Sensitive parameter dependence of the self-similar dynamics in the bubble breakup in a confined geometry

Abstract: Formation of a fluid drop, such as observed in dripping faucet, has been extensively studied for understanding singular dynamics widely observed in nature. The singular dynamics is often self-similar, i.e., the shape at different times are collapsed onto a master curve after rescaling. Here, we investigate the bubble breakup in an original setup, where a metal disk entrains air into viscous fluid with lubricating films on its surfaces in a confined cell, focusing on the dependence of the dynamics on the film thickness e. As a result, we find out the dynamics is self-similar as expected, but the shape of the master curve and the scaling exponents characterizing the self-similar dynamics are revealed to be sensitively dependent on e. We discuss analogy between the present study and critical phenomena in thermodynamic transitions, to suggest a promising future direction of the singular dynamics.