Elongational Flow Research Articles

Spontaneous symmetry breaking in two dimensions under non-equilibrium laminar flows

Abstract We study the long-range order in two dimensions, where an order parameter is advected by laminar flows such as rotational, shear and elongational flows. Under these flows, we analyze the ordered state of the O(N) scalar model in the large-N limit. We show that the stability of the ordered state depends on the flow pattern; shear and elongational flows stabilize the long-range order but rotational flow does not. We discuss the physical mechanism underlying our results by connecting static correlations between fluctuations and their dynamics based on the interaction representation used in quantum mechanics. We find that advective transport induces superdiffusion under shear and elongational flows, thereby stabilizing the long-range order.

Tribological and Hygroscopic Behavior of Polybutylene Terephthalate/Acrylonitrile Styrene Acrylate (PBT/ASA) Nanocomposites with Graphene Nanofiller

Fogging in automotive headlamps is a significant issue that affects both aesthetics and functionality. This study investigates the use of graphene-based nanocomposites to mitigate fogging by enhancing the hygroscopic properties of polybutylene terephthalate/acrylonitrile styrene acrylate (PBT/ASA) composites commonly used in headlamps. The incorporation of functionalized graphene improved the tensile and flexural strength of the nanocomposites, though it led to a reduction in elongation and melt flow. Additionally, the solid lubrication properties and increased surface hardness of the graphene contributed to enhanced wear resistance. The presence of graphene in the nanocomposites also reduced moisture diffusion, lowering the rates of both hygroscopic and desorption when compared to commercial PBT/ASA composites. Furthermore, the nanocomposites exhibited a reduction in maximum moisture uptake. These improvements are expected to reduce the absolute humidity inside the headlamp, thereby effectively mitigating the fogging issue.

Exploring interfacial tension role in the laminar morphology development in reactive compatibilized PP/EVOH

AbstractLaminar-like structures in PP/EVOH (80/20 wt%) blends were developed by in situ reactive compatibilization using a co-rotating intermeshing twin-screw extrusion without the imposition of post-die-forming elongation flows, i.e., draw ratio (DR) = 0. For that, a maleic anhydride-grafted homopolymer polypropylene (PP-g-MA) was added at 1, 1.5, and 3 wt% using a simple mixing protocol. The correlation between the laminar morphology observed via SEM with interfacial parameters was conducted by nonlinear regression of PP/EVOH viscoelastic response (Gʹ and Gʹʹ) applying the Monomodal Palierne Model to estimate interfacial tension. Uncompatibilized PP/EVOH formed a droplet-matrix morphology with high interfacial tension, indicating incompatibility. As PP-g-MA is added, a laminar-like structure is developed. The remaining droplets become smaller at higher content, with lower interfacial tension between the phases. This scenario hampers the stratification of the dispersed phase. At 3 wt% of PP-g-MA, the morphology returns to being a droplet-matrix, although with high adhesion between the phases. Graphical abstract

Understanding the effect of physical aging on slip dynamics in soft-glassy materials using pure elongation flow

Slip over a solid surface is a very common occurrence in industrial scale transport and the processing of complex fluids. The knowledge of slip also plays a huge role in the correct estimation of rheological properties. In this work, we have studied the slip dynamics in a model soft-glassy material that exhibits physical aging, wherein the structure evolves gradually toward a more solid-like character via rearrangement of constituents. More precisely, we have investigated the impact of physical aging on slip associated with pure elongation flow of the material. We have allowed the sample to age over different waiting times, followed by the sample being deformed slowly in elongation mode by pulling the top plate to achieve a pure elongation flow. Normal force as a function of gap has been recorded during such pure elongation. These normal force–gap curves demonstrated a remarkable gap-waiting time superposition, manifesting the strong signature of self-similarity in the pure elongation flow of the soft-glassy system. We have adopted a slip layer model, which predicted these normal force–gap flow curves remarkably well. Such prediction also rendered slip layer thickness as a function of waiting time, using which we have explained the intriguing self-similar nature of normal force–gap dependence. Finally, we have established a relationship between the slip layer thickness and the age-dependent bulk rheological properties. We have provided a possible physical reasoning to explain this link between the physical aging-driven state of material and the slip dynamics.

Mixing screw design and high density polyethylene toughening modification for recycled polypropylene based on screw 3D printing

AbstractThe recycling of waste plastics primarily involves physical modification and the addition of modifiers, often utilizing equipment such as twin‐screw extruders for miscible modification. Considering the widespread use of single‐screw 3D printing, improving the mixing efficiency of the single‐screw is crucial to achieve a “one‐stop” recycling modification that is suitable for 3D printing. This paper introduces a 3D printer equipped with a mixing screw (MS) and compares it with a conventional screw (CS). We conduct numerical simulations to investigate the pressure build‐up capacity, velocity streamline distribution, and the mixing effect of the MS. The mechanical properties, thermal characteristics, and molecular orientation of the recycled Polypropylene (rPP) and high density polyethylene (HDPE) mixture are investigated through experiments. The results show that the MS provides more effective elongational flows compared to the CS by breaking down the reinforcing materials into smaller particles. Additionally, toughening and modification experiments are performed on rPP and HDPE. The composites treated with the MS showed improved elongation at break (increased by ~111%), a stable melt crystallization temperature, and an enhanced mixing effect. This study on single‐screw 3D printers lays the groundwork for streamlining the plastic recycling process and increasing the reuse rate of recycled plastics.

Simulating the dynamics of a 2D multicomponent vesicle in time-dependent elongation flow

Abstract This paper is concerned with the nonlinear dynamics of multicomponent vesicles in a time-dependent elongational flow. Using a nonstiff, pseudospectral boundary integral method, we investigate the dynamical patterns induced by negative surface tension and inhomogeneous bending for a two phases system. For both quasi-circular and elongated vesicles, high frequency wrinkles can be excited in flow with strong elongational rate after the flow’s direction is reversed. Unevenly distributed phase diagram leads to asymmetric wrinkling pattern, and the characteristic wavelength for each phase is well reserved. In weak flow, bucking behaviours are observed for elongated vesicles and the membrane bends inward at regions with lower bending moduli.

Enhancing the thermal conductivity of polystyrene/polyamide 6/graphene nanoplatelets composites through elongational flow

Migration and distribution of thermal conduct fillers in polymer blend are key factors in the preparation of enhanced thermal conductivity composite. In this study, polystyrene(PS)/polyamides 6(PA6)/graphene nanoplatelets(GNPs) composites with enhanced thermal conductivity were prepared under elongational flow, and the migration and distribution of GNPs were investigated by molecular dynamics simulation and experiments. The results showed that when GNPs immigrate from PA6 phase to PS phase, the elongational flow caused the orientation of the PS phase and GNPs, reducing the migration rate of GNPs from the PA6 phase to the PS phase. At the same time, the stretching viscosity of the PS phase increases, which prevents GNPs entering the PS phase. As a result, GNPs remain within the PA6 phase near the interface of the two phases. The effective distribution density of GNPs increased, making it easier for them to interconnect and form thermal conduction paths, thereby improving the thermal conductivity of the composites. Particularly, the composite prepared under the elongational flow with the 50/50 vol ratio of PS/PA6, the in-plane thermal conductivity of PS/PA6/GNPs composites reached a maximum of 1.64 W/(m·K).

Scalable In-situ Microfibrillar dielectric films: Achieving exceptional energy density and efficiency

It is a formidable challenge to develop a feasible strategy for the scalable fabrication of all-organic dielectrics with simultaneous improvements in both discharged energy density (Ud) and efficiency (η). Herein, an innovative technology of “melting extrusion-hot stretching-quenching” was put forward for the large-scale preparation of all-organic polymer dielectric films, where polymethyl methacrylate (PMMA) was miscible with polyvinylidene fluoride (PVDF) to form single dispersed phase in the polypropylene (PP) matrix and in-situ transformed into microfibrils with the aid of elongational flow field. Thereby, a simultaneous enhancement in the dielectric constant and breakdown strength was achieved and the as-prepared PP-based all-polymer dielectric film exhibited an unprecedented ultrahigh Ud of 9.6 J cm−3 and an exceptional η of 90.9 %. Experimental verification and computational simulation confirmed that the formation of highly oriented PMMA/PVDF microfibrils and well-aligned interfaces are constructive to enhancing breakdown strength by suppressing electric field distortion. The highly oriented dipoles in PVDF and PMMA, coupled with the eliminated ferroelectric behavior of PVDF, synergistically contributed to the heightened Ud and η. The approach presented in this work opens up a promising avenue for the large-scale production of all-organic capacitor films with enhanced Ud and η, heralding a new era of advanced dielectric materials.

Inducing melt elongation flow and controlling cooling temperature facilitate the texturization of high-moisture soy protein extrudates

The texturization of high-moisture extrudates is crucial for assessing their texture and palatability. Inducing melt elongation flow and controlling cooling temperature are effective strategies for improving protein texturization in the cooling zone. In this study, a multihole die assembly composed of an 89-hole plate and a cooling die was employed for the high-moisture extrusion of soy proteins. The morphology, textural characteristics, and water distribution of the resulting extrudates at different cooling temperatures were investigated. The results showed that the utilization of a multihole die significantly increased the texturization degree of the extrudates by approximately 30%. Extrudates produced at a cooling temperature of 40 °C exhibited anisotropic and fiber-rich structures. These extrudates had superior elasticity and chewiness compared to conventionally extruded proteins, and they also displayed even water distribution in the textured protein matrices. The acquired knowledge would offer valuable insights into the cooling-induced protein texturization facilitated by multihole die technology, which holds significance for the structural design of plant-based meat analogs.

Enhanced carbon black exfoliation through elongational flows for faster and higher value-added rubber recycling

The recycling of rubber featuring intricate three-dimensional crosslinked networks necessitates the application of cutting-edge technology and specialized machinery. In this study, the rubber was recycled by mechanochemistry under elongational flow field. The crosslink bonds in the rubber were rapidly broken through the high extension of molecular chains, without the need for additives or additional refinements. At 200 °C, the waste rubber is devulcanized in only 2 min so that the sol molecular weight reached an impressive 3.3 × 104 g/mol, and the mechanical properties of the reclaimed rubber were significantly enhanced, reaching a tensile strength of 17.44 MPa. The elongational flow field devulcanizes the waste rubber while simultaneously achieving rapid refinement of rubber particles and exfoliating the carbon black from the crosslinked network. These making reclaimed rubber forms a micro-nano microstructure in natural rubber (NR), which makes particle reinforcement of the NR-matrix. Faster and high-value-added rubber recycling achieved successfully through elongational flows.

Mixing and Thermal Transport Behavior in a Pin or Non-Pin Extruder Equipped with a Field Synergy Elongation Screw.

The ductile forming process of a polymer in a standard screw extruder and pin-barrel extruder, equipped with or without a field synergy elongation screw, was investigated by the finite element method. In order to assess the mixing and heat transfer capabilities of screws, characteristic parameters such as the mixing efficiency, segregation scale, and temperature distribution of different structures were analyzed and compared. The results indicated that the flow pattern of the polymer melt in the extruder was significantly influenced by the screw structure and was improved by the newly designed field synergy screw configuration, which brought a desirable elongational flow to enhance the radial convection. This was attributed to the unique radial wedge-shaped repeated convergence region of the field synergy elongation screw, increasing the synergistic effect between the velocity field, velocity gradient field, and temperature gradient field and thus improving the heat transfer and mixing efficiency. After adding barrel pins, the flow was forced to split, resulting in a more significant stretching effect on the melt. The field synergy effect in the pin mixed region was strengthened, which further increased the heat and mass transfer efficiency of the screw. However, increasing barrel pins could also lead to undesired temperature fluctuation and flow resistance, which have a negative impact on the melt uniformity. This study offers an important reference for optimizing screw structure to obtain strong mixing and heat transfer performances.

Experimental study on the continuous preparation of high‐performance thermal conductivity CNTs/EG/SSBR composite based on the shear and elongation flow fields with the assistance of the silanization reaction

AbstractA self‐developed Serial Rubber Continuous Mixing Device (SRCMD) based on the shear and elongation flow fields was adopted to continuously prepare the carbon nanotubes (CNTs)/expanded graphite (EG)/Solution‐polymerized styrene butadiene rubber (SSBR) composite. Meanwhile, the silanization reaction between the Silica and Si69 was introduced to improve the performance of the CNTs/EG/SSBR composite. When comparing the sample prepared using the two‐stage mixing process based on the shear flow field in the internal mixer, the continuously prepared CNTs/EG/SSBR composite with 3 wt% CNTs and 15 wt% EG demonstrates a higher thermal conductivity of 1.32 W/m·K. At the same time, it exhibits significant advantages in terms of mechanical properties, processability and dispersion rating. In addition, the mechanism for the continuous preparation of CNTs/EG/SSBR composite was revealed through visual experiments. This study aims to achieve the real continuous production of high‐performance thermally conductive polymer composites to meet the urgent demand for thermal conductivity materials in 5G technology.Highlights Real continuous preparation of CNTs/EG/SSBR composite was realized. The silanization index of 92.26% between Silica and Si69 was achieved. Good silanization promotes the construction of thermal conductivity networks. High‐performance CNTs/EG/SSBR composite with low Payne effect was obtained.

Preparation and properties of thermoplastic starch under the synergism of ultrasonic and elongational rheology

Thermoplastic starch, as an eco-friendly alternative to petroleum-based plastics, possesses numerous advantages, including cost-effectiveness, complete biodegradability, and renewable sourcing. Nevertheless, the plasticizer dispersion and starch plasticization efficiency are poor via the processing method dominate by shear deformation. Thus, the aim of this study is proposing a new approach combining ultrasonic treatment and elongational rheology to prepare thermoplastic starch and evaluate its properties. This innovative approach facilitated the production of thermoplastic starch with glycerol as the plasticizer at varying rotor speeds. Furthermore, this study was carried out by using a self-developed ultrasonic-assisted vane mixer (UVM) based on elongational flow. The samples were analyzed using FTIR, WAXD, polarized optical microscope, dynamic rheometer, universal testing machine and thermogravimetric analysis. FTIR and dynamic rheological analysis showed that elongational rheology and ultrasonics stimulate hydrogen bond formation between starch and glycerol, elevating starch thermoplasticity. Tensile tests and thermogravimetric analysis highlighted that high-intensity elongational field improved the mechanical properties and thermal stability of the thermoplastic starch. Additionally, the incorporation of ultrasonic treatment yielded further improvements, yielding remarkable tensile strength (6.09 MPa) and elongation at break (139.3 %). This synergistic interplay between ultrasonics and elongational rheology holds immense potential for advancing thermoplastic starch manufacturing.

Influence of plasticity on inertialess viscoelastic instabilities in elongational flow regimes

Influence of plasticity on inertialess viscoelastic instabilities in elongational flow regimes

Enhancing dynamic mixing and heat transfer of polymer by inducing ductile flow applying field synergy principle

An innovative and effective approach for screw design and optimization has been proposed, derived from multi-field synergy to address a growing challenge affected by the inadequate mixing and thermal management in plasticizing process of extrusion or injection. Dimensionless field synergy equations for incompressible non-Newtonian viscous polymers were established, and subsequently, two new types of screw structures—field synergy torsion element (FST) and field synergy elongation element (FSE)—were designed, fabricated, and validated through both simulation and experiment. Spiral and elongational flows were established in the newly designed screws owing to their unique structures of torsion channel and convergent channel, promoting the shear and stretch ductile deformations of polymer melt, documented to be a meaningful progress on flow patterns generated by conventional screw. A comparative investigation in this work of the newly designed screw with a conventional one showed that the newly proposed screws equipped with FSTs or FSEs performed better mixing and improved heat transfer and thermal uniformity. Multi-field synergy analysis revealed that the spiral and elongational flow enhanced the radial convection, improved the dependence of velocity and velocity gradient fields to facilitate melt stretching deformation as well as the dependence of velocity and temperature gradient fields to achieve heat transfer enhancement.

Mechanosensitive membrane domains regulate calcium entry in arterial endothelial cells to protect against inflammation.

Endothelial cells (ECs) in the descending aorta are exposed to high laminar shear stress, and this supports an anti-inflammatory phenotype. High laminar shear stress also induces flow-aligned cell elongation and front-rear polarity, but whether these are required for the anti-inflammatory phenotype is unclear. Here, we showed that Caveolin-1-rich microdomains polarize to the downstream end of ECs that are exposed to continuous high laminar flow. These microdomains were characterized by high membrane rigidity, filamentous actin (F-actin), and raft-associated lipids. Transient receptor potential vanilloid-type 4 (TRPV4) ion channels were ubiquitously expressed on the plasma membrane but mediated localized Ca2+ entry only at these microdomains where they physically interacted with clustered Caveolin-1. These focal Ca2+ bursts activated endothelial nitric oxide synthase (eNOS) within the confines of these domains. Importantly, we found that signaling at these domains required both cell body elongation and sustained flow. Finally, TRPV4 signaling at these domains was necessary and sufficient to suppress inflammatory gene expression, and exogenous activation of TRPV4 channels ameliorated the inflammatory response to stimuli both in vitro and in vivo. Our work revealed a polarized mechanosensitive signaling hub in arterial ECs that dampens inflammatory gene expression and promotes cell resilience.

Predicting maximum strain hardening factor in elongational flow of branched pom-pom polymers from polymer architecture

We present a model-driven predictive scheme for the uniaxial extensional viscosity and strain hardening of branched polymer melts, specifically for the pom-pom architecture, using the small amplitude oscillatory shear mastercurve and the polymer architecture. A pom-pom shaped polymer is the simplest architecture with at least two branching points, needed to induce strain hardening. It consists of two stars, each with q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q$$\\end{document} arms of the molecular weight Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document}, connected by a backbone of Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Despite the pom-pom constitutive model, experimental data of systematic investigations lack due to synthetic complexity. With an optimized approach, we synthesized polystyrene pom-pom model systems with systematically varied Mw,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,a}$$\\end{document} and Mw,b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${M}_{w,b}$$\\end{document}. Experimentally, we identify four characteristic strain rate dependent regimes of the extensional viscosity, which can be predicted from the rheological mastercurve. Furthermore, we find that the industrially important maximum strain hardening factor depends only on the arm number by [q2/ln(3q)]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[{q}^{2}/{{{{{\\mathrm{ln}}}}}}({\\sqrt{3}}q)]$$\\end{document}. This framework offers a model-based design of branched polymers with predictable melt flow behavior.

TTCF4LAMMPS: A toolkit for simulation of the non-equilibrium behaviour of molecular fluids at experimentally accessible shear rates

We present TTCF4LAMMPS, a toolkit for performing non-equilibrium molecular dynamics (NEMD) simulations to study the fluid behaviour at low shear rates using the LAMMPS software. By combining direct NEMD simulations and the transient-time correlation function (TTCF) technique, we study the fluid response to shear rates spanning 15 orders of magnitude. We present two examples for simple monatomic systems: one consisting of a bulk liquid and another with a liquid layer confined between two solid walls. The small bulk system is suitable for testing on personal computers, while the larger confined system requires high-performance computing (HPC) resources. We demonstrate that the TTCF formalism can successfully detect the system response for arbitrarily weak external fields. We provide a brief mathematical explanation for this feature. Although we showcase the method for simple monatomic systems, TTCF can be readily extended to study more complex molecular fluids. Moreover, in addition to shear flows, the method can be extended to investigate elongational or mixed flows as well as thermal or electric fields. The high computational cost needed for the method is offset by the two following benefits: i) the cost is independent of the magnitude of the external field, and ii) the simulations can be made highly efficient on HPC architectures by exploiting the parallel design of the algorithm. We expect the toolkit to be useful for computational researchers striving to study the nonequilibrium behaviour of fluids under experimentally-accessible conditions. Program summaryProgram title: TTCF4LAMMPSCPC Library link to program files:https://doi.org/10.17632/hh2rkcxbrf.1Developer's repository link:https://github.com/edwardsmith999/TTCF4LAMMPSLicensing provisions: GNU General Public License 3Programming language: Python 3Nature of problem: Measuring the nonequilibrium behaviour of bulk and confined fluids under experimentally accessible strain rates in non-equilibrium molecular dynamics (NEMD) simulations.Solution method: Creating a Python-based code that utilises the transient-time correlation function method and the LAMMPS software to enable the bulk fluid properties (e.g. viscosity) and confined fluid interfacial properties (e.g. shear stress and slip velocity) to be computed at low shear rates with NEMD.

Analysis on Isotropic and Anisotropic Samples of Polypropylene/Polyethyleneterephthalate Blend/Graphene Nanoplatelets Nanocomposites: Effects of a Rubbery Compatibilizer.

Over the past few years, polymer nanocomposites have garnered a significant amount of interest from both the scientific community and industry due to their remarkable versatility and wide range of potential uses in various fields, including automotive, electronics, medicine, textiles and environmental applications. In this regard, this study focuses on the influence of a compatibilizer rubber on a nanocomposite incorporating graphene nanoparticles (GNPs), with a polymer matrix based on a blend of polypropylene (PP) and polyethylene terephthalate (PET). This effect has been investigated on both isotropic samples and on anisotropic/spun fiber samples. The influence of the compatibilizer rubber on morphological, rheological and mechanical properties was analysed and discussed. Mechanical and morphological properties were evaluated on both isotropic samples obtained by compression moulding and melt-spun fibers. The addition of the rubbery compatibilizer increased the viscosity, improving interfacial adhesion, and the same effect was observed for the melt strength and breaking stretching ratios. Mechanical properties, including the elastic modulus, tensile strength and elongation at break, improved in both types of samples but more significantly in the fibers. These improvements were attributed to the orientation of the matrix, the formation of PET microfibrils, and the reduction in the size of graphene nanoparticles due to the action of the elongational flow. This reduction, facilitated by the elongation flow and the action of the compatibilizer, improved matrix-nanofiller adhesion due to the increased contact area between the two polymeric phases and between the filler and matrix. Finally, a transition from brittle to ductile behaviour was observed, particularly in the system with the compatibilizer, attributed to defect reduction and improved stress transmission.

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF’s unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5000\\,\ ext {s}^{-1}$$\\end{document}. We then use the theoretical model to predict VWF’s behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately 2000s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2000\\,\ ext {s}^{-1}$$\\end{document}, matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between 2000and3200s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2000\ ext { and }3200\\,\ ext {s}^{-1}$$\\end{document} depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.