Table 2 The main characteristics of turbulence for various systems
From: Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling
| Â | Newtonian fluids | Polymer solutions | Epithelial multicellular systems |
|---|---|---|---|
compressibility | incompressible | incompressible | compressible |
Rheological behaviour | Turbulent liquids | Viscoelastic liquids | -Viscoelastic solids for epithelial phenotype -Viscoelastic liquid for mesenchymal phenotype |
Linearity of the constitutive model | Nonlinear | Nonlinear | -Linear for cell packing density \({n}_{e}<{n}_{j}\) -Non-linear for the cell state near jamming, i.e. when \({n}_{e}\to {n}_{j}\) (where \({n}_{j}\) is the cell packing density in the jamming state) |
Main characteristics of the constitutive models | Stress and strain cannot relax Changes of stress and strain occur on the same time-scale | Stress can relax under constant strain condition Strain cannot relax Changes of stress and strain occur on the same time-scale | Stress can relax for the condition that \({n}_{e}={n}_{conf}\) In this case stress relaxes under: (1) constant strain rate conditions for viscoelastic liquids and (2) constant strain for viscoelastic solids The stress relaxation occurs on a time scale of minutes, while strain change and residual stress generation occur on a time scale of hours |
Reynolds number | For Couette flow \({R}_{eo}=0\) \({R}_{ei}>1500\) | For Couette flow \({R}_{eo}=0\) \({R}_{e}<1\) for elastic turbulence \({R}_{ei}\ge 200\) for elasto-inertial turbulence | \({R}_{e}\ll 1\) |
Inertial effects | Short-time inertial effects | The elastic turbulence is inertia-less unstable flow of polymer solutions The elasto-inertial turbulence is a product of inertial effects | Long-time inertial effects (the effective inertia) |