While we are all familiar with surface tension in liquids and the variety of phenomena it influences, its role or even its existence has been moot for solids. For conventional stiff solids, by which we mean materials with Young’s modulus greater than a few mega-Pascal, surface tension or, more appropriately, surface stress is weak in the sense that its influence is negligible except at length scales smaller than a few nanometers. This length scale over which such “solid capillarity” matters is given by an elastocapillary length: the ratio of characteristic surface stress and elastic modulus. That is, surface stress exerts an important and sometimes dominant influence on the deformation of compliant solids – those with Young’s modulus less than a few mega-Pascal – at continuum length scales. The influence of surface stress can thus strongly alter the mechanics of phenomena that involve deformation of a surface. This talk will discuss three such phenomena:
(a) Flattening of an undulating surface due to surface stress
We show that a hydrogel replica of a periodically patterned surface deforms into one that has significantly attenuated amplitude. Reduction in amplitude can be modeled as elastic deformation driven by surface stress.
(b) Role of surface stress in wetting problems
A liquid drop placed on a compliant substrate causes it to deform and, in general, invalidates Young’s equation for contact angles. Now, equilibrium shapes must satisfy conditions of both configurational and force equilibrium. In particular, we study the deformation of elastomeric film due to a water droplet. For sufficiently thin films, the equilibrium shape of the bulge is governed by balance of surface tensions, Neumann’s triangle, which is different from Young's equation.
(c) Effect of surface stress on contact mechanics
For sufficiently compliant materials or small indenters, the Johnson-Kendall-Roberts theory of adhesive contact is no longer valid as stress in the surface becomes the dominant agent resisting deformation. We discuss experiments and theory of indentation in the presence of surface stress, particularly the special case of indentation of a clamped film, in which surface stress plays an important role for relatively stiff materials.
Anand Jagota is Professor of Chemical and Biomolecular Engineering and Director of Bioengineering at Lehigh University. His training is all in Mechanical Engineering: PhD in 1988 from Cornell University and B.Tech. in 1983 from the Indian Institute of Technology, Delhi. Jagota worked at the DuPont Company from 1988 – 2004 except for a two-year teaching stint at the Indian Institute of Technology, Delhi from 1994-1996. He has been at Lehigh University since 2004. His interests are in interfacial mechanical properties ranging from the molecular to the continuum scale. This includes an interest in adhesion, friction, contact problems, fracture, and the role of surface stress.