Brownian motion in a single relaxation time maxwell fluid

A simple model of Brownian motion in a single relaxation time Maxwell fluid is described and compared to diffusing wave spectroscopy measurements of colloidal motion in representative viscoelastic fluids, namely, CTAB/KBr wormlike micelle solutions. The experimentally measured Brownian motion conforms to the model predictions at long times (low frequencies) and is an additional confirmation of the essentially Maxwellian stress relaxation behavior of wormlike micelle solutions at low frequencies. Surprisingly, the Maxwell model predicts a plateau onset time which, while capable of reducing the measured mean-square displacements to a master curve, also grossly underestimates the actual plateau onset time. The predicted rescaling is shown to be essentially that also predicted by the Doi-Edwards tube model for polymer solutions under good solvent (excluded volume) conditions where a more proper accounting of the short-time dynamics is made. This indicates that the success of the predicted Maxwell model plateau onset time rescaling is purely fortuitous.