Capillary-flow dynamics in open rectangular microchannels

• Published in: Journal of fluid mechanics 2021-01, Vol.911, Article A32
• Main Authors: Kolliopoulos, Panayiotis, Jochem, Krystopher S., Johnson, Daniel, Suszynski, Wieslaw J., Francis, Lorraine F., Kumar, Satish
• Format: Article
• Language: English
• Subjects: Adhesives; Aspect ratio; Capillary flow; Complexity; Contact angle; Dynamics; Electron microscopy; Experiments; Fluid mechanics; Free surfaces; Geometry; Heat pipes; JFM Papers; Lab-on-a-chip; Liquids; Lubrication; Microchannels; Morphology; Propellant management; Scanning electron microscopy; Self-similarity; Silicon wafers; Theories; Viscosity
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.986

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.