Oscillations of bubbles attached to a capillary: case of pure liquid

Abstract

An oscillating bubble attached to a tip of a capillary is used for probing interfacial properties of liquids containing surface-active agents. Nevertheless, available theories even for the case of pure liquid are not satisfactory. In this contribution, we therefore present results of a linear inviscid theory for shape oscillations of a spherical bubble, which is in contact with a solid support. The theory allows determining eigenmodes (i.e. eigenfrequencies, eigenmode shapes and damping of eigenmode oscillations), but also response of the bubble shape to a motion of its support or to volume variations. Present theory covers also the cases previously analyzed by Strani and Sabetta (J. Fluid Mech., 1984) and Bostwick and Steen (Phys. Fluids, 2009), and it can be applied to both bubbles and drops. The theory has been compared to experiments. Good agreement is found for the case of small bubbles, which have spherical static shape. Experimental results for larger bubbles and drops deviate from the theory, if a neck is formed. It is shown that this deviation correlates well with a ratio of bubble volume to the maximum volume, when a detachment occurs.