In <resistive-force theory>, the force per unit length is local and linear in the filament velocity relative to the fluid:
$$
\boxed{\mathbf f=-c_\parallel(\mathbf u\mathbin\cdot\mathbf t)\mathbf t
-c_\perp[\mathbf u-(\mathbf u\mathbin\cdot\mathbf t)\mathbf t].}
$$
The distinct parallel and perpendicular drag coefficients encode the anisotropic resistance of a slender filament. Neglecting nonlocal hydrodynamic interactions makes this a leading logarithmic approximation to <slender-body theory>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 355 / 2 / a / Solution

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Slender-body theory approximates the hydrodynamic force on a long thin body by a force density determined primarily by its local tangent and velocity, with logarithmic dependence on the aspect ratio.


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 Incoming links: Slender-body theory