Effects of dynamic surface tension and fluid flow on the oscillations of a supported bubble

Abstract

Oscillating bubble techniques are commonly used to infer dynamic surface tension (DST) from the measurement of the dynamic pressure difference across an interface. In inferring DSTs from such measurements, the hydrodynamic effects are assumed to be negligible, so that the surface tension is uniform and the static Young-Laplace (Y-L) equation is valid. To examine these assumptions, the Navier-Stokes and continuity equations governing the flow of a liquid outside an axisymmetric bubble supported by a narrow tube are solved simultaneously by a finite element method with the equations governing surfactant transport and adsorption. Surface densities of adsorbed surfactant monolayers are examined to find the limits for accurate DST measurements. At low pulsation or oscillation rates (compared to the reciprocal of capillary time scale) and moderate area amplitudes, surface densities on the interface are found to be uniform, and DST measurements from pressure differences are quite accurate unless low surface tensions are attained. At high frequencies, however, because of strong convection around the surface of the bubble, the surface density along the liquid–gas interface becomes non-uniform while the bubble shape becomes highly deformed. The latter findings have analogs in the closely related problem of oscillating supported drops and can have profound ramifications for popular techniques for measuring DSTs.