= Spherical-particle wrapping by a fluid membrane
{title2=$E/(\pi\kappa)=(4-2\bar w)\xi+\bar\sigma\xi^2$}
In a bound-cap model, an adhered sphere of <radius> $r$ covers <area> $A=2\pi r^2\xi$ with $\xi=1-\cos\alpha\in[0,2]$. Its excess <area> over its circular footprint is $\pi r^2\xi^2$. The <Helfrich energy> of that spherical cap is $4\pi\kappa\xi$, adhesion gives $-wA$, and <membrane tension> gives $\sigma\pi r^2\xi^2$. Setting $\bar w=wr^2/\kappa$ and $\bar\sigma=\sigma r^2/\kappa$ yields the displayed expression. Free-surface deformation, neck structure, <Gaussian curvature> and <topology> changes are omitted. Full wrapping alone does not prove scission.
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