Beyond the Cassie–Baxter model: New insights for predicting imbibition in complex systems

We revisit the classical problem of liquid imbibition in a single tube with spatially varying wettability. Starting from the Lucas–Washburn equation, we derive analytical solutions for the imbibition time (crossing time) in systems where wettability alternates between different materials. For ordered arrangements, we demonstrate that the imbibition speed depends non-trivially on the spatial distribution, with the ”more hydrophobic-first” configuration being optimal. For disordered systems, where segment lengths follow a Gaussian distribution, we show that the classical Cassie–Baxter contact angle, originally derived for static wetting, fails to predict the dynamics of capillary-driven flow. To address this, we propose a new weighted harmonic averaging method for the contact angle, which accurately describes the viscous crossing time in such heterogeneous systems. Our findings reveal fundamental insights into the role of wettability heterogeneity in capillary-driven flow, offering a basis for understanding imbibition dynamics in complex heterogeneous systems. The research data and the software supporting this study are openly available at DOI:10.5281/zenodo.14537452 . • Imbibition speed depends strongly on the wettability arrangement. • “Hydrophobic-first” order yields the fastest capillary imbibition. • Cassie–Baxter contact angle fails for dynamic heterogeneous imbibition. • A new harmonic contact angle model predicts the crossing time. • The Python code for all simulations is openly available.