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Asymmetric microstructures are of particular interest to many technical fields. Such structures can produce anisotropic flow-fields, which, for example, can be used to control heat and mass transport processes. Anisotropic wicking structures can now be systematically engineered with unique micro-pillar geometries and spatial pillar-placement distributions. Such asymmetric wicking structure designs are of particular interest to the thermal management community due to need to cool heterogeneous materials with specific heat load configurations. In this study, asymmetric half-conical micropillars have been fabricated utilizing two-photon polymerization. Macroscopic characterization of anisotropic flow-field velocities is performed via high-speed videography. High-speed thin-film interferometry and microscopic side-angle videography are also used to characterize the microscale evolution of meniscus curvature during inter-pillar wicking. The wicking velocity is observed to be directly proportional to both the meniscus curvature and the cross-sectional area of the micro-pillars (normal to the flow). An anisotropic hemiwicking model is also described with comparisons to experimental data. The hemiwicking model predicts the macroscopic wicking behavior (within 20% or less) for the relatively broad range of pillar geometries and pillar spacing configurations. These anisotropic flow-field predictions can help engineers design the next-generation of micro-structured heat sinks, fluid-based sensors and chemical harvesting systems. 

Abstract Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$ $\left({10}^{-7}\lesssim \mathrm{Re}\lesssim {10}^{-3}\right)$. Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$ $\mathrm{Re}=\frac{v_0{x}_0}{\nu }$, wherev₀corresponds to the maximum wetting speed on a flat, dry surface andx₀is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv₀andx₀measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left(v_0\approx 2m/s,25\mu m\lesssim x_0\lesssim 28\mu m\right)$, viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left(v_0\approx 0.3m/s,18.6\mu m\lesssim x_0\lesssim 38.6\mu m\right)$and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left(v_0\approx 1.2m/s,11.8\mu m\lesssim x_0\lesssim 33.3\mu m\right)$.