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Einstein-Smoluchowski equation


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A relation between the diffusion coefficient D and the distance λ that a particle can jump when diffusing in a time τ. The Einstein-Smoluchowski equation, which is D = λ2/2τ, gives a connection between the microscopic details of particle diffusion and the macroscopic quantities associated with the diffusion, such as the viscosity. The equation is derived by assuming that the particles undergo a random walk. The quantities in the equation can be related to quantities in the kinetic theory of gases, with λ/τ taken to be the mean speed of the particles and λ their mean free path. The Einstein-Smoluchowski equation was derived by Albert Einstein and the Polish physicist Marian Ritter von Smolan-Smoluchowski.


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