Slender-body theory

In fluid dynamics and electrostatics, slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an approximation to a field surrounding it and/or the net effect of the field on the body. Principal applications are to Stokes flow — at very low Reynolds numbers — and in electrostatics.

Consider slender body of length ${\displaystyle \ell }$ and typical diameter ${\displaystyle 2a}$ with ${\displaystyle \ell \gg a}$, surrounded by fluid of viscosity ${\displaystyle \mu }$ whose motion is governed by the Stokes equations. Note that the Stokes' paradox implies that the limit of infinite aspect ratio ${\displaystyle \ell /a\rightarrow \infty }$ is singular, as no Stokes flow can exist around an infinite cylinder.

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