Interfacial slip in entrained soap films containing associating hydrosoluble polymer

Frankel's law predicts that the thickness of a Newtonian soap film entrained at small capillary number scales as Ca-2/3 provided the bounding surfaces are rigid. Previous studies have shown that soap films containing low concentrations of high molecular weight (M-w) polymer can exhibit strong deviations from this scaling at low Ca, especially for associating surfactant-polymer solutions. We report results of extensive measurements by laser interferometry of the entrained film thickness versus Ca for the associating pair SDS/PEO over a large range in polymer molecular weight. Comparison of our experimental results to predictions of hydrodynamic models based on viscoelastic behavior shows poor agreement. Modification of the Frankel derivation by an interfacial slip condition yields much improved agreement. These experiments also show that the slip length increases as M-w(,)zeta where zeta= 0.58 +/- 0.07. This correlation is suggestive of the Tolstoi-Larsen prediction that the slip length increases in proportion to the characteristic size of the fluid constituent despite its original derivation for liquid-solid interfaces.