A perturbation method for solving the micro-region heat transfer problem

A perturbation method is proposed and used to model the two-dimensional equations governing evaporation in the micro-region of a meniscus on a heated substrate. The novelty of the method lies in the choice of the physical quantities which are used to describe the hydrodynamic and heat transfer phenomena. The chosen quantities are the pressure jump function across the liquid-vapor interface and a modified-shape function. The problem is thus transformed into a set of decoupled initial-value sub-problems that can be solved recursively from lower to higher orders. This approach represents many advantages compared with existing theories. The model is then applied, accounting for the effect of gravity, to describe the micro-region shape and heat transfer. The results obtained following this approach are then validated against those given in literature. The comparison demonstrated the validity of the developed model as well as its wider range of applicability. The influence of the interaction between liquid, vapor, and the solid substrates (mainly through the dispersion constant) as well as gravity on heat transfer and meniscus shape is also discussed. In particular, it is found that although gravity affects the shape of the micro-region and the apparent contact angle, it has no significant effect on the magnitude and distribution of the evaporation flux. (C) 2011 American Institute of Physics. [doi:10.1063/1.3643265]