Rotational Version of Fick's Law
A rotational version of Fick's law of diffusion can be defined. Let each rotating molecule be associated with a vector n of unit length n·n=1; for example, n might represent the orientation of an electric or magnetic dipole moment. Let f(θ, φ, t) represent the probability density distribution for the orientation of n at time t. Here, θ and φ represent the spherical angles, with θ being the polar angle between n and the z-axis and φ being the azimuthal angle of n in the x-y plane. The rotational version of Fick's law states
This partial differential equation (PDE) may be solved by expanding f(θ, φ, t) in spherical harmonics for which the mathematical identity holds
Thus, the solution of the PDE may be written
where Clm are constants fitted to the initial distribution and the time constants equal
Read more about this topic: Rotational Diffusion
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