Abstract
The K-BKZ constitutive model is now 50 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experiment, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction a historical perspective is given on developments in the last 50 years of the K-BKZ model. Then a section follows on mathematical modeling of polymer flows, including governing equations of flow, rheological constitutive equations (with emphasis on viscoelastic integral constitutive equations of the K-BKZ type), dimensionless numbers, and boundary conditions. The Method of Solution section reviews the major developments of techniques necessary for particle tracking and calculation of the integrals for the viscoelastic stresses in flow problems. Finally, selected examples are given of successful application of the K-BKZ model in polymer flows relevant to rheology.
Highlights
The following constitutes in the simplest possible terms a guide along that pathway that led from the original ideas to the current use of the model and its variants in engineering applications
The present paper reviewed the 50 years since the appearance of the K-BKZ model in the rheological community around 1962
This review followed and borrowed from Tanner’s article [9], which had reviewed the relevant publications for the 25th anniversary of the model in 1988
Summary
Rheology is defined as the “study of deformation and flow of matter” [1, 2]. In our days the term “rheology” was first used in 1920 by the American chemistry professor Eugene Bingham in Lafayette College, Indiana, USA. Bingham consulted with colleagues in the Department of Classical Studies in his effort to explain the peculiar behavior of various colloidal solutions [4]. The term “rheology” and its above definition were accepted by the (American) Society of Rheology (SOR), founded in 1929 with its first president being Prof. Many other national rheological societies have since come to being, with the European Society of Rheology (ESR) established in 1996 and encompassing many individual European societies. The various rheology societies celebrate every four years the advancements in rheology at the International Congress on Rheology. The last one took place in Lisbon, Portugal, in August 2012 [5]
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