A drop on a floating sheet: boundary conditions, topography and formation of wrinkles

Abstract

The radial wrinkle pattern generated by a liquid drop on a floating elastic sheet has stimulated a number of advances in the understanding of wrinkle patterns in ultrathin sheets. A puzzle associated with the spatial extent of this simple, highly symmetric pattern has only recently been resolved, but several other basic aspects of the pattern remain unexplained. Our previous experiments have studied the extent and wavenumber of the pattern via 2-dimensional images. In the current study we report a full 3-dimensional topographical characterization of this archetypical problem, and of its counterpart, a bubble beneath a sheet. In addition to measurements of the wrinkle amplitude, these studies reveal the elastic deformation and the resulting wrinkle pattern beneath the drop. We also show that the flat boundary condition at the contact line of the drop is achieved by a cascade of wrinkles on both sides of the boundary. Finally, we report studies by high-speed video imaging of the propagation of the wrinkle pattern, with the unexpected result that the wavenumber is established early in the development of the pattern, before it has reached its full spatial extent.

Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases

“…1c). However, for concreteness and clarity we focus on the classical Lamé set-up, whose numerous variants were studied extensively, allowing us to exploit a host of experimental [20][21][22], numerical [23], and analytic techniques [23,24]. A schematic of the model is shown in Fig.…”

“…Our experimental system consists of a liquid drop placed at the center of a large, ultrathin floating sheet (see main text). While this "drop on sheet" problem has been a subject of intensive studies in recent years [20,21,26], the aspect that is most relevant for the current paper is the wrinkle pattern observed in the exterior of the sheet-drop contact line, namely, where the sheet is flat except azimuthal undulations (i.e dθζ(r, θ) ≈ 0). As was shown in previous studies [26,35] this part of the sheet can be thought of as a Lamé set-up, where the tension γ out = γ lv is given by the liquid-vapor surface tension that pulls on the sheet's edge and γ in ∝ γ 2/3 lv Y 1/3 is induced by the capillary tension of the drop that pulls the sheet inward at the contact line.…”

Capillary Deformations of Bendable Films

“…The measurement of the wrinkle length is described in [17]. (c) The measured profile beneath the drop, obtained by confocal microscopy [14] and the predicted profile (blue).…”

“…The radius R o = 23 mm, and the Young modulus is E = 3.4 GPa. The distinct values of liquid surface tensions (γ = γ) are obtained by adding surfactants to the liquid bath [14]. We define R(V, ϑ Y ) to be the radius of the contact line on an undeformed sheet:…”

Radial wrinkles on film–substrate system induced by local prestretch: A theoretical analysis

“…Wang et al (2014) found that each spiral wrinkle has the shape of an Archimedean spiral curve. Besides, an elastic sheet floating on a fluid may buckle due to the capillary force at the solid-liquid contact line, referred to as elastocapillary buckling (Huang et al, 2007;Liu and Feng, 2012;King et al, 2012;Toga et al, 2013;Vella et al, 2010).…”