Saturday, July 31, 2010

An Approximate Formula for the Diffusion Coefficient

From the Kinetic Theory of Gases* one can find an approximate formula for the Diffusion Coefficient.

We can use this formula to estimate the rate of diffusion for oil droplets if we substitute the particle mass and cross-sectional radius for the moleculelar mass and cross-sectional radius. The particle mass is also dependent on the cross-sectional radius since it is the product of the density of oil and the droplet's volume. So one would expect the diffusion coefficient to increase rapidly with the decrease in size of the oil droplets. The particle number density would be the number of molecules per unit volume of seawater.
*see Castellan, Physical Chemistry, 3rd ed., p. 756.

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