A Boundary Value Model for an Evaporating Meniscus

The constrained vapor bubble (CVB) experiment is an experiment to study the effect of low Bond numbers on the microscopic and macroscopic transport in a heat pipe. The microscopic (∼30 μm) contact line region, where the solid, liquid and vapor phase meet, is of fundamental importance in this study of fluid flow and heat transfer. This region, while dominated by interfacial forces, is controlled by the boundary conditions set by physics at the macroscopic scale (∼1 mm) on one side and the microscopic scale (∼ 0.1 μm) on the other. Recent experimental investigation by our group has shown that an effective means of changing the microscopic boundary conditions (the wettability of the fluid) is by introducing surface roughness at the nanoscale to the solid surface. Here we attempt to examine some of the experimental results in the light of a model. The model solves a nonlinear, fourth order evolution equation for the film thickness. It also provides the contact angle, interface curvature and heat transfer profile in the contact line region. The model agrees well with the experimental data. The presence of hydrodynamic slip at the solid liquid interface seems to improve the agreement.