= Capillary origami
\b[Capillary origami] uses <surface tension> to fold an initially flat <elastic plate> around a <liquid> <droplet>. The fold trades a reduction in <surface energy> for an increase in <bending energy>; the initial outline helps select the resulting enclosure.<Capillary origami by Charlotte Py and others>[p.091104-1: capillary driving force, bending resistance and initial-cut control]{ref}
In the 2007 experiments of <Charlotte Py> and collaborators, 40–80 <micrometre> <polydimethylsiloxane> sheets rested on a water-repellent support. A <water> <droplet> reached the sheet's corners; time-lapse images followed its <evaporation>. Squares changed from four-corner bending to a tubular shape; triangles formed a <tetrahedron>. Smaller or thicker sheets could bend and then reopen without enclosing the <droplet>.<Capillary Origami: Spontaneous Wrapping of a Droplet with an Elastic Sheet by Charlotte Py and others>[pp.156103-1–156103-2: preparation and square/triangular evaporation sequences]{ref}
The <elastocapillary length> makes the thickness dependence quantitative. For fixed <Young's modulus>, <Poisson's ratio> and <surface tension>, the <bending stiffness> obeys $B\propto h^3$ and $\ell_{\rm ec}\propto h^{3/2}$. Halving thickness therefore reduces $\ell_{\rm ec}$ by $2^{3/2}$, about $2.83$. At the same lateral size $L$, the <sheet elastocapillary energy ratio> $\eta=\gamma L^2/B$ increases eightfold. This calculation explains why making the sheet thinner can enable wrapping even without changing its outline.
The <sheet elastocapillary energy ratio> compares available <energy> scales; it does not determine a unique final shape. The <contact angle>, initial <liquid> <volume> and outline also matter. A cut chosen to permit several panels to meet is a mechanical design choice, while the <surface tension> supplies the driving <force>. Predicting the complete folding path requires more than the scalar <energy> comparison. The same group reported cross-shaped templates forming a <cube> and flower-shaped templates forming nearly spherical enclosures.<Capillary origami by Charlotte Py and others>[p.091104-1: triangle, cross and flower templates]{ref}
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