A capillary flow model for discretely graded porous media in two phase heat transfer applications

The ability to predict imbibition in porous media is important for our understanding of engineered systems such as heat pipes and vapour chambers. If the microstructure of the porous media, or wick, changes along its length, it can be termed a graded wick. Such graded wicks have been shown to exhibit enhanced performance in many engineered systems. However, accurate prediction models for imbibition within graded wicks are not fully developed but are essential for optimising designs to maximise potential enhancements. This deficit is addressed herein by developing a new analytical model for imbibition prediction in discretely graded porous media. Benchmark rate-of-rise experiments are first conducted in homogenous sintered copper particulate wicks using particle sizes of 40 µm, 70 µm, 100 µm and ≥ 250 µm. Two-layer graded particulate wicks of varying length ratios are also manufactured and tested in configurations with large particles followed by smaller particles and vice versa. Results obtained are used to validate the proposed model, and to quantify attainable enhancement/control of imbibition rates. The findings show very good agreement between measured and predicted data, with standard error ≤10%. Results are also validated in the context of previously published experimental data for homogeneous wicks. Findings for graded wicks show that imbibition rates are maximised when wicks are designed to have larger, 100− 250 µm, particles in permanently wetted sections of the wick and smaller, 70− 100 µm, particles in sections where the liquid/air interface is expected to reside. The relative length of graded wick layers is also shown to strongly influence obtainable enhancements over homogenous wicks. Imbibition rates were enhanced by ~21% for 78:22 length ratio graded wicks, and >175% for 95:5 length ratio graded wicks. Alternatively, imbibition can be controlled by tailoring the sizes of particles used in different sections of the wick. This is useful for applications requiring maximized flow control, such as gravity opposing heat pipes or vapor chambers. Overall, the findings of this study help with understanding imbibition in graded wick structures and provide a validated prediction model that aids the design of improved graded wicks for engineered applications.