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 and equilibrium contact angles. We demonstrate that for large the two model predictions are indistinguishable, whereas for smaller 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, although as 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.
Bibliographical noteFunding Information:
The authors thank D. Frisbie for helpful discussions. Portions of this work were conducted at the Minnesota Nano Center, which is supported by the NSF through the National Nano Coordinated Infrastructure Network under Award ECCS-1542202.
This work was supported by the National Science Foundation (NSF) under grant no. CMMI-1634263. K.S.J. acknowledges support from the NSF Graduate Research Fellowship Program under grant no. 00039202.
© The Author(s), 2021. Published by Cambridge University Press
- Key words capillary flows
- lubrication theory