Stokes flow, reynolds flow, molecular flow: restrictions on modeling thin films

摘要

Under ordinary conditions fluids are modeled as continua and the Navier-Stokes equation and the equation of continuity can be employed to study their motion. However, to find solutions to these equations is far from elementary, and in applications we look for ways to simplify them. Such simplification is made particularly easy for thin films. We make use of thin film geometry to derive the Reynolds theory of lubrication. The Reynolds equation is employed extensively in various technical fields; it breaks down, however, when there are sudden changes in film thickness or when the film is too thin for the continuum model to apply.