Liquid Drops and Globules, Their Formation and Movements / Three lectures delivered to popular audiences

by Charles R. Darling

Shape of Detached Masses of Liquid.—Let us now pay a little attention to the small drop of syrup which remains hanging from the rod. It is in contact with the glass at the top part only, and the lower portion is only prevented from falling by the elastic skin around it, which sustains the weight. We may compare it to a bladder full of liquid, in which case also the weight is borne by the containing skin. Now suppose we could separate the drop of syrup entirely [pg 9] from the rod; what shape would it take? We know that its surface, if not prevented by outside forces from doing so, would become of minimum area. Assuming such extraneous forces to be absent or counterbalanced, what would then be the shape of the drop? It would be an exact sphere. For a sphere has a less surface-area in proportion to its volume than any other shape; and hence a free drop of liquid, if its outline were determined solely by its elastic skin, would be spherical. A numerical example will serve to illustrate this property of a sphere. Supposing we construct three closed vessels, each to contain 1 cubic foot, the first being a cube, the second a cylinder of length equal to its diameter, and the third a sphere. The areas of the surfaces would then be:—

Cube	. . . .	6 square feet.
Cylinder	. . . .	5·86 ,, ,,
Sphere	. . . .	4·9 ,, ,,

And whatever shape we make the vessel, it will always be found that the spherical form possesses the least surface.

Fig. 4.—Drops of different sizes resting on flat plate.

Now let us examine some of the shapes which drops actually assume. I take a glass plate covered with a thin layer of grease, which prevents adhesion of water to the glass, and form upon it drops of water of various sizes by the aid of a pipette. You see them projected on the screen ([Fig. 4]). The larger drops are flattened above and below, but possess rounded sides and resemble a teacake in shape. Those of intermediate size are more globular, but still show signs of [pg 10] flattening; whilst the very small ones, so far as the eye can judge, are spherical. Evidently, the shape depends upon the size; and this calls for some explanation. If we take a balloon of indiarubber filled with water, and rest it on a table, the weight of the enclosed water will naturally tend to stretch the balloon sideways, and so to flatten it. A smaller balloon, made of rubber of the same strength, will not be stretched so much, as the weight of the enclosed water would be less; and if the balloon were very small, but still had walls of the same strength, the weight of the enclosed water would be incompetent to produce any visible distortion. It is evident, however, that so long as it is under the influence of gravitation, even the smallest drop cannot be truly spherical, but will be slightly flattened. The tendency of drops to become spherical, however, is always present.

Fig. 5.—Formation of a sphere of orthotoluidine.

Production of True Spheres of Liquids.—Now it is quite possible to produce true spheres of liquid, even of large size, if we cancel the effect of gravity; and we may obtain a hint as to how this may be accomplished by considering the case of a soap-bubble, which, when floating in air, is spherical in shape. Such a bubble is merely a skin of liquid enclosing air; but being surrounded by air of the same density, there is no tendency for the bubble to distort, nor would it [pg 11] fall to the ground were it not for the weight of the extremely thin skin. The downward pull of gravity on the air inside the bubble is balanced by the buoyancy of the outside air; and hence the skin, unhampered by any extraneous force, assumes and retains the spherical form. And similarly, if we can arrange to surround a drop of liquid by a medium of the same density, it will in turn become a sphere. Evidently the medium used must not mix with the liquid composing the drop, as it would then be impossible to establish a boundary surface between the two. Plateau, many years ago, produced liquid spheres in this manner. He prepared a mixture of alcohol and water exactly equal in density to olive oil, and discharged the oil into the mixture, the buoyancy of which exactly counteracted the effect of gravity on the oil, and hence spheres were formed. The preparation of an alcohol-water mixture of exactly correct density is a tedious process, and we are now able to dispense with it and form true spheres in a more convenient way. There is a liquid known as orthotoluidine, which possesses a beautiful red colour, does not mix with water, and which has exactly the same density as water when the temperature of both is 75° F. or 24° C. At this temperature, therefore, if orthotoluidine be run into water, spheres should be formed; and there is no reason why we should not be able to make one as large as a cricket-ball, or even larger. I take a flat-sided vessel for this experiment, in order that the appearance of the drop will not be distorted as it would be in a beaker, and pour into it water at 75° F. until it is about two-thirds full. I now take a pipette containing [pg 12] a 3 per cent. solution of common salt, and discharge it at the bottom of the water. Being heavier, the salt solution will remain below the water, and will serve as a resting-place for the drop. The orthotoluidine is contained in a vessel provided with a tap and wide stem, which is now inserted in the water so that the end of the stem is about 1 inch above the top of the salty layer. I now open the tap so as to allow the orthotoluidine to flow out gradually; and we then see the ball of liquid growing at the end of the stem [pg 13] ([Fig. 5]). By using a graduated vessel, we can read off the quantity of orthotoluidine which runs out, and thus measure the volume of the sphere formed. When the lower part reaches the layer of salt solution, we raise the delivery tube gently, and repeat this as needed during the growth of the sphere. We have now run out 100 cubic centimetres, or about one-sixth of a pint, and our sphere consequently has a diameter of 5¾ centimetres, or 2¼ inches. To set it free in the water we lift the delivery tube rapidly—and there is the [pg 14] sphere floating in the water ([Fig. 6]). We could have made it as much larger as we pleased, but the present sphere will serve all our requirements.