Particle Brownian movement

Avogadro s number, L The number of particles (atoms or molecules) in one mole of any pure substance. L = 6 023 x 10. It has been determined by many methods including measurements of Brownian movement, electronic charge and the counting of a-particles. 

Brownian movement The rapid and random movement of particles of a colloidal sol, observed brightly lit against a dark ground. First observed with a pollen suspension. The Brownian movement is due to the impact on the dispersed particles of the molecules of the dispersion medium. As the particles increase in size, the probability of unequal bombardment from different sides decreases, and eventually collisions from all sides cancel out and the Brownian movement becomes imperceptible at a particle size of about 3-4/z. From the characteristics of the movement, Perrin calculated Avogadro s number L. 

Consider an ensemble of Brownian particles. The approach of P2 to as 00 represents a kmd of diflfiision process in velocity space. The description of Brownian movement in these temis is known as the Fo/c/cer-PIanc/c method [16]- For the present example, this equation can be shown to be... 

Smaller particles, particularly those below about 0.3//m in diameter, exhibit consideroble Brownian movement and do not move uniformly along the gas streamline. These particles diffuse from the gas to the surface of the collecting body and are collected. 

The ultra-microscope reveals bright particles in vigorous motion (Brownian movement). 

Brownian movement becomes appreciable for particles under 3 microns and predominates when the particle size reaches 0.1 micron [13]. This motion usually has little effect in the average industrial process settling system except for the very fine fogs and dusts. However, this does not mean that problems are not present in special applicauons. 

In the rapid motions of small particles floating about in a liquid — Brownian movements —we have an example of motions produced, and maintained, in a medium of uniform temperature. This is probably a case in which the simplicity of the system is, comparatively speaking, too great to allow of the legitimate application of the statistical method, which lies at the basis of the second law. A mean value of the kinetic energy cannot be found. 

The nature and intensity of the attractive or repulsive forces among particles in a state of suspension in a liquid medium depend primarily on the electrostatic charges of the particle. Other factors contributing to these forces are particle size and surface area of the solid, the physical properties of the suspending medium, the presence of adsorbed gases or liquids, the proximity of the particles, and Brownian movement (5). 

In terms of the two-phase system which comprises dispersions of solids in liquids, the minimum energy requirement is met if the total interfacial energy of the system has been minimized. If this requirement has been met, chemically, the fine state of subdivision is the most stable state, and the dispersion will thus avoid changing physically with time, except for the tendency to settle manifest by all dispersions whose phases have different densities. A suspension can be stable and yet undergo sedimentation, if a true equilibrium exists at the solid-liquid interface. If sedimentation were to be cited as evidence of instability, no dispersion would fit the requirements except by accident—e.g., if densities of the phases were identical, or if the dispersed particles were sufficiently small to be buoyed up by Brownian movement. 

Independent bacterial motion is a true movement of translation and must be distinguished from the quivering or back-and-forth motion exhibited by very small particles suspended in a liquid. This latter type of motion is called Brownian movement and is caused by the bombardment of the bacteria by the molecules of the suspending fluid. 

A colloid is a suspension of particles with diameters between 1 nm and 100 nm. The particles are charged and can be subjected to cataphoresis (electrophoresis). They are subject to Brownian movement and have a large amount of surface activity. Their properties lie between those of true solutions and coarse suspensions. 

The rate of coagulation of particles in a liquid depends on the frequency of collisions between particles due to their relative motion. When this motion is due to Brownian movement coagulation is termed perikinetic when the relative motion is caused by velocity gradients coagulation is termed orthokinetic. 

It was only in 1905 that the reality of atoms was finally demonstrated. In that year, the same year that he published the first papers on his special theory of relativity, Albert Einstein published a paper on Brownian movement, the irregular motion of small particles suspended in a liquid. Einstein showed that the patterns of movement that were observed could be explained only by assuming that the particles are constantly buffeted by the molecules that make up the liquid. Thus, observations of Brownian movement provided evidence that molecules—and consequently atoms—are indeed real. 

Although Stokes law does not apply to particles so small that the Brownian movement influences the rate of gravitational settling, yet for the relatively coarse emulsions prepared in this way, no sensible error is introduced. 

As has already been indicated a dilute disperse system may be regarded as obeying the ordinary gas laws. If we imagine a small volume of the disperse system as separated from the bulk of the solution it will contain at any instant a certain number of particles n. Since these particles are agitated by Brownian movement the number of particles in the small volume will alter from moment to moment but always maintaining a mean value of n over long periods of time. If at any instant the number in the small volume be n< then the relative alteration from the mean value m will be... 

Coagulation, the result of approach, contact and coalescence of the particles of the suspensoid, is evidently hindered by any factor which may retard one of these three actions. The approach of one particle to another is brought about by the thermal or Brownian movement of the particles within the medium and factors such as low temperature, high viscosity of the medium or large particle size will evidently diminish the rate of approach. When the particles are in close proximity to one another, actual contact will be prevented if the particles possess electric charges similar in sign, due to the action of electrostatic repulsion. The particles will possess no net charge, i.e. their surface will be covered with the same number of cations and anions and will not repel one another at the isoelectric point when the capillary attraction can operate effectively (Hardy, Proc. Roy. Soo. LXVI. 110,1900). 

Smokes. The particles range from 0.1 to 0.01 micron. Such particles are small enough to be pushed about by the impact of surrounding air molecules (which are in constant motion at average velocities of about a quarter of a mile per second). They show Brownian movement and settle very slowly or not at all, in still air. They tend to diffuse slightly. 

We begin by considering an array of spherical particles with motion that is totally governed by Brownian movement. Let us assume that there are particles of two different radii, Rs l and Rs 2- We assume the spheres interact on contact, in which case they adhere, forming a doublet. Although this is a highly oversimplified picture, it provides a model from which more realistic models can be developed in subsequent stages of the presentation. 

Diffusion effects become important in the removal of dispersed droplets smaller than about 3 microns in diameter. If there it a difference in the concentration of dispersed panicles of this size there is a tendency for the panicles to move from the areas of high concentration to areati of lower concentrations. This tendency results from Brownian Movement and will continue as long as there is a concentration gradient. Fortunately, we have not had to be too concerned with this diameter particle in oilfield liquid-gas separations. 

The result is visible in the Brownian movement of microscopic particles suspended in a fluid. If an individual particle is followed, it is seen to undergo a "random walk," moving in first one direction then another. Albert Einstein showed that if the distances transversed by such particles in a given time A t are measured, the mean square of these Ax values A2 can be related by Eq. 9-24 to the diffusion constant D (which is usually given in units of cmV1). 

To estimate the rate constant for a reaction that is controlled strictly by the frequency of collisions of particles, we must ask how many times per second one of a number n of particles will be hit by another of the particles as a result of Brownian movement. The problem was analyzed in 1917 by Smoluchowski,30/31 who considered the rate at which a particle B diffuses toward a second particle A and disappears when the two codide. Using Fick s law of diffusion, he concluded that the number of encounters per milliliter per second was given by Eq. 9-26. 

Several workers undertook this task. The most notable of these was Perrin. Perrin s special success was due to his technique for preparing particles to suspend that were of uniform and known size. The uniformity was achieved by fractional centrifuging, and the size was established by noting that they could be coagulated into chains whose length could be measured and whose links could be counted. The microscopic observation of these uniform particles enabled Perrin and his students to verify the Einstein results and to make four independent measurements of Avogadro s number. See Fig. 1. These results not only established an understanding of Brownian movement, but also they silenced the last critics of the atomic view of matter. 

Colloidal particles move at random through a suspension due to the fact that they possess kinetic energy (i.e. movement energy as a result of temperature) and because they collide with other particles. This movement is called Brownian movement (figure 5.8). 

---