The finite-difference/front-tracking method is used to study the motion and deformation of a large bubble moving through a capillary tube in the presence of both insoluble and soluble surfactants. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. The film thickness is first computed for the clean bubble case and the results are compared with the lubrication theory in the limit of small capillary numbers, i.e., Ca ≪ 1, and found to be in good agreement with the predictions of Bretherton [1]. Thereafter, the method is used to investigate the effects of insoluble and soluble surfactants on the film thickness for a wide range of governing non-dimensional numbers. It is found that both the insoluble and soluble surfactants have a thickening effect on the liquid film, which compares well with both the experimental results of Krechetnikov and Homsy [2] and analytical predictions of Daripa and Pasa [3].
Measurement of thin liquid film drainage using a novel high-speed impedance analyzer
