Elastocapillary lifting and encapsulation of water by a triangular elastic film under gravity

Abstract

We investigate the encapsulation of water by a thin elastic film as a minimal model of elastocapillary self-folding with fluid transport. An equilateral triangular polydimethylsiloxane film is lifted quasi-statically from a water surface, while its side length and thickness are systematically varied. Depending on these parameters, the film exhibits three distinct morphologies: folding, recoiling, and liquid encapsulation. We show that the observed morphology is selected by the competition between surface energy, gravitational energy of the liquid, and bending energy of the film. In particular, encapsulation occurs in a narrow parameter region corresponding to the intersection of the elastocapillary, elastogravity, and capillary length scales. This result provides a simple physical criterion for liquid encapsulation by elastic films, based on the balance of bending, capillary, and gravitational energies.

Figures (4)

• Figure 1: (a) Geometry of the PDMS film. The film thickness $h$ and side length $w$ were systematically varied. (b) Schematics of experimental setup. The PDMS film was lifted vertically from the water surface by a wire attached at its center. (c) Representative snapshots showing three distinct deformation modes of the film: folding (F; $h$ = 98 µm, $w$ = 20 mm), recoiling (R; $h$ = 132.25 µm, $w$ = 12.5 mm), and capsulating (C; $h$ = 98 µm, $w$ = 10 mm). The time $t=0$ corresponds to the onset of lifting. Scale bar: 10 mm.
• Figure 2: (a) Phase diagram of the deformation modes of the lifted film as a function of film thickness $h$ and side length $w$. Green squares, orange triangles and blue circles represent folding, recoiling, and capsulating modes, respectively [see Fig. \ref{['fig:experimentalsystem']}(c)]. The deformation modes were classified based on the final configuration of the film observed during the lifting process. The dashed line indicates the parameter set used in panel (c). All experimental data points are plotted in the phase diagram. (b) Weight of water, $mg$, lifted by the film as a function of film thickness $h$, measured for a fixed side length $w$ = 10 m m.
• Figure 3: Characteristic deformation modes of the elastic film, classified as (a) Mode I, (b) Mode II, and (c) Mode III. The dashed lines indicate regions of large mean curvature. Bottom images show the corresponding regions of high mean curvature in the experimental snapshots shown in Fig. \ref{['fig:experimentalsystem']}(c).
• Figure 4: The characteristic length of the system, elastogravity, $L_{eg}$ (black solid line), elastocapillary, $L_{ec}$ (red dash-dotted line), and capillary length $L_{cg}$ (green dotted line). Each line is drawn based on Eq. \ref{['Eq:characteristic_length']}.