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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.
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This content will become publicly available on August 30, 2026
Complex Dependence of Calcite Crack Kinetics on Salinity: The Role of DLVO and Hydration Forces
Abstract Subcritical crack growth (SCG) plays an important role in many geological processes such as delayed earth rupture and rock weathering. The complex dependency of SCG on the in‐crack fluid chemistry, however, is still poorly understood. In this study, we utilize the newly developed surface force‐based fracture theory (SFFT) to elucidate the relative contributions of surface forces and solute transport to the crack growth kinetics of calcite in NaCl solutions. Expanding on Barenblatt's cohesive crack model, SFFT introduces an effective stress intensity at the crack tip that encompasses all the relevant intermolecular forces across the crack in addition to the external far‐field stresses. The nonlinear system of equations portraying the crack opening profile, the solute distribution in a propagating crack, and the crack growth velocity are numerically solved via an implicit scheme. After carefully calibrating the model for calcite‐water systems, the SFFT is used to predict the SCG response of calcite at different NaCl concentrations, based on various hypotheses. These predictions are then compared to existing SCG data from the literature. We demonstrate that the experimentally observed variation of SCG rate with NaCl concentration cannot be explained solely by DLVO forces (electrostatic and Van der Waals interactions). This can be remediated by introducing an exponentially decaying hydration force with a nonlinear, nonmonotonic dependence on NaCl concentration. Furthermore, we demonstrate that accounting for both diffusive and advective transport of ions is important in explaining the absence of a stage‐II SCG response for calcite in electrolyte solutions.
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- Award ID(s):
- 2237332
- PAR ID:
- 10648442
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Solid Earth
- Volume:
- 130
- Issue:
- 9
- ISSN:
- 2169-9313
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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