This study investigates the impact of elasticity and plasticity on two-dimensional flow past a circular cylinder at Reynolds number Re=100. Ten direct numerical simulations were performed using the Saramito-Herschel–Bulkley model to represent viscoelastic and elastoviscoplastic (EVP) fluids. The flow evolves from a periodic von Kármán vortex street to chaotic-like regimes. Proper Orthogonal Decomposition (POD) and Higher Order Dynamic Mode Decomposition (HODMD) are applied to extract dominant flow structures and their temporal dynamics. For viscoelastic fluids, increasing the Weissenberg number Wi elongates the recirculation bubble and shifts it downstream, resulting in more intricate but still periodic behavior. In EVP fluids, seven cases explore variations in Bingham number Bn, solvent viscosity ratio βs, and power law index n, aiming to qualitatively assess their influence rather than determine critical thresholds. Results indicate that stronger plastic effects, especially with n≥1, lead to increased flow complexity. Three dynamic regimes are identified: (i) periodic; (ii) transitional, with elongated recirculation and disrupted periodicity; and (iii) fully complex, with breakdown of recirculation. Overall, the study highlights the interplay between inertia, elasticity, and yield stress in non-Newtonian flows past obstacles and identifies key parameters driving the transition from periodic to complex regimes.

Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at a sufficiently large yield stress, these models predict complete motionlessness; below a critical value, yielding and motion onset can be delayed in viscoplastic models. In both cases, however, experiments observe immediate motion onset. We present numerical simulations of the transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated side walls, exploring the role of elasticity in reconciling theoretical predictions with experimental observations. We consider motion onset in EVP fluids under two initial temperature distributions: (i) a linear distribution characteristic of steady pure conduction, and (ii) a uniform distribution representative of experimental conditions. The Saramito EVP model exhibits an asymptotic behaviour similar to the Kelvin-Voigt model as, where material behaviour is primarily governed by elasticity and solvent viscosity. The distinction between motion onset and yielding, a hallmark of EVP models, is the key feature that bridges theoretical predictions with experimental observations. While motion onset is consistently immediate (as seen in experiments), yielding occurs with a delay (as predicted by viscoplastic models). Scaling analysis suggests that this delay varies logarithmically with the yield stress and is inversely proportional to the elastic modulus. The intensity of the initial pre-yield motion increases with higher yield stress and lower elastic modulus. The observed dynamics resemble those of under- and partially over-damped systems, with a power-law fit providing an excellent match for the variation of oscillation frequency with the elastic modulus.

Abstract: A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence. Graphical abstract: (Figure presented.).

The thermal boundary layer flow is a canonical flow with characteristics that are present in most natural and industrial convection flows. An approximate self-similar solution is proposed for the first time for the thermal boundary layer of steady laminar flow of viscoelastic fluids, described by the finitely extensible nonlinear elastic constitutive equation with Peterlin's closure (FENE-P model). This semi-analytical ther-mal solution is obtained by performing an order of magnitude analysis and ensuing simplifications of the governing equations by assuming that the fluid properties are independent of temperature therefore de-coupling the flow governing equations from the energy equation. The effects of viscoelasticity quantified with the Weissenberg number based on the streamwise coordinate (x) (W-ix) up to W-ix = 1 and viscous dissipation (results are presented for Brinkman numbers between-40 and + 40) on thermal boundary layer characteristics are investigated comprehensively for both constant wall temperature and constant wall heat flux. At low elasticity levels (Wi(x) < 0.01 ) the solution exhibits a global self-similar behavior in which flow and thermal quantities collapse on the corresponding Newtonian curves, and the polymer characteristics show a unique behavior if adequately normalized. However, by increasing flow elasticity the unique self-similar behavior of the approximate solution is lost, with the elasticity dependent results exhibiting local variations. In addition, the effects of elasticity are intensified by viscous dissipation. For the present study cases, it is observed that elasticity may change Nusselt numbers by more than 8%, and the thermal boundary layer thickens by up to 10%.

Experimental studies of natural convection in yield stress fluids have revealed transient behaviours that contradict predictions from viscoplastic models. For example, at sufficiently large yield stress, these models predict complete motionlessness; below a critical value, yielding and motion onset can be delayed in viscoplastic models. In both cases, however, experiments observe immediate motion onset. We present numerical simulations of transient natural convection of elastoviscoplastic (EVP) fluids in a square cavity with differentially heated sidewalls, exploring the role of elasticity in reconciling theoretical predictions with experimental observations. We consider motion onset in EVP fluids under two initial temperature distributions: (i) a linear distribution characteristic of steady pure conduction, and (ii) a uniform distribution representative of experimental conditions. The Saramito EVP model exhibits asymptotic behaviour similar to the Kelvin-Voigt model as t→ 0⁺, where material behaviour is primarily governed by elasticity and solvent viscosity. The distinction between motion onset and yielding, a hallmark of EVP models, is the key feature that bridges theoretical predictions with experimental observations. While motion onset is consistently immediate (as seen in experiments), yielding occurs with a delay (as predicted by viscoplastic models). Scaling analysis suggests that this delay varies logarithmically with the yield stress and is inversely proportional to the elastic modulus. The intensity of the initial pre-yield motion increases with higher yield stress and lower elastic modulus. The observed dynamics resemble those of under- and partially over-damped systems, with a power-law fit providing an excellent match for the variation of oscillation frequency with the elastic modulus.

The flow of complex fluids past a circular cylinder is a canonical flow configuration of broad industrial and scientific interest. We present numerical simulations investigating the flow of Boger fluids (modelled with the Oldroyd-B constitutive equation), viscoelastic shear-thinning fluids with anisotropic mobility (using the Giesekus model), and elastoviscoplastic fluids (using Saramito's model) past a circular cylinder in a channel of height twice the cylinder diameter. Through direct numerical simulations, we investigate for the first time the onset of the three-dimensional elastic wake instability discovered by McKinley et al. [Philos. Trans., Math. Phys. Eng. Sci. vol. 334, no. 1671 (1993)], and its development with increasing Deborah number. Our results for Boger fluids show the onset of a steady three-dimensional cellular structure above a critical Deborah number, with a wavelength and appearance consistent with experiments. When the Deborah number increases, both simulations and experiments show a transition to time-dependent behaviour. Further, we show that increasing shear-thinning and anisotropic drag through the Giesekus mobility parameter, α, rapidly suppresses the instability, an effect we attribute to the shear-thinning first-normal stress coefficient of the Giesekus model. Finally, our simulations predict onset of the three-dimensional wake instability in elastoviscoplastic fluids, with velocity perturbations in the wake extending smoothly into the surrounding un-yielded regions. Parametric studies in Deborah-Bingham (De-Bn) space reveal that increasing De increases the instability amplitude and non-linearity, and shows transition to time-dependent behaviour, while increasing Bn primarily increases the volume of un-yielded regions and the instability amplitude.