= Hydrodynamic interaction of a Hookean dumbbell
{title2=$\dot{\mathbf R}=L\mathbf R-2H(1-3a/(2R))\mathbf R/\zeta$}
For identical no-slip <spheres> of radius $a$ linked by a <zero-rest-length spring>, with $R\gg a$ and $\zeta=6\pi\mu a$, the leading <Oseen tensor> interaction reduces their relative spring relaxation rate by $3a/(2R)$. The midpoint follows an imposed incompressible <linear velocity field>. Add the two bead <force balance> equations to prove midpoint advection; subtract them and use $\mathsf G(\mathbf R)\mathbf R=\mathbf R/(4\pi\mu R)$ to obtain the displayed equation. This deterministic far-field model omits bead inertia, thermal forcing, connector drag and near-contact lubrication.
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