Brownian movements

To determine Avogadro s number from observations of Brovuiian movement. 

Perrin (Ann. Chim. Phys. 1909, 18, 77) describes the observations by his student Chaudesaigues of the Brownian movement of a suspension of rubber latex in water. 

From observations on 50 such particles the mean square displacement in a chosen direction over various intervals of time was determined. The values found are shown in table 1. 

The mean square displacement f in a given direction over a time t is related to the diffusion coefficient D by 

If furthermore the particles are large enough to obey Stokes law, (l) is equivalent to 

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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... 

Einstein A 1956 Investigations on the Theory of Brownian Movement (New York Dover). This book is based on a series of papers Einstein published from 1905 until 1908... 

Fox R F 1998 Rectified Brownian movement in molecular and cell biology Phys. Rev. E 57 2177... 

A. Einstein, Investigations of the Theory of the Brownian Movement, Dover, New York, 1956. 

Controlling mechanism for mist collection Brownian movement Impaction Impaction... 

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. 

Perrin, J. (1909) Annales de Chimie et de Physique 18, 1. English translation by F. Soddy, Brownian Movement and Molecular Reality (Taylor Francis, London) 1910. 

Thermal copulation The process by which Brownian movement causes particulate matter to collide and adhere. 

Furth, R. (ed.), 1956. Albert Einstein, investigations on the theory of Brownian movement. New York Dover. 

Smoluchowski, M.V., 1916. Three lectures on diffusion. Brownian movement and coagulation of colloidal systems. Physik Zeitung, 17, 557. 

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. 

Dust venting nomographs, 514-520 Calculations, 513-517 Dust, mist calculations, 226-236 Brownian movement, 226. 236 Drag coefficients, chart, 235 Intermediate law, 226 Newton s law, 226, 228... 

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. 

This kinetic explanation of osmotic pressure has recently received experimental support in the beautiful researches of Perrin on the Brownian movement (Urcwnian Movement and Molecular lteality, J. Perrin, trails. F. Soddy, 1910). 

Simha, R. The Influence of Brownian Movement on the Viscosity of Solutions. J. Phys. Chem. 44, (1940) 25-34. 

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. 

The principal axis of the cone represents the component of the dipole under the influence of the thermal agitation. The component of the dipole in the cone results from the field that oscillates in its polarization plane. In this way, in the absence of Brownian motion the dipole follows a conical orbit. In fact the direction of the cone changes continuously (because of the Brownian movement) faster than the oscillation of the electric field this leads to chaotic motion. Hence the structuring effect of electric field is always negligible, because of the value of the electric field strength, and even more so for lossy media. 

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. 

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