Analysis of the Properties of a Nonlinear Shear Flow Model of Thixotropic Media Taking into Account the Mutual Influence of Structural Evolution and Deformationстатья
Статья опубликована в журнале из списка Web of Science и/или Scopus
Аннотация:A systematic analytical study was conducted on the mathematical properties of a previously proposed prototype of a nonlinear Maxwell-type constitutive equation for describing the shear flow of thixotropic substances (viscous liquid polymers, viscoelastic melts, concentrated solutions, pastes, emulsions), which takes into account the mutual influence of deformation and structural evolution (the kinetics of intermolecular bond formation and breaking) on viscosity and shear modulus and the effect of deformation on this kinetics. In the uniaxial case, the constitutive equation is governed by a nondecreasing material function and six positive parameters. The equation is reduced to a system of two nonlinear autonomous differential equations for the stress and the crosslinking degree. It is proved that the equilibrium point of this system is unique. The dependences of the point coordinates on all material parameters and on the shear rate for an arbitrary nondecreasing material function are investigated in general form, and all the dependences are proved to be monotonic. Equations for the flow and viscosity curves are derived and investigated
