The Einstein-Smoluchowski equation, also known as the Stokes-Einstein-Smoluchowski equation, is a fundamental equation in the study of Brownian motion. It relates the diffusion coefficient of a particle to its size, temperature, and viscosity of the surrounding medium. The equation was first developed independently by Albert Einstein and Marian Smoluchowski in 1905 and 1906.
The equation states that the diffusion coefficient of a particle is directly proportional to the temperature and inversely proportional to the viscosity of the surrounding medium and the size of the particle. Mathematically, the equation can be written as follows:
D = kT / 6πηr
where: D = diffusion coefficient k = Boltzmann constant T = temperature η = viscosity of the medium r = radius of the particle
The equation can be used to calculate the diffusion coefficient of particles in various systems, such as gases, liquids, and solids. It is essential in understanding the behavior of small particles, such as molecules and colloids, and is used in various fields of science, including physics, chemistry, and biology.
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