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Description
Surface tension driven flows in microchannels underpin numerous microfluidic technologies, including biomedical diagnostics, chemical processing and lab on a chip systems. High-fidelity computational fluid dynamics (CFD) simulations provide detailed predictions of the transient evolution of the liquid–gas interface and associated flow field, but their computational cost limits large-scale parametric studies and optimisation. This work presents a physics-based reduced-order model (ROM) for transient capillary filling, validated against CFD simulations.
High-fidelity CFD simulations are performed within the OpenFOAM and Basilisk frameworks using Eulerian–Eulerian and VoF formulations, respectively, to resolve transient capillary filling in rectangular microchannels. In parallel, a ROM is developed by coupling a nonlinear boundary-value problem based on general lubrication theory with Navier-slip regularisation to a Lucas–Washburn type ordinary differential equation governing liquid-column evolution. The resulting coupled BVP–ODE algorithm reconstructs the transient meniscus shape and curvature while simultaneously advancing the filling dynamics.
The ROM accurately reproduces the transient evolution of the meniscus shape, apparent contact angle and overall filling dynamics. Equivalent simulations are completed in approximately two minutes compared with several days for CFD, enabling rapid parametric studies while retaining good agreement with detailed interface dynamics.