= Capillary boundary integral equation for a viscous drop
{title2=$\frac{1+\lambda}{2}u=-\gamma S[\kappa n]+(\lambda-1)D[u]$}
For a drop with internal <viscosity> $\lambda\mu$, exterior viscosity $\mu$, continuous velocity and a decaying exterior <Stokes flow>, use the drop-outward normal $n$ and curvature $\kappa=\nabla_s\cdot n$, twice the <mean curvature>. Constant <surface tension> gives $(\sigma^+-\sigma^-)n=\gamma\kappa n$. Multiply the interior boundary representation by $\lambda$ and add it to the exterior one: the traction difference yields the single-layer term shown, while the viscosity-independent stress kernel yields $(\lambda-1)D[u]$. Here $S,D$ denote the kernels in <boundary integral representation of Stokes flow>. For equal viscosities the double layer vanishes.
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