Page:EB1911 - Volume 05.djvu/280

is made positive it becomes dull and spreads itself out; when it is made negative it gathers itself together and becomes bright again. G. Lippmann, who has made a careful investigation of the subject, finds that exceedingly small variations of the electromotive force produce sensible changes in the surface-tension. The effect of one of a Daniell’s cell is to increase the tension from 30.4 to 40.6. He has constructed a capillary electrometer by which differences of electric potential less than 0.01 of that of a Daniell’s cell can be detected by the difference of the pressure required to force the mercury to a given point of a fine capillary tube. He has also constructed an apparatus in which this variation in the surface-tension is made to do work and drive a machine. He has also found that this action is reversible, for when the area of the surface of contact of the acid and mercury is made to increase, an electric current passes from the mercury to the acid, the amount of electricity which passes while the surface increases by one square centimetre being sufficient to decompose .000013 gramme of water.

[The movements of camphor scrapings referred to above afford a useful test of the condition of a water surface. If the contamination exceed a certain limit, the scrapings remain quite dead. In a striking form of the experiment, the water is contained, to the depth of perhaps one inch, in a large flat dish, and the operative part of the surface is limited by a flexible hoop of thin sheet brass lying in the dish and rising above the water-level. If the hoop enclose an area of (say) one-third of the maximum, and if the water be clean, camphor fragments floating on the interior enter with vigorous movements. A touch of the finger will then often reduce them to quiet; but if the hoop be expanded, the included grease is so far attenuated as to lose its effect. Another method of removing grease is to immerse and remove strips of paper by which the surface available for the contamination is in effect increased.

The thickness of the film of oil adequate to check the camphor movements can be determined with fair accuracy by depositing a weighed amount of oil (such as .8 mg.) upon the surface of water in a large bath. Calculated as if the density were the same as in a normal state, the thickness of the film is found to be about two millionths of a millimetre.

Small as is the above amount of oil, the camphor test is a comparatively coarse one. Conditions of a contaminated surface may easily be distinguished, upon all of which camphor fragments spin vigorously. Thus, a shallow tin vessel, such as the lid of a biscuit box, may be levelled and filled with tap-water through a rubber hose. Upon the surface of the water a little sulphur is dusted. An application of the finger for 20 or 30 seconds to the under surface of the vessel will then generate enough heat to lower appreciably the surface-tension, as is evidenced by the opening out of the dust and the formation of a bare spot perhaps 1½ in. in diameter. When, however, the surface is but very slightly greased, a spot can no longer be cleared by the warmth of the finger, or even of a spirit lamp, held underneath. And yet the greasing may be so slight that camphor fragments move with apparently unabated vigour.

The varying degrees of contamination to which a water surface is subject are the cause of many curious phenomena. Among these is the superficial viscosity of Plateau. In his experiments a long compass needle is mounted so as to swing in the surface of the liquid under investigation. The cases of ordinary clean water and alcohol are strongly contrasted, the motion of the needle upon the former being comparatively sluggish. Moreover, a different behaviour is observed when the surfaces are slightly dusted over. In the case of water the whole of the surface in front of the needle moves with it, while on the other hand the dust floating on alcohol is scarcely disturbed until the needle actually strikes it. Plateau attributed these differences to a special quality of the liquids, named by him “superficial viscosity.” It has been proved, however, that the question is one of contamination, and that a water surface may be prepared so as to behave in the same manner as alcohol.

Another consequence of the tendency of a moderate contamination to distribute itself uniformly is the calming effect of oil, investigated by B. Franklin. On pure water the propagation of waves would be attended by temporary extensions and contractions of the surface, but these, as was shown by O. Reynolds, are resisted when the surface is contaminated.

Indeed the possibility of the continued existence of films, such as constitute foam, depends upon the properties now under consideration. If, as is sometimes stated, the tension of a vertical film were absolutely the same throughout, the middle parts would of necessity fall with the acceleration of gravity. In reality, the tension adjusts itself automatically to the weight to be supported at the various levels.

Although throughout a certain range the surface-tension varies rapidly with the degree of contamination, it is remarkable that, as was first fully indicated by Miss Pockels, the earlier stages of contamination have little or no effect upon surface-tension. Lord Rayleigh has shown that the fall of surface-tension begins when the quantity of oil is about the half of that required to stop the camphor movements, and he suggests that this stage may correspond with a complete coating of the surface with a single layer of molecules.]

On the Forms of Liquid Films which are Figures of Revolution.— A soap bubble is simply a small quantity of soap-suds spread out so as to expose a large surface to the air. The bubble, in fact, has two surfaces, an outer and an inner Spherical soap-bubble. surface, both exposed to air. It has, therefore, a certain amount of surface-energy depending on the area of these two surfaces. Since in the case of thin films the outer and inner surfaces are approximately equal, we shall consider the area of the film as representing either of them, and shall use the symbol T to denote the energy of unit of area of the film, both surfaces being taken together. If T′ is the energy of a single surface of the liquid, T the energy of the film is 2T′. When by means of a tube we blow air into the inside of the bubble we increase its volume and therefore its surface, and at the same time we do work in forcing air into it, and thus increase the energy of the bubble.

That the bubble has energy may be shown by leaving the end of the tube open. The bubble will contract, forcing the air out, and the current of air blown through the tube may be made to deflect the flame of a candle. If the bubble is in the form of a sphere of radius $r$ this material surface will have an area

${\mbox{S}}=4\pi r^{2}$

(1)

If $T$ be the energy corresponding to unit of area of the film the surface-energy of the whole bubble will be

${\mbox{ST}}=4\pi r^{2}{\mbox{T}}$

(2)

The increment of this energy corresponding to an increase of the radius from $r$ to $r+dr$ is therefore

${\mbox{T}}d{\mbox{S}}=8\pi {\mbox{T}}dr$

(3)

Now this increase of energy was obtained by forcing in air at a pressure greater than the atmospheric pressure, and thus increasing the volume of the bubble.

Let $\Pi$ be the atmospheric pressure and $\Pi +p$ the pressure of the air within the bubble. The volume of the sphere is

${\mbox{V}}={\tfrac {4}{3}}\pi r^{3},$

(4)

and the increment of volume is

$d{\mbox{V}}=4\pi r^{2}dr$

(5)

Now if we suppose a quantity of air already at the pressure $\Pi +p$, the work done in forcing it into the bubble $pd{\mbox{V}}$. Hence the equation of work and energy is

$p\,d{\mbox{V}}={\mbox{T}}ds$

(6)

or

$4\pi pr^{2}dr=8\pi rdr{\mbox{T}}$

(7)

or

$p=2{\mbox{T}}/r$

(8)

This, therefore, is the excess of the pressure of the air within the bubble over that of the external air, and it is due to the action of the inner and outer surfaces of the bubble. We may conceive this pressure to arise from the tendency which the bubble has to contract, or in other words from the surface-tension of the bubble.

If to increase the area of the surface requires the expenditure