= Two-mode tensorial squirmer flow
A spherical <squirmer> with tangential <surface slip velocity> $(I-nn)(A+Bn)$, where $B$ is a <symmetric second-rank tensor> and a <traceless second-rank tensor>, translates with $U=-2A/3$ and does not rotate in an unbounded quiescent fluid. With $S=x\cdot Bx$ its exterior <Stokes flow> is
$$
u=\frac{a^3}{3}\nabla\frac{A\cdot x}{r^3}+\frac{3a^2Sx}{2r^5}+\frac{a^4}{2}\nabla\frac S{r^5},\qquad p-p_\infty=\frac{3\mu a^2S}{r^5}.
$$
This follows from the <Unscaled Papkovich–Neuber representation> using <harmonic functions> as potentials $\Phi=-a^2Bx/(2r^3)$ and $\chi=a^3A\cdot x/(3r^3)+a^4S/(2r^5)$. Matching the surface coefficients proves the formula. The two modes generate a <potential dipole> and a <stresslet>, respectively.
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