Physics Department, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium.
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E. 2023 Mar;107(3-2):035101. doi: 10.1103/PhysRevE.107.035101.
Recent studies of elastocapillary 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 due 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 with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λ_{BC}, and find that the shape of the drop is determined by the ratio A/λ_{BC}^{2}, where A is the area of the drop.
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：即液体滴与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，其中薄片受到外部拉伸载荷，液滴具有明确定义的杨氏接触角θ_{Y}。我们使用数值、变分和渐近技术的组合，讨论了作为施加张力函数的润湿情况。我们发现，对于可润湿的表面，0<θ_{Y}<π/2，由于薄片的变形，在临界施加张力以下可以实现完全润湿，而对于刚性基底，则需要θ_{Y}=0。相反，对于非常大的施加张力，薄片会变平，并恢复经典的 YLD 部分润湿情况。在中间张力下，薄片中会形成一个囊泡，它包围了大部分流体，我们提供了一个在小弯曲刚度极限下这种润湿状态的精确渐近描述。我们表明，弯曲刚度即使很小，也会影响囊泡的整个形状。我们发现了涉及部分润湿和“囊泡”解的丰富分岔图。对于适度小的弯曲刚度，部分润湿可以与囊泡解和完全润湿共存。最后，我们确定了一个与张力有关的弯毛细长度 λ_{BC}，并发现液滴的形状由 A/λ_{BC}^{2}的比值决定，其中 A 是液滴的面积。
