We study the effect of branching on the extensional rheology of series of sodium oleate (Na0A) and octyl trimethyl ammonium bromide (C8TAB) linear and branched wormlike micelle solutions using a filament stretching extensional rheometer and capillary breakup extensional rheometer. The ratio of NaoA to C8TAB is fixed at 70/30 while the surfactant concentration is varied. The shear rheology measurements showed a maximum in shear viscosity at 4 wt% followed by a sharp decrease in viscosity with increasing total surfactant concentration. It has been shown in cryo-TEM imaging that the maximum in shear viscosity for these fluids corresponds to the transition from linear entangled to branched micelles. The extensional rheology measurements for all of the wormlike solutions demonstrated some degree of strain hardening below 4 wt%, however, beyond 4 wt% little strain hardening is observed. The maximum value of Trouton ratio is found to decrease very rapidly with increasing micelle concentration, starting from values of nearly Tr1000 at a concentration of 2 wt% and approaching an asymptote close to Newtonian limit of Tr3 for concentrations of 4 wt% and above. These results are most likely due to the additional stress relief mechanisms available to branched micelles which appear to be extremely efficient in extensional flows. These stress relief mechanisms include the fast and fluid sliding of branch points along the length of the micelle and the increased occurrence of `ghost-like' crossing of micelles at entanglement points with increasing surfactant concentration.
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