刚性基底上多孔弹性液滴中的干燥诱导应力
Drying-induced stresses in poroelastic drops on rigid substrates
摘要：
我们发展了一个理论干燥引起的应力在固着，多孔弹性滴经历蒸发刚性表面。使用润滑近似，三维非线性孔隙弹性的控制方程减少到一个单一的薄膜方程的下降厚度。我们发现，薄滴经历压缩弹性应力，但总的面内应力是拉伸。液滴的机械响应由固体骨架的初始轮廓决定，该初始轮廓控制面内变形、弹性应力的主要分量，并对可能发生的分层深度设定限制。我们的理论表明，胶滴中的干燥裂缝的排列是由胶凝点处的液滴形状选择的。我们提出，在干血滴中出现三种不同的断裂模式是凝胶化时非单调液滴轮廓的结果。我们还表明，耗尽前，分离湿和干固体，可以侵入从接触线和局部化的机械应力的产生在干燥过程中的下降。最后，用有限元法研究了大接触角液滴的应力分布。
英文摘要：
We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a non-monotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localise the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.
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