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Abstract Capillary flow is the spontaneous wicking of liquids in narrow spaces without the assistance of external forces. Examples of capillary flow can be found in numerous applications ranging from controlling and transporting fuel in spacecrafts to printed electronics manufacturing. Open rectangular microchannels often appear in these applications, with the lack of a top resulting in a complex free-surface morphology and evaporation. Here, we present a brief overview of this topic and discuss some recent advances. 

Capillary flow of liquids plays a key role in many applications including lab-on-a-chip devices, heat pipes and printed electronics manufacturing. Open rectangular microchannels often appear in these applications, with the lack of a top resulting in a complex free-surface morphology and evaporation. In this work we develop a theoretical model based on lubrication theory and kinetically limited evaporation to examine capillary flow of evaporating liquid solutions in open rectangular microchannels connected to circular reservoirs. The model accounts for the complex free-surface morphology, solvent evaporation, Marangoni flows due to gradients in solute concentration and temperature and finite-size reservoir effects. Significant differences are predicted in flow behaviour between pure liquids and liquid solutions due to solvent evaporation and solute transport. Marangoni flows are found to promote more uniform solute deposition patterns after solvent evaporation. Model predictions of meniscus position evolution are in good agreement with prior capillary-flow experiments of aqueous poly(vinyl alcohol) solutions in the presence of evaporation. The model reveals that the principal mechanism through which evaporation influences the meniscus position in the experiments is the increase in viscosity with solute concentration. 

Spontaneous capillary flow of liquids in narrow spaces plays a key role in a plethora of applications including lab-on-a-chip devices, heat pipes, propellant management devices in spacecrafts and flexible printed electronics manufacturing. In this work we use a combination of theory and experiment to examine capillary-flow dynamics in open rectangular microchannels, which are often found in these applications. Scanning electron microscopy and profilometry are used to highlight the complexity of the free-surface morphology. We develop a self-similar lubrication-theory-based model accounting for this complexity and compare model predictions to those from the widely used modified Lucas–Washburn model, as well as experimental observations over a wide range of channel aspect ratios $$\lambda$$ and equilibrium contact angles $$\theta _0$$ . We demonstrate that for large $$\lambda$$ the two model predictions are indistinguishable, whereas for smaller $$\lambda$$ the lubrication-theory-based model agrees better with experiments. The lubrication-theory-based model is also shown to have better agreement with experiments at smaller $$\theta _0$$ , although as $$\theta _0\rightarrow {\rm \pi}/4$$ it fails to account for important axial curvature contributions to the free surface and the agreement worsens. Finally, we show that the lubrication-theory-based model also quantitatively predicts the dynamics of fingers that extend ahead of the meniscus. These findings elucidate the limitations of the modified Lucas–Washburn model and demonstrate the importance of accounting for the effects of complex free-surface morphology on capillary-flow dynamics in open rectangular microchannels.