= Elasto-capillarity
{wiki}
= Elastocapillarity
{synonym}
\b[Elastocapillarity] is the coupling between <surface tension> and elastic deformation. Changing an interface can reduce <surface energy> while bending a compliant solid increases <bending energy>. Thin structures can deform strongly when the available capillary energy competes with their elastic resistance.
For an isotropic thin <elastic plate>, its <bending stiffness> is
$$
B=\frac{Eh^3}{12(1-\nu^2)},
$$
where $E$ is <Young's modulus>, $h$ the thickness and $\nu$ <Poisson's ratio>. A sheet bent over a size $L$ has curvature of order $1/L$. Its bending energy scales as $B(1/L^2)L^2\sim B$, while the capillary energy scale is $\gamma L^2$, where $\gamma$ is <surface tension>. Balancing these scales gives the <elastocapillary length>
$$
\boxed{\ell_{\rm ec}=\sqrt{\frac{B}{\gamma}}.}
$$
Here $B$ has units of energy and $\gamma$ energy per area, so the ratio has units of length squared. At fixed material properties, $\ell_{\rm ec}\propto h^{3/2}$; doubling thickness multiplies this length by $2\sqrt2$. Geometry and <contact angle> enter the more detailed wrapping criterion.<Capillary Origami: Spontaneous Wrapping of a Droplet with an Elastic Sheet by Charlotte Py and others>[Equation1 and surrounding thin-plate energy balance]{ref}
The 2007 <capillary origami> experiments of <Charlotte Py> and collaborators provide a direct demonstration. They cut <polydimethylsiloxane> membranes, 40–80 <micrometres> thick, into planar shapes, placed them on a water-repellent support, added a <water> droplet and recorded the deformation during evaporation. Suitable triangular sheets folded around the shrinking drop into a tetrahedral enclosure. Smaller or stiffer sheets failed to close completely. The observations connected a controlled material thickness and initial shape to the competition between <surface energy> and <bending energy>.<Capillary Origami: Spontaneous Wrapping of a Droplet with an Elastic Sheet by Charlotte Py and others>[pp.156103-1–156103-2; Figure1: apparatus, evaporation sequence and shape-dependent wrapping]{ref}
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