Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

Abstract

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.