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The surface slip velocity is the fluid velocity relative to the rigid motion of an active particle at its boundary. For a spherical force-free, torque-free swimmer of radius $a$ with slip $\mathbf u_s$,
$$
\mathbf V=-\frac1{4\pi a^2}\int_{r=a}\mathbf u_s\,dS,
\qquad
\boldsymbol\omega=-\frac3{8\pi a^4}\int_{r=a}\mathbf x\times\mathbf u_s\,dS.
$$


Surface slip velocity

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 329 / 1 / b / Solution

Surface slip velocity

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Surface slip velocity

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