ABSTRACT
The gravity-driven instability of a thin liquid film located underneath a soft solid material is considered. The equations and boundary conditions governing the solid deformation are systematically converted from a Lagrangian representation to an Eulerian representation, which is the natural framework for describing the liquid motion. This systematic conversion reveals that the continuity-of-velocity boundary condition at the liquid-solid interface is more complicated than has previously been assumed, even in the small-strain limit. We then make clear the conditions under which the commonly used simplified version of this boundary condition is valid. The small-strain approximation, lubrication theory, and linear stability analysis are applied to derive an expression for the growth rate of small-amplitude perturbations. Asymptotic analysis reveals that the coupling between the liquid and solid manifests itself as a lower effective liquid-air interfacial tension that leads to larger instability growth rates. Although this suggests that it is more difficult to maintain a stable liquid coating underneath a soft solid, the effect is expected to be weak for cases of practical interest.
ABSTRACT
Short-term leasing is an everyday occurrence. Tax savings cannot account for the ubiquity of leasing by temporary users. Monopoly explanations are inconsistent with concurrent leasing and selling markets for perfect substitutes. Leasing economizes upon the costs of detecting, assuring, and maintaining quality, costs of search, and costs of risk-bearing. This view is based on standard economic reasoning and has numerous specific implications.
