A theoretical framework for steady-state rheometry in generic flow conditions

Abstract

We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of mixed flows. Such a basis is determined solely by the symmetric part of the velocity gradient and allows for a straightforward interpretation of the non-Newtonian response in any local flow conditions. In steady homogeneous flows, the material functions that represent the components of the stress on the adapted basis generalize and complete the classical set of viscometric functions used to characterize the response in simple shear flows. Such a general decomposition of the stress is effective in coherently organizing and interpreting rheological data from laboratory measurements and computational studies in non-viscometric steady flows of great importance for practical applications. The decomposition of the stress in terms with clearly distinct roles is also useful in developing constitutive models.

References in corpus (5)

• Three-dimensional imaging of colloidal glasses under steady shear
• Recent experimental probes of shear banding
• Rheology of dense granular suspensions under extensional flow
• Microstructure and thickening of dense suspensions under extensional and shear flows
• Local Oscillatory Rheology from Echography

Cited by in corpus (10)

• The physics of dense suspensions
• Shear jamming and fragility in dense suspensions
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• Viscometric flow of dense granular materials under controlled pressure and shear stress
• Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology
• The Effect of Shear-Thinning Rheology on the Dynamics and Pressure Distribution of a Single Rigid Ellipsoidal Particle in Viscous Fluid Flow
• Ridge instability in dense suspensions caused by the second normal stress difference
• Shear-thinning in Polymer Melts -- Molecular Origins and Hybrid Multiscale Simulations
• A multi-scale method for complex flows of non-Newtonian fluids
• Dynamic jamming of dense suspensions under tilted impact