A mesoscopic rheological model of moderately concentrated colloids

Abstract

We extend the Maffettone-Minale model by including non-elliptical shapes of dispersed particles, a new family of internal forces controlling particle deformations, and particle-particle interactions. The last extension is made by transposing the way the chain-chain interactions are mathematically expressed in the reptation theory to suspensions. The particle-particle interactions are regarded as a confinement to cages formed by surrounding particles and by introducing a new dissipative motion (an analog of the reptation motion) inside the cages. Nonlinear responses to imposed shear and elongational flows are found to be in qualitative agreement with available experimental data.

On the macroscopic modelling of dilute emulsions under flow

“…Subsequently, Grmela et al (2014), advanced a free energy expression specifically to express the surface energy of the droplets. In this free energy expression the surface area was identified with the second invariant of the conformation tensor, which is a reasonable but significant approximation.…”

“…In this free energy expression the surface area was identified with the second invariant of the conformation tensor, which is a reasonable but significant approximation. Despite this improvement, the main problem with the latest Grmela et al (2014) model is that the conformation tensor used is, like b before, identified with square root of the Maffettone & Minale (1998) contravariant conformation tensor, and therefore this is not a contravariant tensor. A further corroborative proof that this is the meaning of the second order tensor used by Grmela et al (2014) is that it has units of length, leading to a second invariant with units of length squared, therefore making the second invariant suitable to represent the ellipsoid surface as they did.…”

“…Despite this improvement, the main problem with the latest Grmela et al (2014) model is that the conformation tensor used is, like b before, identified with square root of the Maffettone & Minale (1998) contravariant conformation tensor, and therefore this is not a contravariant tensor. A further corroborative proof that this is the meaning of the second order tensor used by Grmela et al (2014) is that it has units of length, leading to a second invariant with units of length squared, therefore making the second invariant suitable to represent the ellipsoid surface as they did. As a consequence, if the correct physics of the Maffettone & Minale (1998) physical picture is to be followed, it is the square of the tensor used by Grmela et al (2014) that is contravariant and for which a relevant Poisson bracket can be built to represent its reversible dynamics; treating its square root as the contravariant tensor object following Grmela et al (2014) makes the developed model equations inconsistent with the physics of emulsion deformation.…”

“…As a consequence, if the correct physics of the Maffettone & Minale (1998) physical picture is to be followed, it is the square of the tensor used by Grmela et al (2014) that is contravariant and for which a relevant Poisson bracket can be built to represent its reversible dynamics; treating its square root as the contravariant tensor object following Grmela et al (2014) makes the developed model equations inconsistent with the physics of emulsion deformation. Still, the model equations developed in Grmela et al (2014) can be used but need to be considered as phenomenological approximations of the underlying physics of droplet deformation dynamics.…”

Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments

“…Necessarily this involves introducing parameters for various structure building and breaking phenomena, as well as functional forms relating viscous and elastic material properties to the structure parameter. Such phenomenological parameters can, in principle, be derived by coarse graining the more fundamental, particle micromechanics equations [18,19].…”