 Axisymmetric stresslet from a Stokeslet pair

Opposite forces $\pm F\mathbf{e}$ applied to the fluid at $\pm (a/2)\mathbf{e}$ have no net force or torque. Their leading Stokeslet difference is $-Fa(\mathbf{e}\cdot \nabla )[J(\mathbf{r})\mathbf{e}]$, equal to the axial stresslet with strength $S=Fa$. Positive $S$ drives outward flow on the axis and inward flow in the equatorial plane, corresponding to a pusher microswimmer; negative $S$ gives a puller microswimmer.