Give it a boost -- The shape of a travling long bubble during the transition between two steady states

When a confined long bubble translates steadily in a cylindrical capillary, with negligible gravity effects, a uniform thin film of fluid separates the bubble surface and the tube wall. Although a wide variety of investigations have been carried out analyzing the relationship between the film thickness profile and the bubble velocity, most of the literature considers the case where the translational velocity is a constant, thus the bubble profile is steady. Instead, in this work, we investigate how this steady state is established by considering the transitional motion of the bubble as it adjusts its film thickness profile between two steady states, characterized by two different bubble speeds. Different sections of the time-dependent film profile will be characterized, and we will further discuss how the "travel history" of the bubble is stored in the bubble shape. The theoretical results are further verified both by experiments and numerical simulations. The results can potentially be applied to a tunable in-situ particle separation process.