New generalized Newtonian fluid models for quantitative description of complex viscous behavior in shear flows

Abstract

Two semiempirical models of generalized Newtonian fluid are discussed. Special attention was focused on the stress dependent model based on the free volume theory. However, the strain‐rate dependent model in form of a modified viscosity function resulting from Oldroyd equation is also presented. Both models (along with specific cases) reflecting pseudoplastic or dilatant behavior of liquids in shear flows are generalized to multimode models (defined as products of two or more basic models), which are able to describe quantitatively the behavior of more complex systems, for example, systems with pseudoplastic and dilatant properties in different shear stress (shear rate) ranges. A number of practical examples for viscosity curves of non‐Newtonian fluids described by these models are given. The questions of inverse models and model efficiency are also discussed. POLYM. ENG. SCI., 58:1446–1455, 2018. © 2017 Society of Plastics Engineers

Effective viscosity and Reynolds number of non-Newtonian fluids using Meter model

“…τ = 2 η( γ) D) (Bird et al, 2007) or deviatoric stress tensor (i.e. τ = 2 η(τ ) D) (Meter and Bird, 1964;Steller and Iwko, 2018;Peters et al, 1999;Matsuhisa and Bird, 1965). Here, D = 1 2 γ = 1 2 (∇u + (∇u) T ), the magnitude of shear-rate is et al, 2007), the magnitude of shear stress is |τ | = τ : τ 2 ( Meter and Bird, 1964), and u is velocity vector.…”

“…polymer fluid flow through pipes in an industrial settings (Bird et al, 1987), capillary bundle model of a porous media (Savins, 1969), pore-Network model (Sochi and Blunt, 2008)). Amongst generalised Newtonian fluid models (Yilmaz and Gundogdu, 2008), Cross (Cross, 1965), Carreau (Yasuda, 1979), Carreau-Yasuda (Yasuda, 1979), Meter (Meter and Bird, 1964;Meter, 1964;Savins, 1969;Tsakiroglou, 2002;Tsakiroglou et al, 2003b,a), and Steller-Ivako model (Steller and Iwko, 2018) can predict S-shaped rheological properties (i.e. constant viscosity at low and high shear values and decreasing viscosity at intermediate shear values) of many shear-thinning fluids.…”

An empirical equation for shear viscosity of shear thickening fluids

“…Galindo-Rosales et al [23,24] developed shear rate-dependent branch of equations based on Cross model [25] to capture first shear thinning, shear thickening and second shear thinning region of shear thickening fluids. Recently, Steller and Iwko [26] proposed an empirical shear stressdependent and shear-rate dependent model for the non-Newtonian fluids based on free volume theory. Steller-Iwko multi-model rheological equation [26] captures the complicated viscosity curve of non-Newtonian fluids.…”

“…Recently, Steller and Iwko [26] proposed an empirical shear stressdependent and shear-rate dependent model for the non-Newtonian fluids based on free volume theory. Steller-Iwko multi-model rheological equation [26] captures the complicated viscosity curve of non-Newtonian fluids. Steller-Iwko [26] modified an empirical equation developed by Doolittle [27] to relate viscosity of the fluid with shear stress and shear rate.…”

“…Steller-Iwko multi-model rheological equation [26] captures the complicated viscosity curve of non-Newtonian fluids. Steller-Iwko [26] modified an empirical equation developed by Doolittle [27] to relate viscosity of the fluid with shear stress and shear rate.…”