An elastic, plastic, viscous model for slow shear of a liquid foam

Abstract

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called "quasi-static") limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.

References in corpus (13)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• A constitutive law for dense granular flows
• Rheology of Soft Glassy Materials
• Direct experimental evidence of a growing length scale accompanying the glass transition
• Strain-Rate Frequency Superposition (SRFS) - A rheological probe of structural relaxation in soft materials
• Deformation and flow of a two-dimensional foam under continuous shear
• Slow flows of yield stress fluids: complex spatio-temporal behaviour within a simple elasto-plastic model
• Nonlinear viscoelasticity of metastable complex fluids
• Local Stress Relaxation and Shear-banding in a Dry Foam under Shear
• Shear-Induced Stress Relaxation in a Two-Dimensional Wet Foam
• Relaxing in foam
• Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow
• Two dimensional foam rheology with viscous drag

Cited by in corpus (9)

• Non-local rheology in dense granular flows -- Revisiting the concept of fluidity
• Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions
• Damping of liquid sloshing by foams
• Rheological properties of the soft-disk model of two-dimensional foams
• Active dynamics of tissue shear flow
• On the study of local stress rearrangements during quasistatic plastic shear of a model glass: do local stress components contain enough information?
• An elasto-visco-plastic model for immortal foams or emulsions
• Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams
• Giant fluctuations in the flow of fluidised soft glassy materials: an elasto-plastic modelling approach