The effective radius of Lucas–Washburn dynamics in periodically constricted tubes

Abstract

Capillary imbibition in periodically constricted tubes (PCTs) plays a critical role in multiple natural and technological processes, where the control of autonomous flows is intrinsically linked to the geometric architecture of the imbibition space. Here we present analytical expressions for the effective radius (\(r_{eff}\)) of PCTs with different wave shapes and analyze how geometric parameters influence the infiltration dynamics. Our analysis reveals that \(r_{eff}\) is strongly dependent on the ratio of maximum to minimum radii (\(\alpha\)) and, for stepped geometries, on the relative segment length proportion (\(\gamma\)). Increasing \(\alpha\) enhances \(r_{eff}\) up to a critical value, beyond which a strong reduction is observed: for \(\alpha >>\) 2, approximately, the infiltration velocity progressively decreases. This counterintuitive behavior arises from the interplay between hydrodynamic resistance and capillary driving forces. We evaluated the effect on different geometries, achieving different \(r_{eff}\) that can be analytically predicted by closed-form expressions. The model was also validated against previously reported experimental data. These findings underline the potential of geometric design to optimize capillary-driven flows, providing a framework for tailoring PCTs to specific applications in microfluidics, porous media, and related fields.