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With $B=0$, the stated biharmonic stream function for planar Stokes flow isRequiring it to vanish at $r=2a\sin \theta$ and $r=4a\sin \theta$ givesThus $A=-6aC$ and $D=8a^{2}C$. Writing $C=\alpha$ yieldsUsing $u_r={\psi }_{\theta }/r$ and $u_{\theta }=-{\psi }_r$, differentiation shows that $u_r\cos \theta +u_{\theta }\sin \theta$ equals $\alpha$ on the inner boundary and $-\alpha /2$ on the outer boundary. Both wall conditions hold precisely whenThis is the Stokes flow between touching counter-rotating cylinders.