On Objectivity, Irreversibility and Non-Newtonian Fluids

Abstract

Early progress in non-Newtonian fluid mechanics was facilitated by the emergence of two fundamental and complementary principles: objective constitutive characterizations and unambiguous identification of irreversible processes. Motivated by practical and economic concerns in recent years, this line of fluid research has expanded to include debris flows, slurries, biofluids and fluid-solid mixtures; i.e., complex nonlinear fluids with disparate flow properties. Phenomenological descriptions of these fluids now necessarily include strong nonlinear coupling between the fluxes of mass, energy and momentum. Here, I review these principles, illustrate how they constrain the constitutive equations for non-Newtonian fluids and demonstrate how they have impacted other areas of fluid research.

Vorticity and helicity decompositions and dynamics with real Schur form of the velocity gradient

“…Forgetting about Eq. (20) and assuming the periodic boundary condition, say, we would have the formal dynamical invariants for the corresponding inviscid Euler equations,…”

“…However, the RSF of (1) rotating around the z axis is still RSF; thus, extra constraint is still wanted to settle down on a unique Q, which, among others, will be left for future studies and which could be of parallel value for turbulence modeling. 20 This work is supported by NSFC (No. 11672102) and Tián-Yuán-Xué-Pài Foundation, and the author thanks WeChat for passing on to him the previous hydrodynamic application of RSF.…”

Can vortex criteria be objectivized?

“…This minimal requirement for flow-feature identification was already pointed out in the 1970s by Drouot (1976), Drouot & Lucius (1976), Astarita (1979) and Lugt (1979). More recent reviews by Haller (2005, 2015), Peacock, Froyland & Haller (2015), Kirwan (2016) and Günther & Theisel (2018) have further elaborated on the need to identify coherent structures in an observer-independent fashion.…”

Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

“…These constitutive relations are properly frame-indifferent models (see [48,55]). Using the second law, we established constraints on the constitutive equations for a fluid model that includes nonlinear processes arising from flow, heat flux, and the redistribution of the particles.…”