Soap-Bubbles and the Forces Which Mould Them

by C. V. Boys

A soap-bubble consisting, as it does, of a thin layer of liquid, which must have of course both an inside and an outside surface or skin, must be elastic, and this is easily shown in many ways. Perhaps the easiest way is to tie a thread across a ring rather loosely, and then to dip the ring into soap water. On taking it out there is a film stretched over the ring, in which the thread moves about quite freely, as you can see upon the screen. But if I break the film on one side, then immediately the thread is pulled by the film on the other side as far as it can go, and it is now tight (Fig. 19). You will also notice that it is part of a perfect circle, because that form makes the space on one side as great, and therefore on the other side, where the film is, as small, as possible. Or again, in this second ring the thread is double for a short distance in the middle. If I break the film between the threads they are at once pulled apart, and are pulled into a perfect circle (Fig. 20), because that is the form which makes the space within it as great as possible, and therefore leaves the space outside it as small as possible. You will also notice, that though the circle will not allow itself to be pulled out of shape, yet it can move about in the ring quite freely, because such a movement does not make any difference to the space outside it.

Fig. 19.

Fig. 20.

Fig. 21.

Fig. 22.

I have now blown a bubble upon a ring of wire. I shall hang a small ring upon it, and to show more clearly what is happening, I shall blow a little smoke into the bubble. Now that I have broken the film inside the lower ring, you will see the smoke being driven out and the ring lifted up, both of which show the elastic nature of the film. Or again, I have blown a bubble on the end of a wide pipe; on holding the open end of the pipe to a candle flame, the outrushing air blows out the flame at once, which shows that the soap-bubble is acting like an elastic bag (Fig. 21). You now see that, owing to the elastic skin of a soap-bubble, the air inside is under pressure and will get out if it can. Which would you think would squeeze the air inside it most, a large or a small bubble? We will find out by trying, and then see if we can tell why. You now see two pipes each with a tap. These are joined together by a third pipe in which there is a third tap. I will first blow one bubble and shut it off with the tap 1 (Fig. 22), and then the other, and shut it off with the tap 2. They are now nearly equal in size, but the air cannot yet pass from one to the other because the tap 3 is turned off. Now if the pressure in the largest one is greatest it will blow air into the other when I open this tap, until they are equal in size; if, on the other hand, the pressure in the small one is greatest, it will blow air into the large one, and will itself get smaller until it has quite disappeared. We will now try the experiment. You see immediately that I open the tap 3 the small bubble shuts up and blows out the large one, thus showing that there is a greater pressure in a small than in a large bubble. The directions in which the air and the bubble move is indicated in the figure by arrows. I want you particularly to notice and remember this, because this is an experiment on which a great deal depends. To impress this upon your memory I shall show the same thing in another way. There is in front of the lantern a little tube shaped like a U half filled with water. One end of the U is joined to a pipe on which a bubble can be blown (Fig. 23). You will now be able to see how the pressure changes as the bubble increases in size, because the water will be displaced more when the pressure is more, and less when it is less. Now that there is a very small bubble, the pressure as measured by the water is about one quarter of an inch on the scale. The bubble is growing and the pressure indicated by the water in the gauge is falling, until, when the bubble is double its former size, the pressure is only half what it was; and this is always true, the smaller the bubble the greater the pressure. As the film is always stretched with the same force, whatever size the bubble is, it is clear that the pressure inside can only depend upon the curvature of a bubble. In the case of lines, our ordinary language tells us, that the larger a circle is the less is its curvature; a piece of a small circle is said to be a quick or a sharp curve, while a piece of a great circle is only slightly curved; and if you take a piece of a very large circle indeed, then you cannot tell it from a straight line, and you say it is not curved at all. With a part of the surface of a ball it is just the same—the larger the ball the less it is curved; and if the ball is very large indeed, say 8000 miles across, you cannot tell a small piece of it from a true plane. Level water is part of such a surface, and you know that still water in a basin appears perfectly flat, though in a very large lake or the sea you can see that it is curved. We have seen that in large bubbles the pressure is little and the curvature is little, while in small bubbles the pressure is great and the curvature is great. The pressure and the curvature rise and fall together. We have now learnt the lesson which the experiment of the two bubbles, one blown out by the other, teaches us.