Journal of Non-Newtonian Fluid Mechanics最新文献

We investigate the transition pathway of low elasticity fluids ($El=0.003-0.008$) in a Taylor-Couette configuration using low-molecular-weight polyacrylamide (PAAM) and visualisation experiments in the Reynolds range from 0 to 300. We report here for the first time an elastically modified wavy vortex flow state with altered spectral and structural characteristics, that precedes the onset of the traditional (inelastic) Newtonian wavy instability. This new wavy regime is characterised by oscillations of both the inflow and outflow boundaries, associated with a weakening of the outflow regions due to low hoop stresses. The modification of the boundaries persists at higher Reynolds numbers, where the spectral characteristics are unaltered compared to the inelastic, Newtonian case. In addition, a hysteretic behaviour is observed for increasing elasticity, as instabilities are shifted towards lower critical Reynolds numbers, confirming the importance of even vanishing elasticity on the stability of Taylor-Couette flows. At higher fluid elasticity ($El=0.06$), the amplitude of inflows/outflows oscillations increases, and momentum is transferred axially between adjacent vortices, which may contribute to the emergence of Rotating Standing Waves.

The formation of a liquid plug inside a human airway, known as airway closure, is computationally studied by considering the elastoviscoplastic (EVP) properties of the pulmonary mucus covering the airway walls for a range of liquid film thicknesses and Laplace numbers. The airway is modeled as a rigid tube lined with a single layer of an EVP liquid. The Saramito–Herschel–Bulkley (Saramito-HB) model is coupled with an Isotropic Kinematic Hardening model (Saramito-HB-IKH) to allow energy dissipation at low strain rates. The rheological model is fitted to the experimental data under healthy and cystic fibrosis (CF) conditions. Yielded/unyielded regions and stresses on the airway wall are examined throughout the closure process. Yielding is found to begin near the closure in the Saramito-HB model, whereas it occurs noticeably earlier in the Saramito-HB-IKH model. The kinematic hardening is seen to have a notable effect on the closure time, especially for the CF case, with the effect being more pronounced at low Laplace numbers and initial film thicknesses. Finally, standalone effects of rheological properties on wall stresses are examined considering their physiological values as baseline.

Polymer-induced drag reduction has yielded great potential benefits for industrial processes after more than 70 years of research. However, the limitation of low shear stability has hindered further applications. This study investigates the rheology, drag reduction rate (DR), and degradation of binary polymer mixtures comprising a rigid polymer (diutan gum, DG) and a flexible polymer (polyethylene oxide, PEO). The solutions all exhibited shear-thinning behavior, and the mixed solution was less viscous than the pure PEO or DG solutions at the total concentration of 100 ppm. When fixing the PEO concentration at 50 ppm, the mixed solution viscosity significantly increased with the DG concentration. The drag reduction performance of the pure PEO solution, pure DG solution, and various proportions of binary polymer mixtures was analyzed using an in-house rotor device. The DRs of the solutions increased with the Reynolds number (Re), and decreased with shearing time. The binary solution significantly improved the shear stability of the solution without loss of DR compared to the pure PEO solution. The theoretical model for molecular degradation in turbulent flow excellently fitted the experimental data of relative drag reduction with time. Furthermore, the synergistic interaction parameter was calculated, and it was positive for most cases in the mixtures. Additionally, when Re was fixed, the synergistic interaction parameter, related to the composition of binary polymer mixtures, initially decreased and then increased with time.

The impulsive viscous flow through an orifice produces vortex rings that self-propagate until total dissipation of the vorticity. This work aims to study numerically such vortex rings for different types of non-Newtonian fluids, including the power-law, Carreau and simplified Phan-Thien-Tanner (PTT) rheological models, with particular focus on the post-formation phase. The simulations were carried out with the finite-volume method, considering small stroke ratios (L/D ≤ 4) and laminar flow conditions (Re_G ≤ 10³), while parametrically varying shear-thinning, inertia and elasticity. The vortex rings generated in power-law fluids revealed some peculiar features compared to Newtonian fluids, such as a faster decay of the total circulation, a reduction of the axial reach and a faster radial expansion. The behavior in Carreau fluids was found to be bounded between that of power-law and Newtonian fluids, with the dimensionless Carreau number controlling the distance to each of these two limits. The vortex rings in PTT fluids showed the most disruptive behavior compared to Newtonian fluids, which resulted from a combined effect between inertia, elasticity and viscous dissipation. Depending on the Reynolds and Deborah numbers, the dye patterns of the vortex rings can either move continuously forward or unwind and invert their trajectory at some point. Elasticity resists the self-induced motion of the vortex rings, lowering the axial reach and creating disperse patterns of vorticity. Overall, this work shows that the particular non-Newtonian rheology of a fluid can modify the vortex ring behavior typically observed in Newtonian fluids, confirming qualitatively some experimental observations.

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable resolution for the solution of viscoelastic flows across a range of Weissenberg numbers. Based on the Local Anisotropic Basis Function Method (LABFM) of King et al. (2020), highly accurate viscoelastic flow solutions are found using Oldroyd B and PPT models for a range of two dimensional problems — including Kolmogorov flow, planar Poiseulle flow, and flow in a representative porous media geometry. Convergence rates up to 9th order are shown. Three treatments for the conformation tensor evolution are investigated for use in this new high-order meshless context (direct integration, Cholesky decomposition, and log-conformation), with log-conformation providing consistently stable solutions across test cases, and direct integration yielding better accuracy for simpler unidirectional flows. The final test considers symmetry breaking in the porous media flow at moderate Weissenberg number, as a precursor to a future study of fully 3D high-fidelity simulations of elastic flow instabilities in complex geometries. The results herein demonstrate the potential of a viscoelastic flow solver that is both high-order (for accuracy) and meshless (for straightforward discretisation of non-trivial geometries including variable resolution). In the near-term, extension of this approach to three dimensional solutions promises to yield important insights into a range of viscoelastic flow problems, and especially the fundamental challenge of understanding elastic instabilities in practical settings.

In this work, we consider a suspension of weakly deformable solid particles within a weakly viscoelastic fluid. The fluid phase is modelled as a second-order fluid, and particles within the suspended phase are assumed linearly elastic and relatively dilute. We apply a cell model as a proxy for mean field flow, and solve analytically within a cellular fluid layer and its enclosed particle. We use an ensemble averaging process to derive analytical results for the bulk stress in suspension, and evaluate the macroscopic properties in both shear and extensional flow. Our viscometric functions align with existing literature over a surprisingly broad range of fluid and solid elasticities.

The suspension behaves macroscopically as a second-order fluid, and we give simple formulae by which the reader can calculate the parameters of this effective fluid, for use in more complex simulations. We additionally calculate the particle shape and orientation, and in simple shear flow show that the leading-order modifications to the angle of inclination $\zeta$ act to align the particle towards the flow direction, giving $\zeta =\pi /4-3{Ca}_e/4+{\alpha }_{0}Wi/2{\alpha }_1$ where ${Ca}_e$ is the elastic capillary number, $Wi$ is the Weissenberg number, and ${\alpha }_i$ are material properties of the suspending second-order fluid, for which the ratio ${\alpha }_0/{\alpha }_1$ is negative.

An experimental study is conducted on the use of a normally impinging turbulent water jet (with the Reynolds number of $Re\approx 11800$), for cleaning thick layers of a Newtonian fluid and two viscoplastic fluids (i.e., transparent Carbopol solutions). The layer thickness is larger than the jet radius. Non-intrusive techniques are used to track the geometrical features of the cleaning process in real time. The effects of layer thickness and fluid yield stress on removal behavior, including cleaning radius, cavity radius, and angle, are investigated. A yield stress promotes the initial formation of a blister rather than a cavity, and the rate of removal decreases with increasing layer thickness and yield stress. A relation is presented for the growth of the cavity radius, which fits our experimental observations well. A comparative analysis of submerged and impinging jets reveals, for the first time, the role of air entrainment in the process, with bubble characteristics such as trajectory, size distribution (diameter), and velocity being determined by the yield stress.

In recent years, many researchers have focused on improving the die design process for polymer extrusion. This study proposes the development of an efficient and robust numerical approach to improve the die-designing process of polymer melts using the Giesekus model. The proposed technique uses a hybrid optimization algorithm to systematically minimize an objective function to achieve the desired extrudate shape. First, we examine the proposed objective function for the 2D axisymmetric test case using the Golden Section optimization algorithm to obtain a circular extrudate of high-density polyethylene (HDPE) with the desired radius at moderate Weissenberg numbers from 1 to 3.75. To provide more insights into the viscoelastic nature of the problem, the optimization was repeated for a viscoelastic fluid with a higher viscosity ratio and a lower mobility factor at very high Weissenberg numbers, specifically 45, 60, 75, and 90. The proposed approach performs quite well across a broad range of Weissenberg numbers. Subsequently, a hybrid optimization algorithm that combines Nelder-Mead and Bayesian optimization algorithms is employed to achieve the desired extrudate shape for various extrudate profiles in 3D cases, including rectangular and square cross-sections, at a Weissenberg number of one. To gain additional insights into the viscoelastic nature of the problem, optimization was conducted for the rectangular extrudate with a 2:1 aspect ratio at higher Weissenberg numbers, i.e. Weissenberg number from 1 to 2.6. The results of the three-dimensional case studies indicate that both the Nelder-Mead and Bayesian optimization algorithms are efficient and robust, converging relatively quickly in all cases studied. The Nelder-Mead algorithm appears to be more robust, exhibiting fewer oscillations when reaching the optimum point. On the other hand, the Bayesian optimization algorithm can reach the global optimum point at a computational cost comparable to Nelder-Mead, while achieving greater accuracy. In conclusion, these findings indicates that using this hybrid optimization algorithm in the polymer extrusion die-designing process can provide a high level of efficiency and robustness.

Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modeling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We present viscoelasticNet, a physics-informed deep learning framework that uses the velocity flow field to select the constitutive model and learn the stress field. Our framework requires data only for the velocity field, initial & boundary conditions for the stress tensor, and the boundary condition for the pressure field. Using this information, we learn the model parameters, the pressure field, and the stress tensor. This work considers three commonly used non-linear viscoelastic models: Oldroyd-B, Giesekus, and linear Phan-Tien-Tanner. We demonstrate that our framework works well with noisy and sparse data. Our framework can be combined with velocity fields acquired from experimental techniques like particle image velocimetry to get the pressure & stress fields and model parameters for the constitutive equation. Once the model has been discovered using viscoelasticNet, the fluid can be simulated and modeled for further applications.

The performance of a spectral element method in the DEVSS-G formulation for the solution of non-Newtonian flows is assessed by means of a systematic analysis of the benchmark lid-driven cavity problem. It is first validated by comparison with the creeping Newtonian and Oldroyd-B flows, where in the latter case a lid velocity regularisation scheme must be employed to remove the singularity at the lid-wall interfaces. In both instances, excellent agreement is found with the literature for stable, time-independent flows, and in fact it is shown that higher Weissenberg numbers can be obtained using the present methodology for these types of flow. Some physical aspects of the solutions are also presented and discussed, however at increasing Weissenberg numbers, the methodology breaks down due to a lack of convergence in the BDF/FPI time advancement scheme. By systematically assessing the effects of the levels of $hp$-refinement and temporal refinement on the flow fields, as well as the introduction of the extension-limiting Giesekus mobility parameter in the constitutive equations, it is demonstrated that in each instance the inability to accurately resolve the stress gradients leads to a compounding of errors in the BDF/FPI regime, ultimately causing it to diverge.