RHEOLOGICAL MATERIAL FUNCTIONS FOR ASSOCIATING COMB-SHAPED OR H-SHAPED POLYMERS - A FRACTIONAL CALCULUS APPROACH

A rheological constitutive equation for associating comb-shaped or H-shaped polymer solutions is derived, which shows a unique power-law zone characterized by two time parameters and one power-law exponent in the terminal relaxation region. The constitutive equation is of fractional integral or fractional differential type and contains two additional parameters. A comparison with experimental data demonstrates very good agreement with the theoretical predictions. The material functions in the frequency domain represent a generalization of the well known Cole-Cole behaviour.