Surface slip velocity
= Surface slip velocity
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 $\mathbf u_s$,
$$
\mathbf V=-\frac1{4\pi a^2}\int_{r=a}\mathbf u_s\,dS,
\qquad
\boldsymbol\omega=-\frac3{8\pi a^4}\int_{r=a}\mathbf x\times\mathbf u_s\,dS.
$$