Surface tension

“ Effect of Surface-tension on the Velocity of Waves.—When a series of waves is propagated on the surface of a liquid, the surface-tension has the effect of increasing the pressure at the crests of the waves and diminishing it in the troughs. ”

“ From the simple fact that the sphere is of all surfaces that whose surface-area for a given volume is an absolute minimum, we have already seen it to be plain that it is the one and only figure of equi­lib­rium which will be assumed under surface-tension by a drop or vesicle, when no other disturbing factors are present. One of the most important of these disturbing factors will be introduced, in the form of complicated tensions and pressures, when one drop is in contact with another drop and when a system of intermediate films or partition walls is developed between them. ”

“ The simple fact is that the agreement of cell-forms with the forms which physical experiment and math­e­mat­i­cal theory assign to liquids under the influence of surface tension, is so frequently and often so typically manifested, that we are led, or driven, to accept the surface tension hypothesis as generally applicable and as equivalent to a universal law. The occasional difficulties or apparent exceptions are such as call for further enquiry, but fall short of throwing doubt upon our hypothesis. ”

“ This implies that the tension of the free surface of the solid is greater than that of the surface of contact of the solid with the liquid . Now consider the tension of the free surface of the liquid . All round its edge there is a tension acting at an angle with the vertical. The circumference of the edge is , so that the resultant of this tension is a force acting vertically upwards on the liquid. Hence the liquid will rise in the tube till the weight of the vertical column between the free surface and the level of the liquid in the vessel balances the resultant of the surface-tension. ”

“ The surface-tension, destroyed upon one side, will remain in action in the unruptured film, and therefore we should expect the thread to be pulled toward the uninjured side. We can easily put the matter to the test of experiment. I break one side by touching it with a hot wire, and what we foresaw occurs, the thread is instantly pulled toward the side which the wire did not tear. This experiment proves that the surface of a liquid is in a state of tension. ”

“ But this phenomenon, while it brings about a certain departure from complete symmetry, is still compatible with, and coexistent with, many of the phenomena which we have seen to be associated with surface-tension. The symmetry of tensions still leaves the cell a solid of revolution, and its surface is still a surface of equi­lib­rium. The fluid pressure within the cylinder still causes the film or membrane which caps its ends to be of a spherical form. ”

“ When sufficient time has elapsed after the extension of a surface originally in equilibrium between coexistent phases, the superficial tension will evidently have sensibly its original value, unless there are substances at the surface which are either not found at all in the adjacent masses, or are found only in quantities comparable to those in which they exist at the surface. But a surface newly formed or extended may have a very different tension. ”

“ The world now knew, by the word of scientists, that nothing but a thin surface of molecules, strengthened by a million times, lay between them and the water their bodies thirsted for. Surface tension, acted upon by a strange force, broadcasted from a mechanism ten miles beneath the surface of the Atlantic. ”

“ But a liquid has no power of recovering from such internal shear, and the only force that checks the spread, and ultimately causes the recovery of shape, is the surface tension, which arises from the fact that the surface layers are always in a state of extension and always endeavouring to contract. ”

“ We can easily calculate this pressure, and so satisfy ourselves that, when the radius of curvature is of molecular dimensions, the {207} pressure is of the magnitude of thousands of atmospheres,—a conclusion which is supported by other physical con­si­de­ra­tions.
The contraction of a liquid surface and other phenomena of surface tension involve the doing of work, and the power to do work is what we call energy. It is obvious, in such a simple case as we have just considered, that the whole energy of the system is diffused throughout its molecules ”

“ In like manner we shall find that the form of all small organisms is largely independent of gravity, and largely if not mainly due to the force of surface-tension: either as the direct result of the continued action of surface tension on the semi-fluid body, or else as the result of its action at a prior stage of development, in bringing about a form which subsequent chemical changes have rendered rigid and lasting. ”

“ The expression for the superficial tension is most readily found with the aid of the idea of superficial energy, introduced into the subject by Gauss. Since the tension is constant, the work that must be done to extend the surface by one unit of area measures the tension, and the work required for the generation of any surface is the product of the tension and the area. ”

“ And accordingly, so long as our purpose is morphological, so long as what we seek to explain is regularity and definiteness of form, it matters little if we should happen, here or there, to confuse surface tension with elasticity, the contractile forces manifested at a liquid surface with those which come into play at the complex internal surfaces of an elastic solid. ”

“ When the establishment of equilibrium is rapid, the variation of the tension from its normal value will be manifested especially during the extension or contraction of the surface, the phenomenon resembling that of viscosity, except that the variations of tension arising from variations in the densities at and about the surface will be the same in all directions, while the variations of tension due to any property of the surface really analogous to viscosity would be greatest in the direction of the most rapid extension. ”

“ It is necessary for the stability of a surface of discontinuity that its tension shall be as small as that of any other surface which can exist between the same homogeneous masses with the same temperature and potentials. ”

“ This precision has not been used for the sake of the mechanical part of the problem, which does not require the surface to be defined with greater nicety than we can employ in our observations, but in order to give determinate values to the superficial densities of energy, entropy, and the component substances, which quantities, as has been seen, play an important part in the relations between the tension of a surface of discontinuity, and the composition of the masses which it separates. ”

“ The effect of the tension at every point of and is double of that which we have just calculated, that is, it is equal to that of forces whose potential is acting on the whole volume of the figure. The effect of the pressure acting on the whole surface is by hydrostatics equal and opposite to that of this system of forces, and will keep the figure in equilibrium. ”

“ When there are two components, neither of which is confined to the surface of discontinuity, we may regard the tension as a function of the temperature and the pressures in the two homogeneous masses. The values of the differential coefficients of the tension with respect to these variables may be represented in a simple form if we choose such substances for the components that in the particular state considered each mass shall consist of a single component. ”

“ We note here that the term surface is to be interpreted in a wide sense; for wherever we have solid particles imbedded in a fluid, wherever we have a non-homogeneous fluid or semi-fluid such as a particle {206} of protoplasm, wherever we have the presence of “impurities,” as in a mass of molten metal, there we have always to bear in mind the existence of “surfaces” and of surface tensions, not only on the exterior of the mass but also throughout its interstices, wherever like meets unlike. ”

“ If the spheres were entirely removed from each other's influence, the state of stress would be uniform round each sphere, and the pulls on its surface-elements would balance, giving no resultant force on the sphere. ”

“ But the strained normal piling which surrounds the surface, and propagates with the surface, being of less density than the mean density of the medium, represents a displacement of the negative mass of the inequality, i.e., of the grains absent, and in whatever new direction the surface is propagating, the motion of the medium, outside the surface, is such as represents equal and opposite momentum, as when a bubble rises in water. ”

“ Propagated to the interior of the heavenly bodies, the pressure would produce the effect that all layers of equal thickness will inclose the same quantity of matter, and that the mean density is three times that of the surface. ”

“ The necessary condition is that the impacts shall follow each other sufficiently rapidly. We have, in fact, a complete analogy in the pressure produced on the surface of a solid sphere immersed in a gas. ”

“ According to our arguments for a hollow earth, at 817 miles from the surface the two halves—outer and inner—of the matter composing it meet and balance each other, so that all the pressure required would be what is necessary to overcome the inertia, viscosity, or cohesion of the matter in the vents. ”

“ Hence, if at any part of the surface of the sphere is positive, there must be some other part of the surface where it is negative, and if the body be displaced in a direction in which is negative, it will tend to move from its original position, and its equilibrium is therefore necessarily unstable. ”

“ If we denote by and , its energy, entropy, volume, and mass, we have Now the mechanical conditions of equilibrium for the surface where a solid meets a fluid require that the traction upon the surface determined by the state of strain of the solid shall be normal to the surface. ”

“ And therefore the globe meets with a resistance, which is to the force by which its whole motion may be either taken away or generated in the time in which it describes two thirds of its diameter moving uniformly forwards, as the density of the medium to the density of the globe. ”

“ In consequence of the supposed equilibrium of its several elements, such a film may be treated as a simple surface of discontinuity between the contiguous gas-masses (which may be similar or different) , whenever its radius of curvature is very large in comparison with its thickness,—a condition which we shall always suppose to be fulfilled. ”

“ I have here a light wooden surface, say, one yard square; the pressure of the air against the surface is equal, as I just stated, to about nine tons; but the air presses equally on both sides, and the molecules have such great mobility that, when we move the surface slowly, they readily give way, and we encounter but little resistance. ”

“ Want of support on the faces of hills.—When a wave of elastic compression is propagated through a medium, we see that the energy of motion is being continually transmitted from particle to particle of that medium. A particle, in moving forwards, meets with an elastic resistance of the particles towards which it moves, but, overcoming these resistances, it causes these latter particles to move, and in turn to transmit the energy to others further on. ”

“ Where the surface moves in a line perpendicular to its plane, the resistance is proportional to the extent of the surface, to the square of the speed with which the surface is moved through the air, and to a coefficient, the mean value of which is 0.125. ”

“ We conclude from all these evidences that there exists on the surface of solid bodies an extremely thin layer, the density of which diminishes the more nearly we approach the free surface. Let us assume, consequently, such a special constitution for the superficial layer of solids, and, by a new effort of our imagination, witness the unrelaxing work of our particles of air in the immediate vicinity of some solid body ”

“ Further, as the elasticity of the medium which regulates the pressure is proportional to the density, so the pressure must decrease, as the elasticity decreases--that is, as the electric potential decreases, or the electric density is diminished. ”

“ It may be compared to an elastic band, but there is no intermediate tangible substance to influence bodies that are affected by it, and it remains in undying tension, unlike all elastic material substances known, neither losing nor acquiring energy as time passes. ”