Fluid Dynamics
In the calculation of the Stokes' law for the drag that a viscous fluid exerts on a small spherical particle, the velocity distribution obeys Navier-Stokes equations neglecting inertia, i.e.
with the boundary conditions
being the relative velocity of the particle to the fluid far from the particle. In spherical coordinates this velocity at infinity can be written as
The last expression suggest an expansion on spherical harmonics for the liquid velocity and the pressure
Substitution in the Navier-Stokes equations produces a set of ordinary differential equations for the coefficients.
Read more about this topic: Vector Spherical Harmonics
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