Brownian motion and translational diffusion

The motion of individual particles is continually changing direction as a result of random collisions with the molecules of the suspending medium, other particles and the walls of the containing vessel. Each particle pursues a complicated and irregular zig-zag path. When the particles are large enough for observation, this random motion is referred to as Brownian motion, after the botanist who first observed this phenomenon with pollen grains suspended in water. The smaller the particles, the more evident is their Brownian motion. 

Treating Brownian motion as a three-dimensional random walk , the mean Brownian displacement x of a particle from its original 

The diffusion coefficient of a suspended material is related to the frictional coefficient of the particles by Einstein s law of diffusion  

Perrin (1908) studied the Brownian displacement (and sedimentation equilibrium under gravity see page 35) for fractionated mastic and gamboge suspensions of known particle size, and calculated values for Avogadro s constant varying between 5.5 x 1023 mol1 and 8 x 1023 mol-1. Subsequent experiments of this nature have 

As a result of Brownian motion, continual fluctuations of concentration take place on a molecular or small-particle scale. For this reason, the second law of thermodynamics is only valid on the macroscopic scale. 

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