A new constitutive equation for elastoviscoplastic fluid flows

Abstract

International audienceFrom a thermodynamic theory, a new model for elastoviscoplastic fluid flow is presented. It extends the Bingham viscoplastic model and the Oldroyd viscoelastic model. Fundamental flows are studied: simple shear flow, uniaxial elongation and large amplitude oscillatory shear. The complex moduli (G',G'') are founded to be in qualitative agreement with experimental data for materials that present microscopic network structures and large scale rearrangements. Various fluids of practical interest, such as liquid foams, droplet emulsions or blood, present such elastoviscoplastic behavior: at low stress, the material behaves as a viscoelastic solid, whereas at stresses above a yield stress, the material behaves as a fluid

“Everything flows?”: elastic effects on startup flows of yield-stress fluids

“…We have not addressed the likely failure of the OldroydPrager formalism following yielding, but there is convincing evidence that a viscoelastic fluid description is necessary for materials like the Carbopol studied here. Indeed, Fraggedakis et al (2016) have employed both kinematic hardening and a viscoelastic model by Saramito (2007) to describe the kinematics and settling dynamics of a spherical particle through a Carbopol gel.…”

Two-dimensional constriction flows of foams

“…In the future, we can further validate simulations by comparing fields such as pressure and plasticity (T1s) in simulations and experiments; this would be a benchmark to test tensorial continuum models [5,7] and their predictions of the flow, as in [8]. …”

“…A recurrent question is whether the foam can be described as a continuous material. This would mean that its behaviour could be understood and described by a smaller number of variables and of equations [5,6,7,8], for example with fields such as velocity and stress. In this respect simulations are a crucial step to link the discrete to the continuous behaviour and the predictions of theory to experiment.…”

Issues in the flow of yield-stress liquids

“…This behavior is inconsistent with Oldroyd's notion of a linearly elastic solid prior to yielding (Eq. 5b), but it is suggestive of linearly viscoelastic behavior, as mentioned by White (1979) and discussed by Saramito (2007). Suppose we presume, for example, that the rheology of the unyielded material is described by a Kelvin-Voigt solid, for which the shear stress satisfies τ = Gγ + ηγ , where γ is the shear strain.…”