Anisotropic Diffusion: Perrin Ellipsoid

Diffusion tensor for prolate/oblate ellipsoids, Brownian trajectories, and mean displacement
Aspect ratio a/b2.00
Viscosity η1.00
Temperature T300
Particles N20
Perrin equations give exact translational diffusion coefficients for ellipsoids of revolution (semi-axes a, b=c):
D_∥ (along symmetry axis) = kT·S/(8πηb)·f_∥ where S = shape factor (elliptic integral).
D_⊥ (perpendicular) = kT/(16πηb)·(1/f_⊥). For prolate (a>b): D_∥ > D_⊥; for oblate (a<b): D_∥ < D_⊥.
Rotational diffusion D_r ~ kT/(8πηb³) also anisotropic — visualized as ellipsoid orientation drift.
Color encodes orientation angle; displacement ellipse shows the anisotropic MSD.