Capillary-flow dynamics in open rectangular microchannels

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) -> 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.

Automated summary

This study examines the capillary-flow dynamics in open rectangular microchannels using a combination of theory and experiment. The lubrication-theory-based model shows better agreement with experiments at smaller channel aspect ratios and equilibrium contact angles, highlighting the limitations of the modified Lucas-Washburn model. The model also quantitatively predicts the dynamics of fingers that extend ahead of the meniscus.