Oscillating bubble tensiometry: A method for measuring the surfactant adsorptive-desorptive kinetics and the surface dilatational viscosity

Abstract

Mobilities of surfactant laden interfaces are determined by both surfactant-mass-transfer kinetics and surface viscosities. In this paper, a theoretical framework for measuring these parameters by analyzing forced radial oscillations of a spherical pendant bubble about an equilibrium, quiescent base state is developed. Because of the Gibbs-Marangoni elasticity caused by hindered surfactant mass transfer, and the surface viscosities, oscillations in the gas phase pressure and bubble radius are out of phase. Using a linear analysis of the governing fluid mechanical and mass-transfer equations, the phase lag (θ) and the amplitude ratio of these two quantities (Λ) are derived. Three cases are considered for the surfactant mass transfer: a mixed-controlled model in which diffusion and sorption kinetics play a role, along with the limiting cases of diffusion-control and sorption-control, respectively. Both θ and Λ depend upon the bulk diffusivity, the equilibrium physicochemical constants, and two unknowns: the sorption kinetic constant and the surface dilatational viscosity. In this paper, by varying these unknowns, theoretical families of curves for both θ and Λ vs forcing frequency, ω′, are generated using values for the bulk diffusivity and the equilibrium physicochemical constants for decanol at aqueous-air interfaces from Lin et al. (Langmuir 7, 1055, 1991). These curves indicate the potential of the oscillating bubble as a measurement tool, i.e., that experiments in which θ and Λ are measured vs ω′ can be used to determine the adsorption-desorption kinetic constants and the surface dilatational viscosity and to differentiate them from each other. © 1994 by Academic Press, Inc.