Brownian motion Stokes-Einstein theory

In the Stokes-Einstein theory of brownian motion, the particle motion at very low concentrations depends on the viscosity of tne suspending liquid, the temperature, and the size of the particle. If viscosity and temperature are known, the particle size can be evaluated from a measurement of the particle motion. At low concentrations, this is the hydrodynamic diameter. 

Intcrmolecular dipole-dipole relaxation depends on the correlation time for translational motion rather than rotational motion. Intermolecular dipole-dipole interactions arise from the fluctuations which are caused by the random translational motions of neighboring nuclei. The equations describing the relaxation processes are similar to those used to describe the intramolecular motions, except is replaced by t, the translation correlation time. The correlation times are expressed in terms of diffusional coefficients (D), and t, the rotational correlation time and the translational correlation time for Brownian motion, are given by the Debye-Stokes-Einstein theory ... 

The critical nucleus of a new phase (Gibbs) is an activated complex (a transitory state) of a system. The motion of the system across the transitory state is the result of fluctuations and has the character of Brownian motion, in accordance with Kramers theory, and in contrast to the inertial motion in Eyring s theory of chemical reactions. The relationship between the rate (probability) of the direct and reverse processes—the growth and the decrease of the nucleus—is determined from the condition of steadiness of the equilibrium distribution, which leads to an equation of the Fourier-Fick type (heat conduction or diffusion) in a rod of variable cross-section or in a stream of variable velocity. The magnitude of the diffusion coefficient is established by comparison with the macroscopic kinetics of the change of nuclei, which does not consider fluctuations (cf. Einstein s application of Stokes law to diffusion). The steady rate of nucleus formation is calculated (the number of nuclei per cubic centimeter per second for a given supersaturation). For condensation of a vapor, the results do not differ from those of Volmer. 

Early advances in aerosol science were closely lied to the development of certain fundamental physical concepts. For example, aerosol transport theory is based on Stokes law including semiempirical corrections made by Millikan in his measurements of the electronic charge. Einstein s theory of the Brownian motion plays a central role in aerosol diffu.sion which i.s discussed in the next chapter. The Brownian motion results in coagulation first... 

One of the important applications of Stokes law occurs in the theory of Brownian motion. According to Einstein (El a) the translational and rotary diffusion coefficients for a spherical particle of radius a diffusing in a medium of viscosity n are, respectively,... 

The general theory of Brownian motion set forth thus far is a self-contained, purely phenomenological theory which does not depend upon any special hydrodynamic assumptions. If, however, following Einstein, it is further assumed that, on the average, the diffusing particle experiences a hydrodynamic force governed by Stokes equations, the diffusion matrix is then found to be (B26a)... 

The continuous and erratic motion of individual particles (i.e., pollen grains) as the result of random collisions with the adjoining molecules of fluid (water) was observed by the botanist Robert Brown in 1827. The term Brownian diffusion is used for colloidal particles to distinguish it from solute molecular diffusion. However, both are end members of a continuum of particle sizes and a fundamental consequence of kinetic theory is that all particles have the same average translational kinetic energy. The average particle velocity increases with decreasing mass (Shaw, 1978). The Stokes-Einstein s equation for particle diffusivity is based on this concept. It is... 

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