Surface heterogeneity: dynamics of contact-line motion within a straight capillary tube*

The process of one fluid displacing another immiscible fluid within small confined spaces is vital in numerous natural processes such as water infiltration into soil and groundwater flow. Modelling the dynamics of the contact line, where the two fluids and a solid interface meet, is crucial for the direct numerical simulation (DNS) of multi-phase flow in these confined spaces. In this study, we present a numerical investigation of two-phase flow within a straight capillary tube, focusing on the dynamics dictated by the contact-line motion. This motion, combined with viscous and Rayleigh-Plateau instabilities, leads to a bubble pinch-off phenomenon. We focus on a critical yet often overlooked aspect of such systems: the impact of surface heterogeneity on the flow dynamics, driven by contact-line motion and quantified by the capillary number. Our results propose, for the first time, a mechanism that explains how surface heterogeneity affects the stability and behaviour of the contact line, ultimately influencing the formation and dynamics of bubbles in a straight capillary tube. By incorporating the effects of surface heterogeneity, we demonstrate that variations in contact-line dynamics can significantly alter the flow regime and the onset of instabilities. Our findings highlight the importance of accurate contact-line modelling and of accounting for surface heterogeneity in the simulation of two-phase flow within confined micro-scale spaces.