A modeling approach for capillary-driven flow of a wetting fluid in a rectangular open microchannel of arbitrary axisymmetric width profile: Application to heat pipes

With the continuous advancement of our technologies, they get smaller in size than ever before. They generate high-intensity heat loads that need to be transported effectively such that they may function properly. Heat pipes have proven to be very effective in transporting relatively large heat loads from miniature components. They are of seamless structure that involves a working fluid capable of evaporation and condensation at the working temperature of the electronic chips. The working fluid is derived to move from the condenser to the evaporator via multiple microgrooves using capillary forces. It is important that the condensate reaches the evaporator at a proper rate such that no dry-out or flooding occur. In this work, we are particularly interested in the case of capillary-driven flows in rectangular microchannels. A generalized model is developed that works for axesymmetric rectangular channels of arbitrary, moderately varying width profiles. It also accounts for any contrast of viscosity between the liquid and the vapor under isothermal conditions. The model shows to reduce to the special case of imbibition in straight and uniform microchannels, for which comparisons with experimental and modeling works show an excellent match. Cases representing linearly and quadratically varying converging/ diverging width profiles have been explored. It is found that the viscosity ratio has a significant influence on the rate at which the meniscus advances. The model also negates the common practice found in the literature of using the formula developed for imbibition rates in capillary tubes for rectangular microchannels by replacing the diameter of the tube with the hydraulic diameter. It is also found that the channel profile has an influential effect on the imbibition rates. For tapered microchannels, the capillary force increases along the channel length while it decreases for diverging ones. It is interestingly demonstrated that, for quadratically tapered microchannel, the speed of the meniscus increases towards the end of the microchannel compared with linearly varying microchannels. On the other hand, for diverging microchannels, the speed of the meniscus decreases due to the increase in the cross-sectional area. Computational fluid dynamics (CFD) analysis has been conducted to provide a framework for confirmation and verification for which very good match has been established, which builds confidence in the modeling approach.