BROWNIAN MOVEMENT. A liquid at rest, such as water in a glass, appears homogeneous, continuous and motion less throughout. If we put into the water a denser substance, such as a glass marble, it sinks, and we know that once it reaches the bottom it will not rise again of its own accord. If with the water we mix certain powder consisting of extremely minute particles, we shall see by observation of the powder that the motion of these different lots of water, which at first resolves itself into parallel currents, becomes less and less defined. Eventually the particles are diffused in all directions throughout the water until the whole appears to be quite motionless.
These familiar motions, which are based on the powers of the naked eye, are shown by microscopic investigation to be abso lutely false. Many particles which are put in water (or into any fluid) instead of sinking steadily, are at once endowed with a very vigorous motion, which is quite haphazard and irregular. The particle continuously moves to and fro ; it rotates and rises and sinks, showing no tendency to come to rest, and maintaining in definitely the same average state of agitation. This wonderful phenomenon, which was anticipated by Lucretius and all but discovered by Buffon, was definitely established by Brown in 1827, and is generally described as Brownian movement.
The phenomenon is not peculiar to water, but is met with in all fluids, and is present in inverse proportion to the viscosity of the fluids. Thus it is scarcely perceptible in glycerine but is extremely active in gases. It can also be observed in the case of water globules supported by the "black spots" of soap bubbles, the size of the globules, as compared with the thickness of the film, being much the same as that of an orange compared with a sheet of paper ; the Brownian movement, which is negligible in a direction at right angles to the film, is very lively in the plane of the film, being almost what it would be in a gas. In a given fluid the movement of the particles is more intense as the size of the particle dimin ishes. This property was pointed out by Brown when he first made his discovery. The nature of the particles is immaterial. In the same fluid two particles exhibit practically the same activity when they are of the same size, no matter of what substance they are composed, and no matter what is their density. The higher the temperature, the more rapid is the movement.
The motion cannot be due to vibration of the slide supporting the droplet under observation, because if such vibration be caused purposely there arise currents in the bulk of the liquid which are at once recognized to be merely superimposed on the irregular movements of the particles. Moreover, Brownian motion occurs in fluids supported by a rigid vessel at night in the country, just as unmistakably as it does in the daytime in a town, when the containing vessel rests on a table which is continually being shaken by the passing of heavy traffic. Similarly, the movement cannot be ascribed to general convection effects produced by variations of temperature. Such convection currents are easily recognizable and are totally unrelated to the characteristic irregular movement. Finally--and this is perhaps its strangest and most startling char acteristic—Brownian movement never ceases, according to many authorities. It can be descried within a cell which has been closed so as to prevent evaporation, for days and even years. It can be seen in liquid occlusions in quartz, which have been sealed up for thousands of years. It is inherent and eternal.
All these features compel us to agree with Wiener (1863) that "the movement does not originate in the particles themselves, nor in any cause exterior to the liquid, but must be attributed to internal movements characteristic of the fluid state"; the smaller the particles are, the more readily do they respond to this motion. In this way we arrive at an essential property of what is com monly termed a fluid in equilibrium : the apparent quiescence of a fluid is an illusion due to the imperfection of our senses, and really represents a permanent condition of violent irregular mo tion. This is an experimental fact quite apart from any question as to theory.
On the other hand, more exact experiments which demonstrate the heating of bodies by friction enable us to state that when the soapy water has come to "rest," its temperature will be slightly higher than when it was moving as a whole before being stopped by the tub. Brownian movement in this quantity of liquid will therefore have become more vigorous, seeing that its activity in creases with the temperature. If we could follow under the micro scope the dissipation of the original mass movement among progressively smaller masses, we should see that an appreciable part of that original movement was conserved by the particles of soapy water. Now the latter are themselves merely "indicat ing" powders, and they show us that in the liquid itself, beside the mass movement which at each moment is being frittered away in all directions among smaller and smaller particles, there is a movement which at each moment automatically redistributes it self in such a way as to impart velocity to any particle which has come to rest. The permanent state which marks the final tempera ture becomes established when, at each moment, exactly as much motion is thus being re-distributed as is being dissipated.
Velocity Distribution.—Since the dissemination of the origi nal movement in a liquid is not indefinite, but inherently limited, it follows that the liquids are composed of particles which can take up all possible motions with regard to one another, but within the interiors of which no dissipation of energy can occur. If such particles did not exist it would be difficult to understand how dissipation, once commenced, could stop. These particles are in unceasing movement, and by colliding with one another mutu ally alter their velocities in magnitude and direction, so that their velocities vary with complete irregularity around a certain average, just as a marksman's bullets are scattered about the target. (Max well's distribution law.) Granting this complete irregularity, it follows, in particular, that in a cell which is large in comparison with the diameter of the particles the number of particles possessing a certain velocity, at any given moment, differs by an infinitesimal amount from the number of particles having the same speed but in the contrary direction. The velocity of the centre of gravity of all these par ticles is, at each instant, therefore, not absolutely zero, but be comes more and more negligible as the size of the cell increases. If the size of the cell diminishes, the mean velocity of the centre of gravity will increase and may be detected under the micro scope. If an indicating powder be present in the cell it will acquire this velocity, which is nevertheless very small as compared with the mean velocity of the particles : this is the explanation of Brownian movement.
These particles have only to be called molecules to recall an ancient hypothesis already envisaged by Epicurus and Lucretius— the hypothesis of the discontinuous structure of matter. In this one instance, however, the hypothesis is the outcome of logical induction, prompted by observation of phenomena. Brownian movement as an experimental reality leads us to postulate mole cules in perpetual motion, and it can then be readily understood that any particle immersed in a fluid is jostled incessantly by neigh bouring molecules and from them receives impulses which, when added together, are the less likely to produce equilibrium the smaller the particle, so that the particle takes on a violently ir regular course.
Study of the molecular agitation is indeed the cause of Brownian movement, and the latter forms a link be tween our ordinary scale of dimensions and that of molecules, then we should be able to arrive at the latter. This, however, depends on the link being properly understood. The study of the Brownian movement of particles in suspension in suitably selected liquids and the comprehension that the laws of dilute solutions applied to such emulsions have led to simple determinations—one of them very direct—of molecular magnitudes.
An emulsion is made by suspending in a fluid a great number of particles all of the same nature. This emulsion is stable if the particles in suspension do not cohere when the chances of Brown ian movement bring them together and if they re-enter the liquid when these chances bring them against the containing vessel or to the surface. A stable emulsion of this kind is comparable to a solution in both of these respects. In addition, if the particles in suspension are of equal size (which can be effected by fractional centrifugation of emulsions of certain resins, as we shall see later), the laws applicable to solutions apply equally in the case of such emulsions.