Derivation of a constitutive model for the rheology of jammed soft suspensions from particle dynamics

Abstract

Considering the rheology of two-dimensional soft suspensions above the jamming density, we derive a tensorial constitutive model from the microscopic particle dynamics. Starting from the equation governing the $N$-particle distribution, we derive an evolution equation for the stress tensor. This evolution equation is not closed, as it involves the pair and three-particle correlation functions. To close this equation, we first employ the standard Kirkwood closure relation to express the three-particle correlation function in terms of the pair correlation function. Then we use a simple and physically motivated parametrization of the pair correlation function to obtain a closed evolution equation for the stress tensor. The latter is naturally expressed as separate evolution equations for the pressure and for the deviatoric part of the stress tensor. These evolution equations provide us with a non-linear tensorial constitutive model describing the rheological response of a jammed soft suspension to an arbitrary uniform deformation. One of the advantages of this microscopically-rooted description is that the coefficients appearing in the constitutive model are known in terms of packing fraction and microscopic parameters.

31 pages, 7 figures Final Version after review

References in corpus (15)

• Scaling description of the yielding transition in soft amorphous solids at zero temperature
• Unified study of glass and jamming rheology in soft particle systems
• Yielding and flow in adhesive and non-adhesive concentrated emulsions
• Microfluidic rheology of soft colloids above and below jamming
• Glass Rheology: From mode-coupling theory to a dynamical yield criterion
• A mode coupling theory for Brownian particles in homogeneous steady shear flow
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Overshoots in stress strain curves: Colloid experiments and schematic mode coupling theory
• Diverging viscosity and soft granular rheology in non-Brownian suspensions
• Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
• Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles
• An elasto-visco-plastic model for immortal foams or emulsions
• Universal scaling for the jamming transition
• Integration through transients approach to the $\mu (\mathcal{I})$ rheology
• Pair correlation function of charge-stabilized colloidal systems under sheared conditions

Cited by in corpus (1)

• Microscopically grounded constitutive model for dense suspensions of soft particles below jamming