Thermodynamics of imbibition in capillaries of double conical structures—hourglass, diamond, and sawtooth shaped capillaries

Spontaneous liquid–liquid imbibition in capillaries with irregular axial geometries is common in the petroleum industry. Monitoring the real-time dynamic contact angle (DCA) of the meniscus is crucial during such processes. In this work, we extend the Bell–Cameron–Lucas–Washburn (BCLW) equation by considering the axial shape of the capillaries, inertial force, and non-wetting fluid viscosity. We also develop a cascaded multi-component Shan–Chen lattice Boltzmann method (CLBM) with a modified mass-conservative curved boundary scheme to accurately simulate imbibition processes in sinusoidal capillaries. The results indicate that the DCA is highly sensitive to variations in the axial geometry of the capillary during imbibition, displaying a periodic time evolution pattern. When the axial geometry diverges, the DCA increases, and when it converges, the DCA decreases. The viscosity ratio affects the imbibition velocity, controlling the evolution period and extreme values of the DCA. A critical contact angle exists for a fixed capillary axial geometry and viscosity ratio. Continuous spontaneous imbibition occurs if the static contact angle is smaller than this critical value. However, if it exceeds this threshold, imbibition ceases within regions where axial geometry divergence. Moreover, we noticed a discrepancy in imbibition lengths predicted by the extended BCLW equation that ignores the DCA compared to those computed through the CLBM. To address this issue, we employed CLBM to monitor the DCA in real time and used the gathered data to refine the extended BCLW equation. As a result, the prediction of imbibition lengths by the extended BCLW equation for coupling the DCA became more accurate.

Investigation on spontaneous liquid–liquid imbibition in capillaries with varying axial geometries using lattice Boltzmann method

Zhang,

Li,

Chen

et al. 2023

Physics-informed neural network for solving Young–Laplace equation and identifying parameters

Pan,

Feng,

Tao

et al. 2024

Capillarity is prevalent in nature, daily life, and industrial processes, governed by the fundamental Young–Laplace equation. Solving this equation not only deepens our understanding of natural phenomena but also yields insight into industrial advancements. To tackle the challenges posed by traditional numerical methods in parameter identification and complex boundary condition handling, the Young–Laplace physics-informed neural network (Y–L PINN) is established to solve the Young–Laplace equation within tubular domain. The computations on the classical capillary rise scenario confirm the accuracy of the proposed method on the basis of the comparison with Jurin's law, experimental data, and numerical results. Furthermore, the Y–L PINN method excels in parameter identification, e.g., contact angle, Bond number, and so on. These numerical examples even demonstrate its excellent predictive ability from the noisy data. For the complex boundary, it is rather convenient to obtain the liquid meniscus shapes in vessels, which is in good agreement with the experimental results. We further examine the variation of meniscus profile with wetting condition or discontinuous boundary. Importantly, the Y–L PINN method could directly solve the Young–Laplace equation with discontinuous wetting boundary without additional techniques. This work provides valuable insight for material wettability assessments, microstructure preparation, and microfluidics research.

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip

Iwamatsu

2024

The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen–Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, the capillary imbibition and the time evolution of meniscus in tubes with non-uniform cross sections such as a conical tube, a power-law-shaped diverging tube, and a power-law-shaped converging tube are reconsidered. The perturbation parameters and the corrections due to the non-slowly-varying effects are elucidated, and the new scaling formulas for the time evolution of the meniscus of these specific examples are derived. Our study could be useful for understanding various natural fluidic systems and for designing functional fluidic devices such as a diode and a switch.