet. It came, as it always does come, from the drawn-out neck. When the large drop is severed, the mass of liquid clinging to the delivery-tube shrinks upwards, as the downward pull upon it is now relieved. The result of this shrinkage--which, as usual, reduces the area of surface to the minimum possible--is to cut off the elongated neck, at its upper part, thus leaving free a spindle-shaped column of liquid. This column immediately contracts, owing to its surface tension, until its surface is a minimum--that is, it becomes practically a sphere; and this constitutes the droplet. In a later experiment, in which the formation is slower still, and the liquid more viscous, the origin of the droplet will be plainly seen, and the correctness of the description verified. The recoil due to the liberation of the stretching force after rupture of the neck was visible on the top of the large drop, and also on the bottom of the portion of liquid which remained attached to the tube, both of which were momentarily flattened (Figs. 19 and 20) before assuming their final rounded shape. This is exactly what we should expect to happen if a filled skin of indiarubber were stretched until it gave way at the narrowest part.

As a variation on the two liquids just used, I now take the yellow liquid _nitrobenzene_, and run it into nitric acid (or other suitable medium) of specific gravity 1.2, and you observe the same sequence of events as in the previous experiment, even to the details. Very rapid photography shows that the breaking away of a drop of water from the end of a tube in air is in all respects identical with what we have just seen on a large scale.

*Ascending or Inverted Drops.*--If we discharge orthotoluidine into water when both are hotter than 75 deg. F., the former liquid will rise, as its density is now less than that of water. If, therefore, I take a funnel with the stem bent into a parallel branch, so as to discharge upwards (A, Fig. 13) and raise the temperature of both liquids above 75 deg. F., we see that the drop gradually grows towards the top of the water, finally breaking away and giving rise to the droplet. Everything, in fact, was the same as in the case of a falling drop, except that the direction was reversed. A slight rise in temperature has thus turned the whole process topsy-turvy, but the action is really the same in both cases. When, on heating, the water acquired the greater density, its buoyancy overcame the pull of gravitation on the orthotoluidine, and accordingly the drop was pushed upwards, the result being the same as when it was pulled downwards. An inverted drop may always be obtained by discharging a light liquid into a heavier one, e.g. olive oil into water, or water into any of the liquids mentioned on p. 19, below the equi-density temperature.

LECTURE II

*Automatic Aniline Drops.*--In the foregoing experiments the drop was enlarged until it broke away by feeding it with liquid; but it is possible to arrange that the formation shall be quite automatic. The experiment, as we shall see, is extremely simple, and yet it contains an element of surprise. Into a beaker containing water nearly boiling I pour a considerable quantity of aniline, which at first breaks up into a large number of drops. After a short time, however, all the aniline floats to the surface, having been warmed by contact with the water to a temperature higher than that of equi-density (147 deg. F., or 64 deg. C.)--which is exactly what we should expect to happen. There it remains for a brief period in the form of a large mass with the lower portion curved in outline. Soon, however, we observe the centre of the mass sinking in the water, and taking on the now familiar outline of a falling drop. Gradually, it narrows at the neck and breaks away; but as aniline is a viscous liquid, the neck in this case is long and therefore easily seen. The large drop breaks away and falls to the bottom of the beaker, its upper surface rising and falling for some time owing to the recoil of its skin after separation, finally becoming permanently convex. Immediately after the large drop has parted, the upper mass shrinks upwards, spreading out further on the surface of the water, with the result that the long neck is severed at the top, its own weight assisting the breakage. Now follows the resolution of the detached neck into two or more spheres, usually a large and a small (Fig. 22). And now, to those who view the experiment for the first time, comes the surprise. The large drop, which was more or less flattened when it came to rest at the bottom of the beaker, becomes more and more rounded, and finally spherical. Then, unaided, it rises to the top and mingles itself with the aniline which remained on the surface. After a brief interval a second drop falls, imitating the performance of the first one; and, like its predecessor, rises to the surface, after remaining for a short time at the bottom of the vessel. And so long as we keep the temperature a few degrees above that of equi-density, the process of partition and reunion goes on indefinitely. The action is automatic and continuous, and the large size of the drop and of the neck, and the slowness of the procedure, enables us to follow with ease every stage in the formation of a parting drop.

And now as to the explanation of this curious performance. When the aniline reaches the surface, and spreads out, it cools by contact with the air more rapidly than the water below. As it cools, its density increases, and soon becomes greater than that of the water, in which it then attempts to sink. The forces of surface tension prevent the whole of the aniline from falling--the water surface can sustain a certain weight of the liquid--but the surplus weight cannot be held, and therefore breaks away. But when the detached drop reaches the bottom of the vessel, it is warmed up again; and when its temperature rises above that of equi-density it floats up to the top. And so the cycle of operations becomes continuous, owing to cooling taking place at the top and heating at the bottom.

Perpetual motion, you might suggest. Nothing of the kind. Perpetual motion means the continuous performance of work without any supply of energy; it does not mean merely continuous movement. A steam-engine works so long as it is provided with steam, and an electric motor so long as it is fed with electricity; but both stop when the supply of energy is withdrawn. So with our aniline drop, which derives its energy from the heat of the water, and which comes to rest immediately the temperature falls below 147 deg. F. or 64 deg. C. But in order that the process of separation and reunion may continue, the cooling at the top is quite as necessary as the heating at the bottom. Our aniline drop is in essence a heat-engine--although it does no external work--and like all heat-engines possesses a source from which heat is derived, and a sink into which heat at a lower temperature is rejected. We might, with certain stipulations, work out an indicator diagram for our liquid engine, but that would be straying too far from our present subject.

*Automatic Drops of other Liquids.*--Liquids which possess a low equi-density temperature with water do not form automatic drops like aniline, as the rate of cooling at the surface is too slow, and hence the floating mass of liquid does not attain a density in excess of that of the water beneath. Aceto-acetic ether, however, behaves like aniline, if the temperature of the water be maintained at about 170 deg. F. (77 deg. C.), but as this liquid is fairly soluble in hot water further quantities must be added during the progress of the experiment. Results equal to those obtained with aniline, however, may be secured by using nitrobenzene in nitric acid of specific gravity 1.2 at 59 deg. F. (15 deg. C.), the acid being heated to 185 deg. F. (85 deg. C.); and here you see the yellow drop performing its alternate ascents and descents exactly as in the case of aniline and water. Other examples might be given; but we may take it as a general rule that when the equi-density temperature of the liquid and medium is above 125 deg. F. (52 deg. C.), the phenomenon of the automatic drop may usually be observed when the temperature is raised by 30 deg. F. (17 deg. C.), above this point.

*Liquid Jets.*--So far we have been observing the formation of single drops, growing slowly at the end of a tube, or breaking away from a large mass of the floating liquid. If, however, we accelerate the speed at which the liquid escapes, the drop has no time to form at the outlet, and a jet is then formed. We are all familiar with a jet of water escaping from a tap; it consists of an unbroken column of the liquid up to a certain distance, depending upon the pressure, but the lower part is broken up into a large number of drops, which break away from the column at a definite distance from the tap. There are many remarkable features about jets which I do not intend to discuss here, as it is only intended to consider the manner in which the drops at the end are formed. To observe this procedure, it is necessary again to resort to our method of slowing down the rate of formation, by allowing the liquid to flow into a medium only slightly inferior in density. For this purpose, orthotoluidine falling into water at the ordinary room temperature is eminently satisfactory; and we see on the screen the projection of a pipe, with its end under water, placed so that a jet of orthotoluidine may be discharged vertically downwards from a stoppered funnel. I open the tap slightly at first, and we then merely form a single drop at the end. Now it is opened more widely, and you observe that the drop breaks away some distance below the outlet, being rapidly succeeded by another and another (Fig. 23). On still further opening the tap the drops form at a still greater distance from the end of the pipe, and succeed each other more rapidly, so that quite a number appear in view at any given moment (Figs. 24 and 25). Notice how the drop is distorted by breaking away from the stream of liquid, and how it gradually recovers its spherical shape during its fall through the water. Finally, I increase the discharge to such an extent that the formation of the terminal drops is so rapid as to be no longer visible to the eye, but appears like the turmoil observed at the end of a jet of water escaping into air.

*Liquid Columns.*--A simple experiment will suffice to illustrate what is meant by a liquid column. Here is a drop of water hanging from the end of a glass tube. I place it in the lantern and obtain a magnified image on the screen, and then bring up a flat plate of glass until it just touches the suspended drop. As soon as contact is established, the water spreads outwards over the plate, causing the drop to contract in diameter at or near its middle part, so that its outline resembles that of a capstan (Fig. 26). The end of the glass tube is now connected to the plate by a column of water of curved outline, which is quite stable if undisturbed. If, however, I gradually raise the tube, or lower the plate, the narrow part of the column becomes still narrower, and finally breaks across. In the same way we may produce columns of other liquids; those obtained with viscous liquids such as glycerine being capable of stretching to a greater extent than water, but showing the same general characteristics. A liquid column, then, is in reality a supported drop, and the severance effected by lowering the support is similar to that which occurs when a pendent drop breaks away owing to its weight.

In our previous experiments we have seen that in order to produce large drops of a given liquid, the surroundings should be of nearly the same density, so as largely to diminish the effective weight of the suspended mass. We might therefore expect that large columns of liquid could be produced under similar conditions; and our conjecture is correct. We may, for example, use the apparatus by means of which large drops of orthotoluidine were formed (Fig. 13), using a shallow layer of water, so that the lower end of the drop would come into contact with the bottom of the vessel before the breaking stage was reached, and thus produce, on a large scale, the same result as that we have just achieved by allowing a hanging drop of water to touch a glass plate. This method, however, restricts the diameter of the top of the column to that of the delivery tube, and in this respect the shape is strained. The remedy for this is to hang the drop from the surface of the water, when a degree of freedom is conferred upon the upper part, which enables the column to assume a greater variety of shapes. In order to show how this may be accomplished, I pour a small quantity of water into the rounded end of a wide test-tube, which is now seen projected on the screen, and then pour gently down the side a quantity of _ethyl benzoate_, a liquid slightly denser than water. You observe that the liquid spreads out on the surface of the water, forming a hanging drop which at first is nearly hemispherical in shape; but as I continue to add the liquid the drop grows in size downwards, and finally reaches the bottom of the tube. There is our liquid column (Fig. 27), which has formed itself in its own way, free from the restriction imposed by a delivery tube. Notice the graceful curved outline, produced by a beautiful balance between the forces of surface tension and gravitation; and notice also how the outline may be varied by the gradual addition of water, which causes the upper surface to rise, and thus stretches the column (Fig. 28). The middle becomes more and more narrow (Fig. 29), and finally breaks across, leaving a portion of the former column hanging from the surface, and the remainder, in rounded form (Fig. 30), at the bottom of the tube. And, as usual, the partition was accompanied by the formation of a small droplet.

It is possible, by using other liquids, and different diameters of vessels, to produce columns of a large variety of outlines. Some liquids spread over a greater area on the surface of water than others, and therefore produce columns with wider tops. Here we see a column of orthotoluidine, which has a top diameter of 2 inches; and here again, in contrast, is a column of aceto-acetic ether, the surface diameter of which is only 1/2 inch (Fig. 31). Other liquids, such as aniline, give an intermediate result. The lower diameter is determined by the width of the vessel; and hence we are able to produce an almost endless number of shapes. It is interesting to note how workers in glass and pottery have unconsciously imitated these shapes; and I have here a variety of articles which simulate the outlines of one or other of the liquid columns you have just seen. It is possible that designers in these branches of industry might obtain useful ideas from a study of liquid columns, which present an almost limitless field for the practical observation of curved forms.

*Communicating Drops.*--There is a well-known experiment, which some of you may have seen, in which two soap-bubbles are blown on separate tubes, and are then placed in communication internally. If the bubbles are exactly equal in size, no alteration takes place in either; but if unequal, the smaller bubble shrinks, and forces the air in its interior into the larger one, which therefore increases in size. Finally, the small bubble is resolved into a slightly-curved skin which covers the end of the tube on which it was originally blown. It is evident from this experiment that the pressure per unit area exerted by the surface of a bubble on the air inside is greater in a small than in a large bubble. The internal pressure may be proved to vary inversely as the radius of the bubble; thus by halving the radius we double the pressure due to the elastic surface, and so on. The reciprocal of the radius of a sphere is called its _curvature_, and we may therefore state that the pressure exerted by the walls of the bubble on the interior vary directly as the curvature.

We have already seen that a drop of liquid possesses an elastic surface, and is practically the same thing as a soap-bubble filled with liquid instead of air. We might therefore expect the same results if two suspended drops of liquid were placed in communication as those observed in the case of soap-bubbles. And our reasoning is correct, as we may now demonstrate. The apparatus consists (Fig. 32) of two parallel tubes, each provided with a tap, and communicating with a cross-branch at the top, which contains a reservoir to hold the liquid used. About half-way down the parallel tubes a cross-piece, provided with a tap, is placed. We commence by filling the whole of the system with the liquid under trial, and the parallel tubes equal in length. Drops are then formed at the ends of each vertical tube by opening the taps on these in turn, and closing after suitable drops have been formed. Then, by opening the tap on the horizontal cross-piece, we place the drops in communication and watch the result.

I have chosen orthotoluidine as the liquid, and by placing the ends of the vertical tubes under water--which at the temperature of the room is slightly less dense than orthotoluidine--I am able to form much larger drops than would be possible in air. You now see a small and a large drop projected on the screen; and I now open the cross-tap, so that they may communicate. Notice how the little drop shrinks until it forms merely a slightly-curved prominence at the end of its tube. It attains a position of rest when the curvature of this prominence is equal to that of the now enlarged drop which has swallowed up the contents of the smaller one. So far the result is identical with that obtained with soap-bubbles; but we can extend the experiment in such a way as to reverse the process, and make the little drop absorb the big one. In order to do this I fasten an extension to one of the tubes, and form a small drop deep down in the water, and a larger one on the unextended branch near the top. When I open the communicating top, the system becomes a kind of siphon, the orthotoluidine tending to flow out of the end of the longer tube. The tendency of the large drop to siphon over is opposed by the superior pressure exerted by the skin of the smaller drop; but the former now prevails, and the big drop gradually shrinks and the little one is observed to grow larger. It is possible by regulating the depth at which the smaller drop is placed, to balance the two tendencies, so that the superior pressure due to the lesser drop is equalled by the extra downward pressure due to the greater length of the column of which it forms the terminus. Both pressures are numerically very small, but are still of sufficient magnitude to cause a flow of liquid in one or other direction when not exactly in equilibrium. In the case of communicating soap-bubbles, containing air and surrounded by air, locating the small bubble at a lower level would not reverse the direction of flow, which we succeeded in accomplishing with liquid drops formed in a medium of slightly inferior density.

*Combined Vapour and Liquid Drops.*--All liquids when heated give off vapour, the amount increasing as the temperature rises. The vapour formed in the lower part of the vessel in which the liquid is heated rises in the form of bubbles, which may condense again if the upper part of the liquid be cold. When the liquid becomes hot throughout, however, the vapour bubbles reach the surface and break, allowing the contents to escape into the air above. Everyone who has watched a liquid boiling will be familiar with this process, but it should be remembered that a liquid may give off large quantities of vapour without actually boiling. A dish of cold water, if exposed to the air, will gradually evaporate away; whilst other liquids, such as petrol and alcohol, will disappear rapidly under the same circumstances--and hence are called "volatile" liquids.

The formation of vapour and its subsequent escape at the surface of the liquid, enable us to produce a very novel kind of drop; if, instead of allowing the bubbles to escape into air, we cause them to enter a second liquid. Here, for example, is a coloured layer of chloroform[1] at the bottom of a beaker, with a column of water above. I project the image of the beaker on the screen, and then heat it below. The chloroform vapour escapes in bubbles; but notice that each bubble carries with it a quantity of liquid, torn off, as it were, at the moment of separation. The vapour bubbles and their liquid appendages vary in size, but some of them, you observe, have an average density about equal to that of the water, and float about like weighted balloons. Some rise nearly to the surface, where the water is coldest; and then the vapour partially condenses, with the result that its lifting power is diminished, and hence the drops sink into the lower part of the beaker. But the water is warmer in this region, and consequently the vapour bubble increases in size and lifting power until again able to lift its load to the surface. So the composite drops go up and down, until finally they reach the surface, when the vapour passes into the air, and the suspended liquid falls back to the mass at the bottom of the beaker. Notice that the drop of liquid attached to each bubble is elongated vertically. This is because chloroform is a much denser liquid than water (Fig. 33). There is a practical lesson to be drawn from this experiment. Whenever a bubble of vapour breaks through the surface of a liquid, it tends to carry with it some of the liquid, which is dragged mechanically into the space above. In our experiment the space was occupied by water, which enabled the bubble to detach a much greater weight than would be possible if the surface of escape had been covered by air, which is far less buoyant than water. But even when the bubbles escape into air, tiny quantities of liquid are detached; so that steam from boiling water, for example, is never entirely free from liquid. All users of steam are well acquainted with this fact.

[1] Mono-brom-benzene is better than chloroform for this experiment, but is more costly. It may be coloured with indigo. Chloroform may be coloured with iodine.