Anisotropic Viscosity Research Articles

Non-homogeneous anisotropic bulk viscosity for acoustic wave attenuation in weakly compressible methods

A major limitation of the weakly compressible approaches to simulate incompressible flows is the appearance of artificial acoustic waves that introduce mass conservation errors and lead to spurious oscillations in the force coefficients. In this work, we propose a non-homogeneous anisotropic bulk viscosity term to effectively damp the acoustic waves. By implementing this term in a computational framework based on the recently proposed general pressure equation, we demonstrate that the non-homogeneous and anisotropic nature of the term makes it significantly more effective than the isotropic homogeneous version widely used in the literature. Moreover, it is computationally more efficient than the pressure (or mass) diffusion term, which is an alternative mechanism used to suppress acoustic waves. We simulate a range of benchmark problems to comprehensively investigate the performance of the bulk viscosity on the effective suppression of acoustic waves, mass conservation error, order of convergence of the solver, and computational efficiency. The proposed form of the bulk viscosity enables fairly accurate modelling of the initial transients of unsteady simulations, which is highly challenging for weakly compressible approaches, and to the best of our knowledge, existing approaches can't provide an accurate prediction of such transients.

Estimating the viscoelastic anisotropy of human skin through high-frequency ultrasound elastography.

The skin is the largest organ of the human body and serves distinct functions in protecting the body. The viscoelastic properties of the skin play a key role in supporting the skin-healing process, also it may be changed due to some skin diseases. In this study, high-frequency ultrasound (HFUS) elastography based on a Lamb wave model was used to noninvasively assess the viscoelastic anisotropy of human skin. Elastic waves were generated through an external vibrator, and the wave propagation velocity was measured through 40MHz ultrafast HFUS imaging. Through the use of a thin-layer gelatin phantom, HFUS elastography was verified to produce highly accurate estimates of elasticity and viscosity. In a human study involving five volunteers, viscoelastic anisotropy was assessed by rotating an ultrasound transducer 360°. An oval-shaped pattern in the elasticity of human forearm skin was identified, indicating the high elastic anisotropy of skin; the average elastic moduli were 24.90±6.63 and 13.64±2.67kPa along and across the collagen fiber orientation, respectively. The average viscosity of all the recruited volunteers was 3.23±0.93Pa·s. Although the examined skin exhibited elastic anisotropy, no evident viscosity anisotropy was observed.

Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence

Various active materials exhibit strong spatio-temporal variability of their orientational order known as active turbulence, characterised by irregular and chaotic motion of topological defects, including colloidal suspensions, biofilaments, and bacterial colonies.In particular in three dimensions, it has not yet been explored how active turbulence responds to changes in material parameters and chirality.Here, we present a numerical study of three-dimensional (3D) active nematic turbulence, examining the influence of main material constants: (i) the flow-alignment viscosity, (ii) the magnitude and anisotropy of elastic deformation modes (elastic constants), and (iii) the chirality. Specifically, this main parameter space covers contractile or extensile, flow-aligning or flow tumbling, chiral or achiral elastically anisotropic active nematic fluids. The results are presented using time- and space-averaged fields of defect density and mean square velocity. The results also discuss defect density and mean square velocity as possible effective order parameters in chiral active nematics, distinguishing two chiral nematic states—active nematic blue phase and chiral active turbulence. This research contributes to the understanding of active turbulence, providing a numerical main phase space parameter sweep to help guide future experimental design and use of active materials.

Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions

AbstractIn this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates.

Grain size prediction for stainless steel fabricated by material extrusion additive manufacturing

Most traditional powder melting-based additive manufacturing (AM) technologies generally yield high-performance parts at the expense of additional cost and energy consumption. As an economical and efficient alternative method, material extrusion (ME) that deploys polymer-based filaments with highly filled metal particles offers the possibility of scalable, low-cost fabrication of metal components. As a critical step, sintering governs the mechanical strength and geometry of the final parts. The grain growth behavior induced during sintering should be well controlled to achieve the parts with the desired mechanical performance. Due to the nature of AM, grain growth kinetics could also involve extremely complex grain boundary migration and atomic diffusion mechanisms caused by the heterogeneous pore distribution. In this work, an analytical model was developed to predict and understand the grain growth behavior of stainless steel (SS) 316L built by ME-based sintering-assisted AM. Such a model accounts for anisotropic viscosity parameters calibrated through a three-dimensional dilatometry test, enabling the prediction of grain size evolution during sintering. Grain growth kinetic parameters were further identified by the grain size data at the heating and holding stages. To validate and generalize the model, we also conducted the grain size evolution prediction under different sintering temperature profiles for as-built SS 316L specimens. This work will provide scientific insights into the grain growth behavior of metal parts built by this AM technique and its understanding can be readily transferred to other sintering-assisted AM processes like binder jetting and ink writing for metal structure creation.

Ergodicity for two class stochastic partial differential equations with anisotropic viscosity

We prove the ergodicity on anisotropic space H˜0,1 for two class stochastic PDEs with anisotropic viscosity: the Navier–Stokes equations, the primitive equations. The Maslowski-Seidler theory and an asymptotic coupling argument are invoked to overcome several aspects challenges causing by the fact that systems only have partial dissipation and the strong nonlinearity construction.

Effect of Resin Bleed Out on Compaction Behavior of the Fiber Tow Gap Region during Automated Fiber Placement Manufacturing.

Automated fiber placement is a state-of-the-art manufacturing method which allows for precise control over layup design. However, AFP results in irregular morphology due to fiber tow deposition induced features such as tow gaps and overlaps. Factors such as the squeeze flow and resin bleed out, combined with large non-linear deformation, lead to morphological variability. To understand these complex interacting phenomena, a coupled multiphysics finite element framework was developed to simulate the compaction behavior around fiber tow gap regions, which consists of coupled chemo-rheological and flow-compaction analysis. The compaction analysis incorporated a visco-hyperelastic constitutive model with anisotropic tensorial prepreg viscosity, which depends on the resin degree of cure and local fiber orientation and volume fraction. The proposed methodology was validated using the compaction of unidirectional tows and layup with a fiber tow gap. The proposed approach considered the effect of resin bleed out into the gap region, leading to the formation of a resin-rich pocket with a complex non-uniform morphology.

Numerical and experimental study of two-vehicle overtaking process

The overtaking process between two simplified Ahmed body models is studied using a set of static experiments to provide a comparison basis for the numerical study. Both steady-state (static) and transient (dynamic) simulations are performed. There are notable differences of the drag and side force coefficients between the predicted and experimental results in the wake effects on the overtaking model as well as under a situation when two models are parallel for the static tests. These differences are attributed to the SST [Formula: see text] model, which is a two-equation Reynolds-averaged Navier-Stokes equation (RANS) turbulence model with an assumption of isotropic eddy viscosity, employed in the simulation. A more advanced turbulence model that simulates large-eddy organized motion in a turbulent flow and which uses an anisotropic eddy viscosity formulation in the near-wall flow subregion would increase the prediction accuracy for the overtaking simulation. A comparison of the results for the steady-state and the transient simulations at various relative velocity ratios ([Formula: see text]) shows that the quasi-steady approach is suited to simulate the dynamic two-vehicle overtaking process when the condition [Formula: see text] is met.

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Treatment for regularity of the Navier-Stokes equations based on Banach and Sobolev functional spaces coupled to anisotropic viscosity for analysis of vorticity transport

The mathematical analysis employed in this study constitutes an essential foundation for a broader investigation into the regularity of the Navier-Stokes Equations. Within this context, this work represents a significant advance with the Smagorinsky model integrated into the LES methodology. Using the Banach and Sobolev functional spaces, we developed a new theorem that points out a path towards the creation of an anisotropic viscosity model, formulated in the present work. Initially, our effort focuses on providing a comprehensive mathematical analysis, with the aim of promoting a deeper understanding of the challenge inherent in the regularity of the Navier-Stokes equations.

Turbulent Flow Analysis with Banach and Sobolev Spaces in the LES Method Incorporating the Smagorinsky Subgrid-Scale Model

The mathematical analysis, applied in this work, serves as a pillar for a broader investigation on the regularity of the Navier-Stokes Equations. In this context, this investigation marks a significant step forward in the advancement of the Smagorinsky model coupled with the LES methodology, resulting, based on the Banach and Sobolev Spaces, a new theorem that points the way to the construction of an anisotropic viscosity model (not yet discussed in the present work). At first, the effort dedicated here aims to present a more comprehensive mathematical analysis, promoting a more leveled understanding of the challenge posed by the regularity of the Navier-Stokes equations.

Rheological characterization and macroscopic modeling and simulation of the molding process of a PA6 Glass Mat Thermoplastic (GMT)

This study targets the characterization and modeling of GMT press molding. The targeted material is TEPEX® flowcore, a long glass fiber mat reinforced polyamide (PA6/GF) manufactured by Lanxess. Press molding of flowcore comprises the sequential stages of material forming and material flow, including challenges like local wrinkling and incomplete mold filling, respectively. Therefore, a sequential modeling approach using a Lagrangian and an Eulerian discretization is pursued. Rheological characterization using rheometer setups and in-mold viscosity measurements reveals a significant anisotropy of viscosity resulting from the predominantly in-plane fiber alignment. Anisotropy of viscosity is successfully modeled and parameterized, enabling a unified material modeling for material forming and material flow. Good predictions are observed for both wrinkling and flow. In summary, molding simulation results reveal that the isotropic modeling of viscosity is sufficient for flow simulation, whereas considering the anisotropic viscosity is essential for the accurate prediction of material forming.

Structural inheritance controlled by olivine viscous anisotropy in fossil mantle shear zones with different past kinematics

Geophysical and geological observations hint for the presence in the lithospheric mantle of both active and fossil shear zones with varied past kinematics. Shear in the lithospheric mantle produces olivine crystallographic preferred orientations (CPO), which lead to dependence of the viscous behavior on the direction of the load. Yet, the role of anisotropic viscosity in the mantle is seldom considered in models of structural reactivation. Here, we present 3-D geodynamic finite-element models that quantify the strain and viscosity distribution in a lithosphere containing a fossil thrust (or extensional) mantle shear zone with variable orientation relatively to a new extensional or compressional tectonics. The results were compared to that of a fossil strike-slip mantle shear zone. The fossil olivine CPO in the shear zone produces an anisotropic response of the lithospheric mantle, which is modelled using a parameterized description of viscous anisotropy derived from polycrystal plasticity simulations. We found that CPO-induced reactivation of fossil extensional or thrust mantle shear zones is favored for dips 30–60°, with maximum strain localization if the load is normal to the trend of a fossil shear zone dipping by 45°-50°. This represents a broader range of reactivation potential than in fossil strike-slip mantle shear zones. Both fossil shear zones trending at 45° to the imposed load are reactivated regardless of their dip. For a given viscous anisotropy in the lithospheric mantle (i.e., fossil shear zone orientation), the associated strain localization in the crust is always higher under extensional reactivation, where strain rates may be up to ∼100 times higher than those in the (isotropic) surrounding crust. These results imply that viscous anisotropy associated with fossil mantle shear zones plays a key role in large-scale structural reactivation during successive tectonic episodes, shaping the current lithospheric architecture, such as in the Pyrenees and Norwegian margin.

ON ASYMPTOTICS OF ATTRACTORS TO NAVIER-STOCKES SYSTEM IN ANISOTROPIC MEDIUM WITH SMALL PERIODIC OBSTACLES

The paper considers a two-dimensional system of Navier–Stokes equations in medium with anisotropic variable viscosity and periodic small obstacles. It is proved that the trajectory attractors of this system tend in a certain weak topology to the trajectory attractors of the averaged system of Navier–Stokes equations with an additional potential in a medium without obstacles.

Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity

Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity

Numerical Study of Shock Wave Boundary Layer Interaction Based on an Anisotropic Turbulence Model

This paper presents numerical simulations of incident oblique shock wave impinging on a flat plate with a turbulent boundary layer using a nonlinear anisotropic turbulence model. Three cases with different incident shock angles under the same free-stream Mach number are studied, including attachment flow, incipient separation flow and outstanding separation flows. Convection terms and diffusion terms are calculated using the third-order Roe’s flux difference splitting scheme and the second-order central difference scheme in the code, respectively. The Runge-Kutta time marching method is employed to solve the governing equations for steady state solutions. Comparisons between the simulated results and experimental data are carried out, which include density contours, pressure distribution, skin friction coefficients distribution and streamline vectors. To capture the essential behavior of this complex anisotropic turbulence separation flow caused by the shock-wave-boundary-layer-interaction (SWBLI), an anisotropic eddy viscosity tensor and a nonlinear Reynolds stress-strain constitutive relationship are used in this model. The anisotropic eddy viscosity tensor is composed of turbulent fluctuation velocity vector and characteristic length vector which are obtained by statistical partial average scheme. With proper modeling of anisotropic eddy viscosity tensor, the numerical results are in good agreement with the experimental data. It is worthy to point it out that the computation accuracy decreases with increasing interaction intensity.

Transformation hydrodynamic metamaterials: Rigorous arguments on form invariance and structural design with spatial variance.

Transformation optics has been a powerful tool to manipulate physical fields if the governing equationsin two spaces satisfy a certain form invariance. A recent interest has been applying this method to design hydrodynamic metamaterials described by the Navier-Stokes equations. However, transformation optics may not be applicable to such a general fluid model while especially the rigorous analysis is still absent. In this work, we give a definite criterion of the required form invariance, i.e., metric of one space and its affine connections that appear in curvilinear coordinates can be incorporated into material properties or interpreted by extra physical mechanisms introduced in another space. Based on this criterion, we prove that the Navier-Stokes equations, as well as its simplification in creeping flows (the Stokes equation), cannot be form invariant due to the redundant affine connections from their viscous terms. On the contrary, the creeping flows under the lubrication approximation, saying the classical Hele-Shaw model and its anisotropic counterpart, can retain the form of their governing equationsfor steady incompressible isothermal Newtonian fluids. Besides, we propose the design of multilayered structures with spatially varying cell depth to mimic the required anisotropic shear viscosity for modulating Hele-Shaw flows. Our results correct previous misunderstandings about the applicability of transformation optics under the Navier-Stokes equations, reveal the decisive role of lubrication approximation in maintaining form invariance (consistent with recent experiments featuring shallow configurations), and provide a feasible approach in experimental fabrication.

Moderate deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity

In this paper, we prove a central limit theorem and establish a moderate deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity. The proof for moderate deviation principle is based on the weak convergence approach.

Influence of fiber breakage on flow behavior in fiber length- and orientation-dependent injection molding simulations

• Orientation dependent fiber breakage modeling approach • Fiber length and orientation dependent flow modeling • Coupling of transient fiber breakage modeling and fiber dependent viscosity and flow modeling Injection molding is one of the most important processes for manufacturing discontinuous fiber reinforced polymers (FRPs). The matrix of FRPs shows a transient chemo-thermomechanical behavior and the fibers create anisotropy influencing physical properties. Hence, FRPs are complex materials, but also likely used in volume production. In this work, the fiber-induced anisotropic behavior during mold filling is modelled with an anisotropic fourth order viscosity tensor. The viscosity tensor takes second and fourth order fiber orientation tensor, fiber length and non-Newtonian matrix viscosity into account. In this way, the macroscopic simulation captures the influence of the flow field on the fiber re-orientation and vice versa. The fiber orientation tensor is used to determine reference fibers in every element for calculation of hydrodynamic forces. This information is used in a novel fiber breakage model, based on buckling of fibers in Jeffery's orbit. The result is a macroscopic molding simulation with not only transient fiber orientation distribution, but also fiber length distribution. Due to the anisotropic viscosity tensor, the predicted fiber breakage influences the material's viscosity and flow behavior, which is also visible in the simulated cavity pressure. The results are validated with injection molding experiments, performed with a glass fiber reinforced phenolic compound, showing good agreement.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.