(1)
The Spriggs model consists of an infinite number of Maxwell elements, each with the same value G for each mode, but with relaxation times related by the inverse power series (Equation 1). This is different to the generalized Maxwell with the strength of the modes G being adjusted for a fixed set of relaxation times when fitting to the experimental data.
(1)
In practice the series is truncated at n = 100 in the TA Instruments software. This gives
(2)
(3)
where
Actually the Spriggs model is a three parameter model, since the relaxation times are not independent and only one relaxation time, a modulus (or viscosity) value, and the a index are required.
The Spriggs model successfully describes experimental data for polymer solutions and because of its uniqueness in combining results from molecular theory with results from the theories associated with continuum mechanics. It was found that the model provides a good description of the rheological data for polymer melts and that some of the model parameters depend upon the molecular characteristics of the polymer. Since this model contains a small number of well defined constants, it is useful in developing dimensionless engineering correlations for the complex flows encountered in processes of industrial importance.
This model is not widely used today.
