Approximations in the measurement of surface tension on the oscillating bubble surfactometer

This paper examines two factors, shape deformation and surface viscosity, that affect measurements of surface tension of lung surfactants with the oscillating bubble surfactometer. At lower surface tensions, the compressed bubble in this apparatus becomes deformed to an oblate ellipsoid that cannot be analyzed rigorously using the simplified (spherical) Laplace equation to calculate surface tension from interfacial pressure drop. However, for the small air bubbles present in this apparatus, analysis with more general equations for ellipsoids of revolution shows that deformation effects are limited to extremely low surface tensions, and the absolute error from the spherical approximation is minimal in practice. In contrast, this was not the case for the effects of surface dilational viscosity in oscillating bubble calculations. Direct measurements and values from the literature indicated that the surface dilational viscosities of lung surfactant, dipalmitoyl phosphatidylcholine, and palmitic acid were sufficient to give substantial errors if their effects on interfacial pressure drop were neglected during dynamic cycling. Surface tension calculations at maximum and minimum radii on the oscillating bubble apparatus remain accurate, because the time derivative of radius becomes zero and viscous effects vanish. However, surface tensions determined at points other than these extremes of bubble size should be interpreted with caution.