Journal of Non-Newtonian Fluid Mechanics最新文献

We prove conditions for global nonlinear stability of Oldroyd-B viscoelastic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude of the polymer perturbations from their steady-state values. The conditions for global stability extend, in a physically natural manner, classical results on global stability of Newtonian Couette flow.

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number ($Re$) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number ($Wi$) and eventually saturates above a critical $Wi$, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (${\kappa }_K=2.32$) and a $Re$-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.

We study Vortex-Induced Vibration (VIV) of a one-degree-of-freedom cylinder placed in inertial-elastic flows experimentally. We show that there is a critical Reynolds number for the onset of VIV in these flows and this critical Reynolds number increases when the elasticity in the fluid is increased. We also show that at a constant Reynolds number, adding elasticity to the fluid reduces the amplitude of oscillations and eventually suppresses VIV entirely. For the cases where VIV is observed, the onset of the lock-in range does not depend on the Reynolds number, as a result of the competing effects of shear-thinning and elasticity. The vortices that are observed in the wake are significantly different from those observed in Newtonian VIV: the vortices are S-shaped with relatively long tails that influence the formation of the vortices that are formed in the following cycle.

Fluid elements passing near a stagnation point experience finite strain rates over long persistence times, and thus accumulate large strains. By the numerical optimization of a microfluidic 6-arm cross-slot geometry, recent works have harnessed this flow type as a tool for performing uniaxial and biaxial extensional rheometry (Haward et al., 2023 [5,6]). Here we use the microfluidic ‘Optimized-shape Uniaxial and Biaxial Extensional Rheometer’ (OUBER) geometry to probe an elastic flow instability which is sensitive to the alignment of the extensional flow. A three-dimensional symmetry-breaking instability occurring for flow of a dilute polymer solution in the OUBER geometry is studied experimentally by leveraging tomographic particle image velocimetry. Above a critical Weissenberg number, flow in uniaxial extension undergoes a supercritical pitchfork bifurcation to a multi-stable state. However, for biaxial extension (which is simply the kinematic inverse of uniaxial extension) the instability is strongly suppressed. In uniaxial extension, the multiple stable states align in an apparently random orientation as flow joining from four neighbouring inlet channels passes to one of the two opposing outlets; thus forming a mirrored asymmetry about the stagnation point. We relate the suppression of the instability in biaxial extension to the kinematic history of flow under the context of breaking the time-reversibility assumption.

In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under the influence of an externally applied temperature gradient. The outer fluid is modelled by the Oldroyd-B equation, and the problem is solved for small Weissenberg and Capillary numbers in terms of a double perturbation expansion. We assume microgravity conditions and neglect the convective transport of energy and momentum. We derive expressions for the droplet migration speed and its shape in terms of the properties of both fluids. In the absence of shape deformation, the droplet speed decreases monotonically for sufficiently viscous inner fluids, while for fluids with a smaller inner-to-outer viscosity ratio, the droplet speed first increases and then decreases as a function of the Weissenberg number. For small but finite values of the Capillary number, the droplet speed behaves monotonically as a function of the applied temperature gradient for a fixed ratio of the Capillary and Weissenberg numbers. We demonstrate that this behaviour is related to the polymeric stresses deforming the droplet in the direction of its migration, while the associated changes in its speed are Newtonian in nature, being related to a change in the droplet’s hydrodynamic resistance and its internal temperature distribution. When compared to the results of numerical simulations, our theory exhibits a good predictive power for sufficiently small values of the Capillary and Weissenberg numbers.

Helical static mixers are often used during the processing of formulated products with complex rheological properties, such as viscoelasticity. Previous experimental studies have highlighted that increasing the viscoelasticity of the flow hinders the mixing performance in the laminar flow regime. In this study, we use computational fluid dynamics to investigate the flow of a FENE-CR model fluid in a helical static mixer. The numerical results show clearly that the reduced mixing performance is caused by flow distribution asymmetries which develop at the mixer element intersections. The results allow us to quantify the degree of asymmetry for the range of conditions studied, which is correlated with the quantified mixing performance for each simulation. The mixing is quantified using a Lagrangian particle tracking technique, and a new mixing index is defined based on the mean nearest distance between the two sets of tracked particles. The results show that the asymmetry parameter does not follow a pitchfork bifurcation, as it typically does for elastic instabilities in symmetrical geometries such as the cross-slot. For low values of the extensibility parameter, $L^2$, the flow remained (Eulerian) steady for all Reynolds $Re$ and Weissenberg $Wi$ numbers studied. At fixed $Re$ and $Wi$, increasing $L^2$ causes the flow to become transient and greatly increases the magnitude of the asymmetry. The results presented in this study help us to understand the effects that viscoelasticity can cause in mixing processes.

The article focuses on the shear-thinning and viscoelastic constitutive modelling and numerical simulation of blood flow in a stenosed and bifurcating artery. Specifically, the shear-thinning and viscoelastic behaviour of blood are modelled and implemented via the Oldroyd-B and Generalized Oldroyd-B constitutive models. A robust and efficient general purpose numerical (and computational) methodology for the simulation of blood flow in a stenosed and bifurcating artery is also developed and implemented. The numerical algorithm is developed more generally to resolve the mathematical model equations arising out of the all-encompassing Generalized Giesekus constitutive model. This model reduces to the Generalized Oldroyd-B model and subsequently also to the standard Oldroyd-B model simply by switching off certain material parameters. The inclusion of the Generalized Giesekus model must therefore be viewed in this context, to facilitate the development of an all encompassing general purpose numerical code. The blood flow modelling is otherwise done via the Oldroyd-B and Generalized Oldroyd-B constitutive models. The shear-thinning effects are implemented via the Cross model for shear-viscosity. The Generalized Oldroyd-B model results all illustrate that the velocity is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher would the velocity spurt through the constriction. This velocity behaviour correspondingly enhances the wall shear-stresses as the constriction increases, caused by the presence of the stenosis. High wall shear-stresses greatly increase the possibility of rupture of the stenosis. This can lead to catastrophic consequences in the usual case where the stenosis is caused, say, by tumor growth. As demonstrated near the contraction of a standard 4:1 contraction flow geometry, dramatic fluid flow effects, which are attributable to the polymeric-stresses, specifically to the first normal stress difference, are observed in the vicinity of the constrictions resulting from the presence of the stenosis. Such effects, include, flow recirculation and reversal, vortex formation, and spurt phenomena.

This study investigates the gas invasion into a porous medium filled with a yield-stress fluid. A pore–throat network model is employed to represent the porous media, and a semi-analytical approach is used for simulating the gas propagation. The effect of throat radii, fluid yield stress and network size on the exit time and gas volume fraction retained inside the porous medium are explored. The stability of the network in response to inflow perturbations is also examined. The uniform network appears to be optimal from the perspective of preventing flow.

The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of uncertainty quantification (UQ) can be used to improve the predictive capabilities of rheological models in such flow scenarios. For this demonstration, we consider the squeeze flow of generalized Newtonian fluids. To systematically study uncertainties, we have developed a tailored squeeze flow setup, which we have used to perform experiments with glycerol and PVP solution. To mimic these experiments, we have developed a three-region truncated power law model, which can be evaluated semi-analytically. This fast-to-evaluate model enables us to consider uncertainty propagation and Bayesian inference using (Markov chain) Monte Carlo techniques. We demonstrate that with prior information obtained from dedicated experiments – most importantly rheological measurements – the truncated power law model can adequately predict the experimental results. We observe that when the squeeze flow experiments are incorporated in the analysis in the case of Bayesian inference, this leads to an update of the prior information on the rheological parameters, giving evidence of the need for recalibration in the considered complex flow scenario. In the process of Bayesian inference we also obtain information on quantities of interest that are not directly observable in the experimental data, such as the spatial distribution of the three flow regimes. In this way, besides improving the predictive capabilities of the model, the uncertainty quantification framework enhances the insight into complex flow scenarios.