Fig. 2: Equilibrium state.
From: Elastocapillary sequential fluid capture in hummingbird-inspired grooved sheets
a Snapshot of the final equilibrium shape of the ribbed structure for various sheet thicknesses e with the same groove geometry: h = 810 ± 40 μm, w = 400 ± 40 μm, d = 700 ± 50 μm. A transition to closure is observed for sufficiently thin sheets. Scale bar: 5 mm. b Schematics of the flexible groove model: the capillary rise ℓI in the groove induces a capillary torque acting on the bottom flexible sheet of length L (in red) via the walls considered as rigid, inducing a radius of curvature R = d/(2β). c The equilibrium closing angle corresponds to the intersection between the curves f(β) and Kβ (defined in Eq. 4). Below a critical value K = Kc no solutions are possible and the structure close completely forming a tube (green area). d Final equilibrium elevations \({\ell }_{I}^{\infty }\) and \({\ell }_{II}^{\infty }\) as a function of the dimensionless transition parameter Λ defined by Eq. (5) for devices with the same groove geometry (given in a) but with varying length L and thickness e. For both capillary rises, a sharp transition occurs at Λ ~ 1. Uncertainties are estimated using the theory of error propagation. e Total captured volume \({{{\mathcal{V}}}}\) as a function of the dimensionless transition parameter Λ and of the sheet thicknesses e. Experiments corresponding to the five structures shown in (a) (black dots) are compared to the theoretical prediction (blue line). Structure closing is associated to a fast increase of the captured volume. Uncertainties are estimated using the theory of error propagation. Source data are provided as a Source Data file.
