Experimental study of entrainment and drainage flows in microscale soap films

The thickness of freely suspended surfactant films during vertical withdrawal and drainage is investigated using laser reflectivity. The withdrawal process conducted at capillary numbers below 10(-3) generates initial film thicknesses in the micrometer range; subsequent thinning is predominantly impelled by capillary and not gravitational forces. Under these conditions, our results show that film thinning above and below the critical micelle concentration (cmc) is well approximated by a power law function in time whose exponents, which range from -0.9 to -1.8, are inconsistent with current descriptions of capillary-viscous drainage in inextensible films which predict exponents close to -0.5. Correlations between the experimental fitting parameters illustrate important differences in film behavior across the cmc. In addition, normalization of the drainage data yields a collapse to a single functional form over 3 decades in time for a wide range of initial withdrawal rates. We demonstrate that modification of the interface boundary condition in current models to account for Marangoni stresses through an effective slip parameter yields values of the exponents and other key parameters in excellent agreement with experiment. This modification also successfully describes the withdrawal thickness below the cmc.