Neukirch S, Antkowiak A, Marigo J-J
CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France and UPMC Université Paris 06, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France.
CNRS, Ecole Polytechnique, UMR 7649, Laboratoire de Mécanique des Solides, F-91128 Palaiseau Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012401. doi: 10.1103/PhysRevE.89.012401. Epub 2014 Jan 2.
We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition to the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet, we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfies the classical Young-Dupré relation.
我们研究了在弯曲和拉伸效应均存在的情况下弹性梁与液滴的相互作用。我们采用变分方法推导梁的平衡方程和本构关系。结果表明，该关系除了经典的杨氏模量项外，还包括一项由表面能引起的项，从而导致胡克定律的修正。在固、液、气三相交汇的三相点处，我们发现作用在梁上的外力与液 - 气界面平行。此外，在固 - 气和固 - 液界面能不依赖于梁的伸长状态的情况下，我们表明梁在三相点处的伸长是连续的，并且润湿角满足经典的杨氏 - 杜普雷关系。
