In nanoscaled solids, the mathematical behavior of a curved interface between two different phases with interface stress effects can be described by the generalized Young-Laplace equations [T. Young, Philos. Trans. R. Soc. London 95, 65 (1805); P. S. Laplace, Traite de Mechanique Celeste (Gauthier-Villars, Paris, 1805), Vol. 4, Supplements au Livre X]. Here we present a geometric illustration to prove the equations. By considering a small element of the curved thin interface, we model the interface stresses as in-plane stresses acting along its edges, while on the top and bottom faces of the interface the tractions are contributed from its three-dimensional bulk neighborhood. With this schematic illustration, simple force balance considerations will give the Young-Laplace equations across the interface. Similar procedures can be applied to conduction phenomena. This will allow us to reconstruct one type of imperfect interfaces, referred to as highly conducting interfaces.
All Science Journal Classification (ASJC) codes
- 物理與天文學 (全部)