Stability of stratified two-phase channel flows of Newtonian/non-Newtonian shear-thinning fluids

Abstract

Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shearthinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the rheology of a shear-thinning fluid, owing to its capability to describe properly the constant viscosity limits (Newtonian behavior) at low and high shear rates. The results are presented in the form of stability boundaries on flow pattern maps (with the phases' superficial velocities as coordinates) for several practically important gas-liquid and liquid-liquid systems. The stability maps are accompanied by spatial profiles of the critical perturbations, along with the distributions of the effective and tangent viscosities in the non-Newtonian layer, to show the influence of the complex rheological behavior of shear-thinning liquids on the mechanisms responsible for triggering instability. Due to the complexity of the considered problem, a working methodology is proposed to alleviate the search for the stability boundary. Implementation of the proposed methodology helps to reveal that in many cases the investigation of the simpler Newtonian problem is sufficient for the prediction of the exact (non-Newtonian) stability boundary of smooth stratified flow (i.e., in case of horizontal gas-liquid flow). Therefore, the knowledge gained from the stability analysis of Newtonian fluids is applicable to those (usually highly viscous) non-Newtonian systems. Since the stability of stratified flow involving highly viscous Newtonian liquids has not been researched in the literature, interesting findings on the viscosity effects are also obtained. The results highlight the limitations of applying the simpler and widely used power-law model for characterizing the shear-thinning behavior of the liquid. That model would predict a rigid layer (infinite viscosity) at the interface, where the shear rates in the viscous liquid are low, and thereby unphysical representation of the interaction between the phases.

Primary cementing of horizontal wells. Displacement flows in eccentric horizontal annuli. Part 1. Experiments

“…(2017), Picchi et al. (2018), Etrati & Frigaard (2018 b ) and de Bertodano et al. (2017), driven partly by the widespread interest in gravity currents (which we do not review).…”

Taylor drop in a closed vertical pipe

“…In upward and downward inclined flows, multiple configurations may exist for fixed operational conditions (Barnea & Taitel 1992;Ullmann et al 2003b;Thibault, Munoz & Liné 2015;Picchi & Poesio 2016;Goldstein, Ullmann & Brauner 2017;Picchi et al 2017Picchi et al , 2018aPicchi, Ullmann & Brauner 2018b). For given fluids flow rates, there exist multiple steady-state solutions that differ in the volume fractions, velocity profiles and the pressure drop, but share the same flux.…”

An incompressible smoothed particle hydrodynamics scheme for Newtonian/non‐Newtonian multiphase flows including semi‐analytical solutions for two‐phase inelastic Poiseuille flows

“…It is shown that the transition from the non‐Newtonian phase b to the Newtonian phase a is captured with great accuracy, both for shear‐thinning (Figure A,B) as well as for shear‐thickening phenomena (Figure C,D). It should be noted that the shear‐thinning power‐law model has been recently found to be unrepresentative of realistic phenomena . However, it is still useful for the mathematical validation of the proposed methodology as shown in this section.…”

“…Moreover, the above solution can be easily generalized to Bingham and power‐law models, by setting τ Y =0 Pa and N =1, respectively. Also to be noted that other validation cases for Newtonian/non‐Newtonian interactions can be found in the literature …”