The creeping flow of a polymeric melt in a converging pipe is analyzed using an in-house finite element code. An introduced power-law model considers the shear thinning behavior of the viscous liquid. Furthermore, distributive and dispersive mixing processes are evaluated with the mean strain function and the Manas-Zloczower mixing index, respectively. Using a parametric study, the dependency of the mixing criteria on the Theological and geometrical factors is investigated. Finally, a new analytical expression for the evaluation of the distributive mixing is suggested, based on simplifying assumptions and a curve fitting method.