60 years of the Kaye–Bernstein, Kearsley, Zapas rheological constitutive law for polymers

The K–BKZ (Kaye–Bernstein, Kearsley, Zapas) rheological constitutive model is now 60 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experimental evidence in polymer melt flow, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction, an historical perspective is given on developments in the last 60 years of the K–BKZ model. Then, a section on mathematical modeling of polymer flows follows, including the governing equations of flow, the rheological constitutive equations (with emphasis on the viscoelastic integral constitutive equations of the K–BKZ type), dimensionless numbers controlling the flow, and relevant boundary conditions. The “Method of Solution” section reviews the major developments of numerical techniques for particle tracking and integral evaluation for the viscoelastic stresses. Finally, selected examples of successful application of the K–BKZ model in polymer flows are presented including considerations of wall slip and non-isothermal flows.