New constitutive equation for simple yield stress fluids (SYSF) and ElastoViscoPlastic fluids (EVP)

This article describes a new rheological model that considers the structural changes of Simple Yield Stress Fluid (SYSF). These fluids exhibit an elastic behavior below a threshold stress and non-Newtonian viscous behavior governed by a model similar to the generalized Casson model proposed by Benhadid et al. [1] above the yield stress. This model represents the complex rheological behavior of SYSFs across the whole shear rate range while taking into account the structural changes found in this type of fluid. This approach is based on the development of a generic model that will encompass most classical models as particular cases by describing the complete flow curve of viscoplastic (VP) materials with an extension to ElastoViscoPlastic fluids (EVP). Thus, the apparent viscosity determined from the proposed model describes a smooth flow curve without discontinuities, where the yield stress is clearly expressed with a maximum Newtonian viscosity (viscosity at zero shear rate \(\eta_{0}\)), which approaches a Newtonian viscosity \(\eta_{\infty }\) at high shear rates.

Graphical abstract