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arXiv 2201.10925cond-mat.soft
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外张力对弹性薄板润湿的影响

Effect of external tension on the wetting of an elastic sheet

Gregory Kozyreff, Benny Davidovitch, S. Ganga Prasath, Guillaume Palumbo, Fabian Brau

摘要:

最近对弹性毛细现象的研究引发了人们对经典Young-Laplace-Dupré(YLD)问题的一个基本变体的兴趣:液滴和低弯曲刚度的薄固体片之间的毛细相互作用。在这里,我们考虑一个二维模型,其中的片材受到外部拉伸载荷和下降的特点是由一个定义良好的杨氏接触角$θ_Y$。使用数值,变分和渐近技术相结合,我们讨论润湿作为施加的张力的函数。我们发现,对于具有$0<θ_Y<π/2$的润湿表面,完全润湿在低于临界施加张力下是可能的,这要归功于与需要$θ_Y=0$的刚性基底相比片材的变形。相反,对于非常大的施加张力,片材变得平坦,并且恢复了部分润湿的经典YLD情况。在中间的紧张局势,囊泡的形式在片材中,其中包括大部分的流体,我们提供了一个准确的渐近描述这种润湿状态的限制小的弯曲刚度。我们表明,弯曲刚度,但小,影响囊泡的整个形状。发现了包含部分润湿和“囊泡”溶液的丰富的分叉图。对于中等小的弯曲刚度,部分润湿可以与囊泡溶液和完全润湿共存。最后,我们确定了张力依赖的弯曲毛细管长度,$λ_\text{BC}$,并发现液滴的形状是由比例$A/λ_\text{BC}^2$,其中$A$是下降的面积。

英文摘要:

Recent studies of elasto-capillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: The capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here, we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle $θ_Y$. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with $0<θ_Y<π/2$, complete wetting is possible below a critical applied tension thanks to the deformation of the sheet in contrast with rigid substrates requiring $θ_Y=0$. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and ``vesicle'' solution are found. For moderately small bending stiffnesses, partial wetting can coexist both with the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendo-capillary length, $λ_\text{BC}$, and find that the shape of the drop is determined by the ratio $A/λ_\text{BC}^2$, where $A$ is the area of the drop.

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