The transition between steady states: A time-dependent Bretherton bubble

When a confined 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. During the transition, two uniform film regimes coexist, separated by a step-like transitional region. The transitional motion also requires modification of the film solution near the rear of the bubble, which depends on the ratio of the two capillary numbers. These theoretical results are further verified by experiments and numerical simulations.