The effect of surfactant on the tail dynamics of elongated bubbles*

Following the classical work by Bretherton and Taylor, the propagation of elongated gas bubbles in micro-channels has received a great deal of attention in the literature due to its relevance to a wide range of applications. Recent work by Magnini {\it et al}. Phys. Rev. Fluids, 023601 (2018) and Moran {\it et al.} (Bulletin of the American Physical Society, vol. 63, D09.00002) has also examined these flows (with concurrent liquid flow) with significant buoyancy and inertial effects in both vertical and horizontal configurations. The present work focuses on bubble tail undulations in the presence of surfactants whose effects merit attention. We carry out three-dimensional direct numerical simulations of the flow using a hybrid front-tracking/level-set method (Shin {\it et al.}, J. Comp. Phys., 359, 409-435, 2018) over a wide range of surfactant properties including diffusivity, elasticity, and solubility. The effect of these properties on the speed of bubble propagation and interfacial shape is examined, paying particular attention to the bubble tail dynamics at high Reynolds number.