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1. Capillary-flow dynamics in open rectangular microchannels

   https://doi.org/10.1017/jfm.2020.986  

   Kolliopoulos, Panayiotis; Jochem, Krystopher S.; Johnson, Daniel; Suszynski, Wieslaw J.; Francis, Lorraine F.; Kumar, Satish (March 2021, Journal of Fluid Mechanics)

   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. 

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2. Capillary flow of liquids in open microchannels: overview and recent advances

   https://doi.org/10.1038/s41526-021-00180-6  

   Kolliopoulos, Panayiotis; Kumar, Satish (December 2021, npj Microgravity)

   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 controlling and transporting fuel in spacecrafts to 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. Here, we present a brief overview of this topic and discuss some recent advances. 

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3. Instability and symmetry breaking in binary evaporating thin films over a solid spherical dome

   https://doi.org/10.1017/jfm.2021.136  

   Shi, Xingyi; Rodríguez-Hakim, Mariana; Shaqfeh, Eric S.G.; Fuller, Gerald G. (May 2021, Journal of Fluid Mechanics)

   null (Ed.)

   We examine the axisymmetric and non-axisymmetric flows of thin fluid films over a spherical glass dome. A thin film is formed by raising a submerged dome through a silicone oil mixture composed of a volatile, low surface tension species (1 cSt, solvent) and a non-volatile species at a higher surface tension (5 cSt, initial solute volume fraction $$\phi _0$$ ). Evaporation of the 1 cSt silicone oil establishes a concentration gradient and, thus, a surface tension gradient that drives a Marangoni flow that leads to the formation of an initially axisymmetric mound. Experimentally, when $$\phi _0 \leqslant 0.3\,\%$$ , the mound grows axisymmetrically for long times (Rodríguez-Hakim et al. , Phys. Rev. Fluids , vol. 4, 2019, pp. 1–22), whereas when $$\phi _0 \geqslant 0.35\,\%$$ , the mound discharges in a preferred direction, thereby breaking symmetry. Using lubrication theory and numerical solutions, we demonstrate that, under the right conditions, external disturbances can cause an imbalance between the Marangoni flow and the capillary flow, leading to symmetry breaking. In both experiments and simulations, we observe that (i) the apparent, most amplified disturbance has an azimuthal wavenumber of unity, and (ii) an enhanced Marangoni driving force (larger $$\phi _0$$ ) leads to an earlier onset of the instability. The linear stability analysis shows that capillarity and diffusion stabilize the system, while Marangoni driving forces contribute to the growth in the disturbances. 

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4. Marangoni-induced reversal of meniscus-climbing microdroplets

   https://doi.org/10.1039/D2SM00979J  

   Sun, Jianxing; Weisensee, Patricia B. (January 2023, Soft Matter)

   Small water droplets or particles located at an oil meniscus typically climb the meniscus due to unbalanced capillary forces. Here, we introduce a size-dependent reversal of this meniscus-climbing behavior, where upon cooling of the underlying substrate, droplets of different sizes concurrently ascend and descend the meniscus. We show that microscopic Marangoni convection cells within the oil meniscus are responsible for this phenomenon. While dynamics of relatively larger water microdroplets are still dominated by unbalanced capillary forces and hence ascend the meniscus, smaller droplets are carried by the surface flow and consequently descend the meniscus. We further demonstrate that the magnitude and direction of the convection cells depend on the meniscus geometry and the substrate temperature and introduce a modified Marangoni number that well predicts their strength. Our findings provide a new approach to manipulating droplets on a liquid meniscus that could have applications in material self-assembly, biological sensing and testing, or phase change heat transfer. 

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5. Assessment of the free shear boundary condition in a capillary meniscus via molecular dynamics

   https://doi.org/10.1063/5.0238573  

   Shuvo, Abdul Aziz; Gonzalez-Valle, C Ulises; Yang, Xiang; Ramos-Alvarado, Bladimir (November 2024, Physics of Fluids)

   Computational fluid dynamics models often employ the free shear boundary condition at free surfaces, a result from the continuity of the stress and the large viscosity contrast at liquid–gas interfaces. This study leverages nonequilibrium molecular dynamics simulations to investigate the validity of the free shear boundary condition on the exposed surface of a liquid meniscus at the nanoscale. The primary objective is elucidating the fundamental mechanisms and behavior of fluid interactions within a capillary meniscus formed between two carbon nanotubes (CNTs) in shear-driven flow. Shear-driven flow simulations were conducted by varying the velocity of a solid slab to induce different shear rates in the adjacent water molecules. The results demonstrate, for the first time, negligible shear at the free surface, supporting the free shear assumption from the nanoscale point of view. A force balance analysis reveals that capillary and surface tension forces dominate within the meniscus, dictating its shape and stability. Meniscus deformation was observed and primarily attributed to interatomic interactions between water molecules and CNTs, driven by a combination of short-range repulsive forces and van der Waals attractions. The minimal contribution from shear forces suggests that interatomic forces, rather than applied shear stress, are the primary drivers of the meniscus deformation. These findings offer valuable insights into fluid behavior and a sound fundamental analysis of the free shear boundary condition at the nanoscale. 

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