The modified Jeffreys model approach for elasto-viscoplastic thixotropic substances

•A new constitutive model, composed by a constitutive and a rate equations, for thixotropic fluids is proposed.•The constitutive equation takes into account the micro-structural dependence of the shear modulus and viscosity coefficients.•The rate equation is based on Brownian motion (coagulation theory of Smoluchowski) and reptation model.•The thermodynamic consistence of the proposed model is proved too.

In this work, a new constitutive model for thixotropic fluids is proposed via a formal analysis of their functional forms. The constitutive model for thixotropic substances is basically composed by a set of two equations: a constitutive equation based on viscoelastic models and a rate equation (an equation related to the evolution of the micro-structural character of the substance). The constitutive equations, in many works, do not have taken into account in the dynamical principles from which is developed the micro-structural dependence of shear modulus and viscosity. To aim this fault, in the current study a new constitutive model (based on Jeffreys model) is proposed, in coherence with expected behavior for thixotropic fluids. In addition a special emphasis has been given to the structural nature of substances (based on coagulation theory of Smoluchowski) and thermodynamic consistency. The proposed model for thixotropic fluids takes into account a simple isothermal laminar shear flows and some important aspects of that are explored.