Porous micropillar structures for retaining low surface tension liquids

The ability to manipulate fluid interfaces, e.g., to retain liquid behind or within porous structures, can be beneficial in multiple applications, including microfluidics, biochemical analysis, and the thermal management of electronic systems. While there are a variety of strategies for controlling the disposition of liquid water via capillarity, such as the use of chemically modified porous adhesive structures and capillary stop valves or surface geometric features, methods that work well for low surface tension liquids are far more difficult to implement. This study demonstrates the microfabrication of a silicon membrane that can retain exceptionally low surface tension fluorinated liquids against a significant pressure difference across the membrane via an array of porous micropillar structures. The membrane uses capillary forces along the triple phase contact line to maintain stable liquid menisci that yield positive working Laplace pressures. The micropillars have inner diameters and thicknesses of 1.5-3 μm and ∼1 μm, respectively, sustaining Laplace pressures up to 39 kPa for water and 9 kPa for Fluorinert™ (FC-40). A theoretical model for predicting the change in pressure as the liquid advances along the porous micropillar structure is derived based on a free energy analysis of the liquid meniscus with capped spherical geometry. The theoretical prediction was found to overestimate the burst pressure compared with the experimental measurements. To elucidate this deviation, transient numerical simulations based on the Volume of Fluid (VOF) were performed to explore the liquid pressure and evolution of meniscus shape under different flow rates (i.e., Capillary numbers). The results from VOF simulations reveal strong dynamic effects where the anisotropic expansion of liquid along the outer micropillar edge leads to an irregular meniscus shape before the liquid spills along the micropillar edge. These findings suggest that the analytical prediction of burst Laplace pressure obtained under quasi-static condition (i.e., equilibrium thermodynamic analysis under low capillary number) is not applicable to highly dynamic flow conditions, where the liquid meniscus shape deformation by flow perturbation cannot be restored by surface tension force instantaneously. Therefore, the critical burst pressure is dependent on the liquid velocity and viscosity under dynamic flow conditions. A numerical simulation using Surface Evolver also predicts that surface defects along the outer micropillar edge can yield up to 50% lower Laplace pressures than those predicted with ideal feature geometries. The liquid retention strategy developed here can facilitate the routing and phase management of dielectric working fluids for application in heat exchangers. Further improvements in the retention performance can be realized by optimizing the fabrication process to reduce surface defects.