Slopes of films and drops on substrates with disjoining pressure.

摘要

Ultra thin films and drops, with thicknesses of less than 100 nm, are ubiquitous in biomedical and electronic devices, as well as throughout nature. In this work, models governing the behavior of an ultra thin drop or a film are derived for a couple of systems in which the effects of the intermolecular forces included. The first is a case of a drop placed on a two substrate composite. We account for all of the interfacial and surface energies, and then take the variational derivative to find the equations governing the equilibrium shape. The intermolecular forces are calculated explicitly leading to an expression for the disjoining pressure. We also derive a model for the case of a film that completely wets the substrate. The equations governing the film thickness are integrated revealing a liquid layer which has a jump due to the effect of the intermolecular forces which are different for different composite substrate materials.;We produce a model for the film evolution using the Navier-Stokes equations, along with the appropriate liquid/gas interface conditions, for the normal and the tangential components of the shear stress. Using lubrication theory, an evolution equation for the thin layer is derived, which, if solved, could allow for a dynamic analysis of the liquid/gas interface.;Finally, the case of a solid/liquid/gas system is examined in which there are no geometrical restrictions established at the interfaces, such as rigidity, i.e. all interfaces can deform either due to stresses (liquid/gas interface) or to phase transition (solid/gas and solid/liquid interfaces). No rest is placed on the movement of the triple junction. In this case, there are eight independent equations derived, one for each of the four interfaces and two at each junction.