Capillary Flow and Evaporation in Open Microchannels

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 lab-on-a-chip devices to printed electronics manufacturing. Open rectangular microchannels often appear in these applications, with the lack of top resulting in a complex free-surface morphology and evaporation. While prior work has demonstrated that evaporation hinders capillary flow, the underlying fundamentals that are vital to the design and optimization of applications such as printed electronics manufacturing are still lacking. In this thesis we investigate the fundamentals of capillary flow and evaporation in open microchannels using theory and experiment. We initially consider flow of nonvolatile liquids to elucidate the capillary-flow dynamics. We develop a novel self-similar lubrication-theory-based (LTB) model accounting for the complex free-surface morphology and compare model predictions to those from the widely used modified Lucas-Washburn (MLW) model, as well as experimental observations over a wide range of channel aspect ratios and equilibrium contact angles. We identify the limitations of the MLW and LTB models and demonstrate the importance of accounting for the effects of the complex free-surface morphology on capillary flow. We also show that the LTB model accurately captures the dynamics of fingers that extend ahead of the front meniscus which are not accounted for by the MLW model. Capillary flow of evaporating liquid solutions are examined using two theoretical models. We first develop a Lucas-Washburn-type one-dimensional (1D) model, which accounts for concentration-dependent viscosity and uniform evaporation. The second model is a lubrication-theory-based model, which accounts for the complex free-surface morphology, non-uniform solvent evaporation, Marangoni flows due to gradients in solute concentration and temperature, and finite-size reservoir effects. Both models are compared to prior capillary-flow experiments of aqueous poly(vinyl alcohol) solutions in the presence of evaporation. While the 1D model qualitatively captures evaporation effects on the flow dynamics, it underestimates their magnitude. The lubrication-theory-based model predictions are in good agreement with experimental observations, and predicted evaporation rates are comparable with experimental estimates. Numerical results also reveal significant qualitative differences in capillary flow of evaporating pure solvents and liquid solutions. Additionally, Marangoni flows are found to promote more uniform solute deposition patterns after solvent evaporation. Ultimately, these findings advance the fundamental physical understanding of capillary flow with evaporation and provide guidelines for the design and optimization of numerous applications.