Modelling of fractional relaxation characteristics in wormlike micelles in the presence of a triblock copolymer

ABSTRACT

Fractional calculus has become an important tool in the analysis of slow relaxation phenomena, such as stress-strain relationships in polymeric materials. The interaction of trilblock copolymer [Pluronics f68] with cetyltrimethylammonium bromide [CTAB]-sodium nitrate [NaNO3] wormlike micellar system in low and high salt concentration is investigated by rheological measurements. Undoped wormlike micellar solution is a viscoelastic fluid which exhibits Maxwellian behavior. Since the rheology of solutions still Maxwellian, a fractional Maxell model is applied to describe any changes. A fractional derivatives of order q and The Maxwell model consists of a spring and dashpot in series. The fractional Maxwell model relating stress to strain is used to fit several experimental results on wormlike micelles in the presence of copolymer. The comparisons between the experimental results and the theoretical predictions are found to be satisfactory