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.