Self-similar pinch-off in surfactant-laden flows in a capillary tube

We study the pinch-off dynamics of a fluid surrounded by a significantly more viscous one during fluid–fluid displacement in straight, cylindrical capillary tubes, where the interface evolves under the influence of a moving contact line. We investigate the influence of insoluble surfactants on the dynamics of both the contact line and pinch-off. We focus on a visco-capillary displacement regime where the imposed flow rate exceeds a critical threshold, beyond which the contact-line velocity is governed by the partial wettability of the confined geometry, becoming independent of the flow rate. Under these conditions, the fluid–fluid meniscus forms an advancing axial finger, leaving behind a thin film of the defending fluid. This unstable film retracts along the partially wetting walls, forming a dewetting rim that grows with the steady contact-line motion. Eventually, a surface-tension-driven Rayleigh–Plateau instability dominates, triggering pinch-off at the rim neck. For a surfactant-free interface, our results show that the early-stage evolution of the neck diameter follows a power law $\tau ^\alpha$ , where $\tau$ is the time to the pinch-off singularity and the scaling exponent $\alpha$ depends on the contact-line velocity determined by the wettability. Over the range resolved in the present simulations, $\alpha$ decreases from values near $1/2$ at large contact-line velocity towards values close to $1/5$ as the contact-line velocity is reduced. We demonstrate that, in the presence of insoluble surfactants, the contact-line velocity, at a given wettability, scales linearly with surfactant elasticity due to Marangoni stresses along the dewetting rim interface, which affect the timing and location of the pinch-off. Despite these effects, at the early-time regime, the pinch-off dynamics exhibits the same self-similar scaling behaviour as in the surfactant-free case.