Entrainment and drainage behavior of thin soap films containing associating hydrosoluble polymer

Frankel's Law predicts that the thickness of an entrained soap film withdrawn vertically from bulk solution at small Capillary number Ca scales as Ca 2/3, for a Newtonian fluid, in the lubrication regime, and subject to a boundary condition that the film interfaces move at the same velocity as the film frame. Previous studies have shown that soap films containing low concentrations of high molecular weight (Mw) polymer can exhibit strong deviations from this scaling at low Ca, especially for surfactant-polymer solutions that undergo complexation. An extensive study of soap film entrainment and subsequent film drainage for aqueous solutions of sodium dodecyl sulfate/poly(ethylene oxide) (SDS/PEO), measured by laser interferometry, is reported, with 10-6 ≲ Ca ≲ 10-2.;For film entrainment, poor agreement is found when comparison is made between experimentally-measured film thicknesses and hydrodynamic models which incorporate non-Newtonian effects and viscoelastic behavior. Good agreement is found with a model which allows the film interfaces a different velocity than the entrainment speed. This simple parameterization employs a Navier slip boundary condition at the air/liquid interface. The slip length is found to scale as Mw3/5, which is consistent with a correlation based on polymer chain size for freely-jointed chains in dilute solution subject to excluded volume effects, suggested by the Tolstoi-Larson prediction. The slip length is also found to have a dependence on polymer concentration. Experiments with SDS and poly(vinyl pyrrolidone) that show similar results are also reported, with similar fitting parameters. This parameterization may represent the effects of Marangoni stresses in inducing a downward flux.;Experiments on pure aqueous SDS films and the PEO/SDS system indicate that pure film drainage (after entrainment has stopped) proceeds through 2-3 distinct regimes, with film thickness initially following an exponential relationship in time. This behavior is followed by 1-2 regions in which thickness appears to follow a power-law relationship in time, but these regions last for less than one decade in time, preventing definitive fits. Simulations of soap film drainage (with and without slip) show qualitative agreement with power-law drainage, generally increasing with slip length, but quantitative agreement remains elusive.