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arXiv 1607.01637cond-mat.soft
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静止液滴引起的弹性基底的变形

Deformation of an Elastic Substrate Due to a Resting Sessile Droplet

Aaron Bardall, Karen E. Daniels, Michael Shearer

摘要:

在非常软的基板上,静止的流体液滴将导致基板的显著变形。这种变形是由接触线处的毛细力和固体表面处的流体压力的组合驱动的。这些力在表面处由基底变形引起的固体牵引应力平衡。预测液滴的平衡接触角的杨氏定律也表明刚性基底的先验径向力平衡,但不一定是在负载下变形的软基底。它仍然是一个悬而未决的问题,是否接触线传递一个非零的径向力的基板表面,除了传统的垂直力。我们提出了一种分析傅里叶变换解决方案的技术,包括一般的界面能条件,管理的接触角的二维液滴。这包括评估重力对液滴形状的影响,以便确定用于较大液滴的基板表面处的正确流体压力。重要的是,我们发现,为了避免在接触线下的非零径向接触线力的应变奇异性,它是必要的,包括一个以前忽略的径向牵引边界条件。为了量化的接触线的影响,并确定关键的数量,将实验访问测试模型,我们评估的解决方案的基板表面位移场的泊松比和零/非零的径向接触线力的函数。

英文摘要:

On a sufficiently-soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates which deform under loading. It remains an open question whether the contact line transmits a non-zero radial force to the substrate surface in addition to the conventional vertical force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a nonzero radial contact line force, it is necessary to include a previously-neglected radial traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally-accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero radial contact line forces.

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