Effects of a surfactant monolayer on the measurement of equilibrium interfacial tension of a drop in extensional flow.

The effect of surfactant monolayer concentration on the measurement of interfacial surface tension using transient drop deformation methods is studied using the Boundary Integral Method. Emulsion droplets with a surfactant monolayer modeled with the Langmuir equation of state initially in equilibrium are suddenly subjected to axisymmetric extensional flows until a steady state deformation is reached. The external flow is then removed and the retraction of the drops to a spherical equilibrium shape in a quiescent state is simulated. The transient response of the drop to the imposed flow is analyzed to obtain a characteristic response time, tau(s)( *). Neglecting the initial and final stages, the retraction process can be closely approximated by an exponential decay with a characteristic time, tau(r)( *). The strength of the external flow on each model drop is increased in order to investigate the coupled effect of deformation and surfactant distribution on the characteristic relaxation time. Different model drops are considered by varying the internal viscosity and the equilibrium surfactant concentrations from a surfactant free state (clean) to high concentrations approaching the maximum packing limit. The characteristic times obtained from the simulated drop dynamics both in extension and retraction are used to determine an apparent surface tension employing linear theory. In extension the apparent surface tension under predicts the prescribed equilibrium surface tension. The error increases monotonically with the equilibrium surfactant concentration and diverges as the maximum packing limit is approached. In retraction the apparent surface tension under predicts the prescribed equilibrium surface tension depends non-monotonically on the equilibrium surfactant concentration. The error is highest for moderate surfactant concentrations and decreases as the maximum packing limit is approached. It was found that the difference between the prescribed surface tension and the apparent surface tension increased as the viscosity ratio decreased. Differences as large as 40% were seen between the prescribed surface tension and the apparent surface tension predicted by the linear theory.