Beyond the Cassie-Baxter Model: New Insights for Predicting Imbibition in Complex Systems

TL;DR

This paper develops a new analytical framework for predicting liquid imbibition in complex heterogeneous systems, revealing the importance of wettability distribution and proposing a novel averaging method for contact angles.

Contribution

It introduces a weighted harmonic averaging approach for contact angles and analyzes imbibition dynamics beyond classical models in heterogeneous systems.

Findings

Optimal wettability arrangement depends on spatial distribution.

Classical Cassie-Baxter contact angle fails for dynamic flow prediction.

Weighted harmonic averaging accurately predicts imbibition times.

Abstract

We revisit the classical problem of liquid imbibition in a single pore 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 two 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.