Popular Science Monthly/Volume 35/September 1889/The Surface Tension of Liquids
|THE SURFACE TENSION OF LIQUIDS.|
By W. H. LARRABEE.
WHAT is it that keeps a drop of water in shape; that enables it to resist a considerable pressure or blow before it will collapse into a spatter; that holds it in its integrity to a leaf or the eaves till it is mature to fall, while it still maintains its round, independent individuality? Whatever the power is, it appears yet more distinctly in a globule of mercury, which will not be hammered out of shape or compelled to spread. Dr. Thomas Young conceived, for the explanation of this and some other phenomena exhibited by small, isolated liquid masses, the idea of their being surrounded by a thin, elastic membrane, less dense than the deeper parts of the drop, and capable of adhering perfectly to them, and more or less strongly to solid bodies. It seemed capable of opposing a certain resistance to being rent, and this was called its superficial tension. Some curious movements take place when certain solid substances are cast upon water, to account for which Dutrochet supposed a new force, which he called epipolic force. These phenomena of the drops, the "epipolic force," the calming effects of oil on storm-disturbed water, and a variety of other curious actions hitherto unaccounted for, have lately been referred to this property of superficial tension. Taking a drop of water as typically embodying the property, M. E. Gossart asserts that all the energies of nature may be found in its tenuous envelope. Besides M. Gossart, studies of the curious and protean properties of this superficial tension, or the envelope of the water-drop, have been published by M. H. Devaux and M. Van der Mensbrugghe. The present article is a summary of some of the results of their studies. Regarding water in a vessel, M. Van der Mensbrugghe finds that whatever may once have been thought on the subject, it is not equally constituted throughout. Its particles are solicited by attractive forces which are exhibited when, upon drawing out a pencil which has been dipped into the mass, a drop is found adhering to the point. If this drop be conceived to be cut by a horizontal plane, all the parts below the plane may be supposed to be sustained by those which are above it. It is also acted upon by repulsive forces tending to scatter the particles, the effects of which are seen in evaporation. When the attractive and repulsive forces are at equilibrium within the liquid, there is supposed to be in the immediate vicinity of the free surface a tendency to the dispersion of the particles which is constantly opposed by the attractive forces. The condition of the superficial layer may be compared with that of a thin, elastic membrane under stretch, the cohesion of which constantly opposes itself to a more considerable elongation. The superficial layer of a liquid is thus subject to a contractile force or tension, by virtue of which it tends to become as small as possible. M. Gossart, comparing the relative situation of two molecules, A within the drop, and B at its surface, against the air or another liquid or a solid body, shows that each molecule is attracted by the others only from a certain distance (less than ten thousandth of a millimetre), which is as formidably great to it as it seems little to us. Those molecules which are at a greater distance from A and B will have no more action upon them than the stars have upon our sun, earth, and planets. Regarding these spheres alone, A, equally solicited in all directions by an equal number of molecules, will be free in its movements, and obedient to Pascal's principle; while B has not the same surrounding in every direction. Hence a kind of rarefaction which extends to only a slight depth in the drop; and hence also, on the surface, the elastic membranous or resistant quality.
This property is illustrated in some experiments described by M. Van der Mensbrugghe. Take two pencils, one of which should be of light wood and thinner than the other (Fig. 1); place them alongside and in contact; drop a little clear water in the angle between them, so as to moisten the line of contact. There will be formed a slight liquid mass, adherent to both pencils, of concave outline, the section of which is represented by a b in the corner diagram of Fig. 1. The lighter pencil will hang from the other by virtue of the tension of the concave surfaces a b, that bound either side of the line of contact. With the pencils twelve centimetres long, a weight of eighteen hundred milligrammes may be sustained in this way. In a second experiment, a ring of copper wire a millimetre thick and three and one quarter inches in diameter, is laid carefully upon the surface of pure water, when—if everything be entirely clean—it will float, as in Fig. 2, section a, and this, notwithstanding copper is 8·8 times heavier than water. This takes place because all the tensions of the liquid that touches upon the ring produce an upward resultant. A ring weighing seventeen hundred and thirty milligrammes may be thus upheld, while the maximum effect of the tensions is three thousand seven hundred and seventy milligrammes, or more than double the weight of the ring. Needles, globules of mercury, a thin ring of platinum, etc., may be similarly made to float on water.
In a third experiment a strip of thin, unglazed paper, say six inches and three quarters long by an inch and a half wide, is folded so as to form a box or trough, as represented in the lower part of Fig. 3. Set the box on a table, moisten the inner faces with a wet brush, and pour in water from an inch or two above. The tension of the liquid surface will at once bring the long sides of the box together, and the vessel will thus shut upon itself.
Fig. 1.—Adherence of one Pencil to another by the Tension of Concave Surfaces of Water.
Again, take a cylindrical cork of about wine-bottle size; fix in the center of one end a fine iron wire terminating in a hook or pan to hold ballast. In the other end fix a ring about four inches in diameter, lifted on branching supports as in Fig. 4. Plunge the apparatus into a vessel containing a suitable depth of water. With a proper weight of ballast, the cork will assume a vertical position, and will rise only to a certain distance above the level of the water. But if the whole is pushed down into the liquid and left there, the ring will not again clear itself from the water; it will only rise a little above its level, producing a double concave meniscus. In this case the effect of superficial tension is to give rise to a downward resultant sufficient to counterbalance the increase of the upward thrust. If the ballast is managed so that the excess of this resultant is but slight, on the application of ether by a wad or sponge, the effect of which will be to diminish the superficial tension of the water, the ring will rise from the liquid and the apparatus assume its original position.
In a fifth experiment a square frame of wire is dipped into a mixture of soap and sugar with water. On withdrawing the frame its inner space will be occupied with a flat film. of so little weight that it does not visibly sag, but becomes more tense as it is attenuated. A closed contour of cotton or silk thread laid upon the film will lie in any form so long as the film is whole and its tension equal in every direction. But the instant it is broken
Fig. 2.—Copper Ring floating on the Surface of Water.
within the contour the thread will stretch and assume a circular form as in Fig. 5, under the influence of the outward tensions of the rest of the film. It takes the shape in which it bounds as great a surface as its length permits, which is that of a circle. Prof. Schoentjes has varied upon this experiment by using, instead of a simple thread, a system composed of portions of rectilinear solids and portions of arbitrary form, made by passing threads loosely through pieces of fine straws (as in the object lying on the table in Fig. 5). This being placed upon the film and the film pierced, as in the previous experiment, invariably assumed a shape in which all the loose thread portions became arcs of a single circumference, of which the rectilinear solid portions (the straws) constituted chords—or the figure, according to Steiner, of the maximum surface that can be limited by a contour so composed, M. Terquem and M. Gossart, by breaking the film at one or more points outside of the contour, make the thread double into loops.
M. Gossart has studied the pressure of this supposed membrane surrounding the drop of water, and its variation under different degrees of curvature. Investigating its behavior in a homogeneous medium, he takes the envelope itself—a drop void of water, or rather full of air—represented for convenience of manipulation by a soap-bubble, and consisting of two films separated by an extremely thin mass of water. The pressure is the same in every part, and the curvature uniform, and that which gives the least possible surface—a sphere. The pressure is strong enough to drive tobacco-smoke back through a pipe-stem or to blow out a candle. The curved film may be deformed by passing it through rigid frames, but it will always preserve a geometrical shape, for it can not continue to exist except upon the condition of exercising an equal pressure throughout upon the air imprisoned within it; but some of the shapes it will assume within this rule are very curious.
If a drop of water is poured upon another liquid, it is still imprisoned in its contractile sac, but in one having two walls of unequal elasticity; the upper wall resting against the air, and the lower one against the liquid. The line of suture of these two
Fig. 3.—A Paper Box closing upon itself when Water is poured into it.
walls floats in three different media—air, water, and the subjacent liquid; or, to use M. Gossart's figure, it is like a cord drawn by three different forces, which are represented in this case by the upper and lower walls of the sac and the uncovered membrane of the inferior liquid, pulling against one another, as when three ropes are pulled by three men of unequal strength. Suppose, as the extreme case, that the attraction of the membrane exterior to the drop so prevails over the tension of the two walls of the sac that they can not rest in equilibrium. Then the sac will be drawn out, and all the superior liquid will spread in an infinitely thin layer over the other. This is what happens to a drop of oil when it is thrown upon water. When a liquid is brought in contact with a solid, as when a first drop of water is let fall upon a horizontal plate of glass, the inclosing sac is flattened where it is in touch with the glass, and bulges where it is in contact with the air. The form of the sac and the angle of its junction with the glass are determined by the fact that the two tensions of the envelope.
Fig. 4.—An Iron Ring having been plunged under Water, holding down the Cork to which it is attached.
the upper and lower, should balance the traction of the exterior glass upon the cordon separating them. In the case of a drop of alcohol, the tensions being much weaker, can not resist the traction of the glass, and the liquid spreads out at once, as also happens with water when the plate has already been moistened. Mercury opposes a very strong tension, and is hardly flattened at all on striking the glass. A drop of water cast upon a hot plate also exhibits a superior tension, and assumes the spheroidal state, which was first analyzed in 1850 by M. Boutigny, of Evreux. He said, "Bodies in a spheroidal state are bounded by a film of matter, the molecules of which are so connected that we can compare them to a solid, transparent, very thin, very elastic envelope, probably less dense than the rest, that protects the liquid within it against any too considerable heating."
This force of superficial tension exists and is manifest in all liquids, but in different degrees. It is stronger in water than in any other of the common liquids except mercury. Its value has been measured, and is usually expressed, in milligrammes per millimetre of superficial length, at 60° Fahr., as 7·5 for distilled water; 49 for mercury; 4 for glycerin; 3·6 for olive-oil; 2·8 for soap-suds; 2·7 for spirits of turpentine; 2·6 for petroleum; 2·5 for absolute alcohol; and 1·88 for ether. It is diminished when the liquid is warmed, and is weakened and even destroyed by impurity. M. Terquem has determined, from observations on the interference of luminous rays, that the envelope is less than 1/20,000 millimetre thick.
Curious effects appear when liquids having different superficial tensions are brought together, and when solids containing volatile properties are thrown upon a liquid. With two liquids that will mix, as water and alcohol or ether, the tension at the point of contact becomes null, and the lighter fluid spreads out over the other. This is followed, according to M. Van der Mensbrugghe,
Fig. 5.—A Contour of Silken Thread expanding into a Circle when the Film on which it has been laid is broken.
by a retreat of this fluid toward the point where it was dropped, in consequence of an increased tension given to that point by the cooling that follows the evaporation of the dropped liquid. If the liquids will not mingle, as when oil or turpentine is dropped on water, the drop spreads over the surface, forming a thin layer upon it which is marked by beautiful plays of colors.
M. Devaux exemplifies one of these effects by an experiment (Fig. 6) in which a tin boat, having a notch cut in the stern, is launched upon the water. On letting a drop of alcohol fall at the notch, the boat moves away as if driven by some repulsion. There is, however, ho repulsion; but the tension astern has been destroyed or diminished, while that forward continues in full force to draw the boat onward. If a bit of camphor be substituted for the alcohol, its vapor has the same effect upon the tension,
Fig. 6.—Tin Boat sailing around on Water by the Aid of a Bit of Camphor.
and the boat may be made to sail regularly, with considerable speed, for hours. The experiment is made more spectacular by furnishing the boat with a mast carrying a flag.
Fig. 7.—Movements of Fine Grains of Camphor on the Surface of Mercury.
In another experiment described by M. Devaux, a few granules of camphor are sprinkled upon mercury, and breathed upon till a kind of lye is formed, when a multitude of long-tailed "tadpoles" appear swimming over the surface of the mercury (Fig. 7). If, now, we breathe continuously from one side upon the mercury, the "tadpoles" will become more lively, and direct themselves against the breath, coming up to the very edge of the mercury. The breath, driving the vapors bank, clears a space in front of the "tadpole," leaving the tension of the mercury free to act upon it and draw it forward, while it clouds the rear, weakening the tension.
M. Devaux has exemplified the strength and persistence of the tensional force by connecting his camphor-boat with a float in the shape of a watch-glass. The movement of the boat continues, carrying
Fig. 8.—Tin Boat causing a Loaded Float to go bound with it.
the float around while it is loaded with weights rising to fifty or a hundred grammes, and even to a kilogramme (Fig. 8); and if forcibly stopped, it will begin again when the obstacle is removed.
The phenomena of capillary attraction are explained under the theory of superficial tension. The liquid rises in the tubes by virtue of the adhesion of its superficial membrane to their walls, and to a less height in the larger than in the smaller tubes because the mass of the liquid to be raised increases more rapidly than the power of the membrane to sustain it. Just as the tension of a liquid is diminished by adding a foreign substance, the capillary force of a tube is diminished by the presence of a foreign vapor. This is illustrated by M. Devaux as in Fig. 9, where water rises to the greatest height in the .tube A, which was filled simply with air, to a less height in E, which has been charged with the vapor of ether, and to a still less height in C, which was occupied with the vapor of camphor.
Other energies than this mechanical energy have been shown by different investigators to reside in the thin envelope of the water-drop; acoustic energy by M. Savart, as noticed in a cascade of water-drops, the envelopes of which underwent rhythmical deformations; calorific energy, due to the displacement of molecules that pass from the surface to the ranks, or which ascend to the superficial layer; luminous energy, as studied by Newton, Boyle, Hooke, Young, and Fresnel; and electrical energy, as manifested in effects that have been observed by M, Lipmann—all of which, according to M. Gossart, are transformable one into another in accordance with the law of conservation of force. A drop of water hangs from a leaf or the eaves of a house, held up as in a bag by its superficial envelope. It continues to increase in size and weight many times faster than the tension of its cordon of attachment is re-enforced, till it overcomes that tension, and then it falls; and, according to M. Gossart, all the drops of water that fall—of themselves—are of the same size. The drops of melted metals, whose superficial tensions are enormous, reach correspondingly enormous magnitude. The purity of liquids can be determined by observing the size of the drops they give; in the case of wines, by counting the number of drops per cubic centimetre; for the superficial tension of all liquids is modified by adulteration.
M. Van der Mensbrugghe has calculated what he calls the potential energy of water, on the basis of the estimation of its superficial tension at 7·5 milligramme-millimetres per square millimetre of free surface. This is resident in a film not more than 1/20,000 of a millimetre thick. Distributed over the whole ocean, it gives an amount of mechanical force which we have no means of accurately calculating. If we suppose that of two equal and adjacent superficial layers of sea-water, one washes over the other by the effect of the wind, for example, the layer that is covered loses its free surface, and with it its proper potential energy, which appears again in an increase of speed. Thus on the ocean the action goes on, the energies of the successive waves being extinguished as to them and transferred to others; so that every wave in course of formation is composed of portions the speeds of which are greatest toward the top. In a violent wind the acceleration produces on each wave a crest that becomes more and more protuberant, and at length is disintegrated, or breaks. It follows that any agent capable of preventing the washing of the superficial slices over one another will constitute an obstacle to the progressive increase of the living force of the liquid masses.
Such an agent is found in oil when it covers a sufficient extent of the surface of the sea. By virtue of its specific levity it keeps on the surface and prevents the washing of one layer of water over another. Thus is explained the soothing action, which appears so mysterious at first sight, of oils upon rough seas. Susceptible of being spread out into laminæ of the incredible thinness of 1⁄100000 or 1⁄200000 of a millimetre, a small quantity of oil is efficacious to cover and prevent overwashing of waves upon a large surface. When this is done, the formation of the crests or breaking waves, so dangerous to ships, can not take place, and the terrible breaker is converted into a harmless swell.
- "A Voyage on the Surface of a Drop of Water." Lecture before the Scientific and Literary Society of Caen, published in the "Revue Scientifique," 1887.
- "Spontaneous Movements of certain Bodies on the Surface of some Liquids," "La Nature," 1888.
- "Superficial Tension." Lecture before the Belgian Society of Microscopy, March 3, 1888, published in "La Nature," 1888.