Elongational Flow Research Articles

Steady elongational flow from rotarance theory

The physics of macromolecular orientation has been used to explain the elasticity of polymeric liquids. Specifically, by first sculpting a rigid bead–rod likeness of the macromolecule, we can then derive its hydrodynamic resistance to orientation. The solution for the orientation distribution function has then been used, by integration in phase space, to get rheological material functions in both (i) small- and (ii) large-amplitude oscillatory shear flow, including its limiting case, and (iii) steady shear flow. However, rheological material functions in steady homogeneous extension from rigid bead–rod theory remain elusive. In this paper, we derive the orientation distribution function, and the rheological material functions, for suspensions of general rigid bead–rod structures. We focus on the time-steady viscosities in extension, and we first do so for general extensional kinematics. We then obtain the viscosities in steady extension for (iv) uniaxial extension, (v) planar extension, and (vi) biaxial extension. We close with a worked example, in which we use our new result for the steady uniaxial extensional viscosity to build a bridge between the macromolecular theory and the Oldroyd framework for rheological constitutive models. We, thus, arrive at a constitutive equation whose parameters are deducible from the moments of inertia of the macromolecule, and thus, deducible from macromolecular architecture alone. Our model is accurate up to third order for time-independent flows and is accurate to second order for time-dependent ones.

A trade-off between hardness and stretchability of associative networks during the sol-to-gel transition

The trade-off between hardness and stretchability is a cornerstone of materials science. Balancing this trade-off is important in the molecular design of both chemical and physical networks. In this study, we report the quantitative trade-off at the molecular level for physical networks. Namely, we analyze, based on the reversible gelation model, a scaling relationship between the characteristic terminal relaxation modulus Gc in linear viscoelasticity and the stretch ratio λmax at the stress overshoot during the nonlinear elongation flow for unentangled randomly associative polymers, i.e., λmax ∼ Gc−0.17 and λmax ∼ Gc−0.33 in the mean-field and critical-percolation regimes, respectively. We use sulfonated polystyrene having different alkali counterions as a model system to test the relationship. The exponent of λmax ∼ Gc−0.25 seen in the experiment is in between the two theoretical values. We also discuss the quantitative deviation with respect to the size distribution of the network strands.

Linear, nonlinear rheological properties and foamability of Surlyn partially neutralized with sodium counterion

Linear viscoelasticity (LVE), elongational rheological behavior, and foamability are examined for ionomer samples based on a commercial Surlyn sample: The Surlyn sample is dialyzed back into the parent acid copolymer and partially neutralized by sodium hydroxide to different degrees. The LVE pseudo-master curves shift to the lower frequency with an increase in the molar fraction of sodium, reflecting the increased activation energy for ionic dissociation. Incorporation of this energy into the sticky-double-reptation model gives good prediction of the LVE behavior. The degree of strain hardening under the extensional flow exhibits a non-monotonous change: the transient hardening first intensifies with increasing the ion content up to ∼50 mol%, and then weakens upon further increasing the ion content. The foamability of these samples in supercritical CO2 appears to be controlled by the flowability as well as the melt strength during the elongational flow. In particular, the foaming T window widens greatly when the strain-hardening has been strengthened by the physical network based on the ionic interaction.

Modeling elongational viscosity of polystyrene Pom-Pom/linear and Pom-Pom/star blends

The elongational rheology of blends of a polystyrene (PS) Pom-Pom with two linear polystyrenes was recently reported by Hirschberg et al. (J. Rheol. 2023, 67:403–415). The Pom-Pom PS280k-2x22-22k with a self-entangled backbone (Mw,bb = 280 kg/mol) and 22 entangled sidearms (Mw,a = 22 kg/mol) at each of the two branch points was blended at weight fractions from 75 to 2 wt% with two linear polystyrenes (PS) having Mw of 43 kg/mol (PS43k) and 90 kg/mol (PS90k), respectively. While the pure Pom-Pom shows strong strain hardening in elongational flow (SHF > 100), strain hardening (SHF > 10) is still observed in Pom-Pom/linear blends containing only 2 wt% of Pom-Pom. The elongational start-up viscosities of the blends with Pom-Pom weight fractions above 10 wt% are well described by the Molecular Stress Function (MSF) model, however, requiring two nonlinear fit parameters. Here we show that quantitative and parameter-free modeling of the elongational viscosity data is possible by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model based on the concepts of hierarchical relaxation and dynamic dilution. In addition, we investigated the elongational viscosity of a blend consisting of 20 wt% Pom-Pom PS280k-2x22-22k and 80 wt% of a PS star with 11 arms of Mw,a = 25 kg/mol having a similar span molecular weight as PS43k and similar Mw,a as the Pom-Pom. This work might open up possibilities toward polymer upcycling of less-defined polymers by adding a polymer with optimized topology to gain the intended strain hardening, e.g., for film blowing applications.Graphical

Role of Rheology in Morphology Development and Advanced Processing of Thermoplastic Polymer Materials: A Review.

This review presents fundamental knowledge and recent advances pertaining to research on the role of rheology in polymer processing, highlights the knowledge gap between the function of rheology in various processing operations and the importance of rheology in the development, characterization, and assessment of the morphologies of polymeric materials, and offers ideas for enhancing the processabilities of polymeric materials in advanced processing operations. Rheology plays a crucial role in the morphological evolution of polymer blends and composites, influencing the type of morphology in the case of blends and the quality of dispersion in the cases of both blends and composites. The rheological characteristics of multiphase polymeric materials provide valuable information on the morphologies of these materials, thereby rendering rheology an important tool for morphological assessment. Although rheology extensively affects the processabilities of polymeric materials in all processing operations, this review focuses on the roles of rheology in film blowing, electrospinning, centrifugal jet spinning, and the three-dimensional printing of polymeric materials, which are advanced processing operations that have gained significant research interest. This review offers a comprehensive overview of the fundamentals of morphology development and the aforementioned processing techniques; moreover, it covers all vital aspects related to the tailoring of the rheological characteristics of polymeric materials for achieving superior morphologies and high processabilities of these materials in advanced processing operations. Thus, this article provides a direction for future advancements in polymer processing. Furthermore, the superiority of elongational flow over shear flow in enhancing the quality of dispersion in multiphase polymeric materials and the role of extensional rheology in the advanced processing operations of these materials, which have rarely been discussed in previous reviews, have been critically analyzed in this review. In summary, this article offers new insights into the use of rheology in material and product development during advanced polymer-processing operations.

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Structure-property correlation of polyvinyl alcohol films fabricated by different processing methods

Polyvinyl alcohol (PVA) films prepared by solution casting method or thermal processing techniques have been widely used in industrial applications. However, the relationship between processing methods and structural properties is still unclear. In this study, three film-forming techniques, namely solution casting, blown film extrusion and extrusion casting, were adopted to prepare PVA films and the influence of processing methods on the structural and physical properties of the films was studied. The results showed that blown film (BF) prepared under biaxial elongational flow had higher crystallinity, larger crystallite size and greater in-plane orientation compared to solution cast film (SCF) and extruded film (ETF). SCF showed the smallest crystallite size, slowest melting temperature, fewer defects, evident skin-core structure and in-plane orientation ascribing to its slow film forming process, stratified solidification and low initial macromolecular concentration. ETF displayed the lowest degree of crystallinity and orientation owing to the fast cooling outside the slit die and the absence of strong flow field. Hence, BF and SCF were endowed with high tensile strength (152.8 and 134.5 MPa), good puncture resistance (245.0 and 245.7 N/mm) and excellent oxygen barrier property (PO2 = 3.07 × 10−19 and 2.33 × 10−18 cm3 cm/(cm2·s·Pa)) while ETF exhibited inferior mechanical properties and oxygen barrier performance. These findings are of significance for building relationships between processing techniques, structural characteristics and practical properties of PVA films and help match appropriate film forming technology to the production of films for different application scenarios.

Image-based flow simulation of platelet aggregates under different shear rates.

Hemodynamics is crucial for the activation and aggregation of platelets in response to flow-induced shear. In this paper, a novel image-based computational model simulating blood flow through and around platelet aggregates is presented. The microstructure of aggregates was captured by two different modalities of microscopy images of in vitro whole blood perfusion experiments in microfluidic chambers coated with collagen. One set of images captured the geometry of the aggregate outline, while the other employed platelet labelling to infer the internal density. The platelet aggregates were modelled as a porous medium, the permeability of which was calculated with the Kozeny-Carman equation. The computational model was subsequently applied to study hemodynamics inside and around the platelet aggregates. The blood flow velocity, shear stress and kinetic force exerted on the aggregates were investigated and compared under 800 s-1, 1600 s-1 and 4000 s-1 wall shear rates. The advection-diffusion balance of agonist transport inside the platelet aggregates was also evaluated by local Péclet number. The findings show that the transport of agonists is not only affected by the shear rate but also significantly influenced by the microstructure of the aggregates. Moreover, large kinetic forces were found at the transition zone from shell to core of the aggregates, which could contribute to identifying the boundary between the shell and the core. The shear rate and the rate of elongation flow were investigated as well. The results imply that the emerging shapes of aggregates are highly correlated to the shear rate and the rate of elongation. The framework provides a way to incorporate the internal microstructure of the aggregates into the computational model and yields a better understanding of the hemodynamics and physiology of platelet aggregates, hence laying the foundation for predicting aggregation and deformation under different flow conditions.

Initial platelet aggregation in the complex shear environment of a punctured vessel model

To analyze flow conditions and cellular behavior at the onset of a hemostatic response in the injury of a microneedle-induced vessel puncture, a combined in silico and in vitro platform is created. A cell-resolved blood flow model is utilized for in-depth flow profile and cell distribution analyses, and a novel punctured vessel flow chamber is set up to complement the simulations with the evaluation of platelet aggregation around the wound neck of the puncture. The respective setups of the platform are explained, and the results of both experiments and simulations with various puncture diameters and pressure drops are combined, providing detailed insight into the basic processes of platelet transport and aggregation in the wound area. A special emphasis of the simulation evaluation is put on the cell distributions and the magnitude of shear rate and elongational flow in the wound neck area, as well as downstream from the puncture. Additionally, possible implications of wound size and pressure difference on the hemostatic response are discussed. The simulations display asymmetric cell distributions between the proximal and distal sides of the wound neck in regard to the flow direction. The flow chamber with the puncture diameter closest to the simulated domains confirms this asymmetry by displaying increased platelet aggregation at the wound neck's distal side. The presented punctured vessel in silico and in vitro experimental setups offer a platform to analyze the hemostatic environment of a vessel injured by a puncture and might assist in identifying differentiating factors between primary hemostasis and arterial thrombosis.

Analysis of viscoelastic flow past a square cylinder in a channel with sudden contraction

The present study examines the effectiveness of the geometric modification in stabilizing the viscoelastic (VE) fluid flow through a planar channel with 5:1 sudden contraction. The geometric modification employed in this study includes a square cylinder positioned in front of the contraction plane. The square cylinder pre-deforms the fluid before entering the contraction region. The cylinder causes elongational flow in the wake region as well as shear and elongational flow between the channel and cylinder walls, significantly changing the nature of the flow. We used the open-source software OpenFoam, which is based on the finite volume method, to solve the mass, momentum, and rheological stress-constitutive equations. The Oldroyd-B model mimics the rheological characteristics of the VE fluid. Our research demonstrates that the pre-deformation of VE fluid stabilizes flow in the Wi range of 0–4. Additionally, the salient corner vortex size in the Wi range of 6–10 is effectively reduced by the square cylinder with a blockage ratio of 0.30. Furthermore, the Pakdel–Mckinley stability criterion demonstrates that an increase in Wi beyond the critical value initiates elastic turbulence in the flow.

Investigating the influence of long chain branching and compositional changes of aliphatic-aromatic copolyesters on their rheological properties under shear and elongational flows

Investigating the influence of long chain branching and compositional changes of aliphatic-aromatic copolyesters on their rheological properties under shear and elongational flows

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

Strengthening-toughening pure poly(lactic acid) with ultra-transparency through increasing mesophase promoted by elongational flow field

Poly(lactic acid) (PLA), as a biodegradable material, finds wide applications in packaging, automotive, and biological industries. However, achieving high strength, toughness, ultra-transparency, and heat resistance simultaneously in pure PLA through continuous one-step manufacturing remains a significant challenge. In this study, we addressed this challenge by utilizing the eccentric rotor extruder (ERE) in combination with cooling rolls to manufacture PLA sheets with outstanding mechanical performance. The ERE's elongational flow field combined with the cooling roller's weak stretching action induced orientation in the PLA molecular chains and promoted the formation of more mesophase, significantly improving mechanical properties. When the extrusion-stretch ratio (λ) value was 3.5, the tensile yield strength, Young's modulus, and elongation at break of ERE-fabricated samples ER-3.5 reached 86.2 MPa, 1777 MPa, and 57.9 %, respectively. Compared to the SE-3.5 samples manufactured with traditional methods, the increases were 38.8 %, 25.8 %, and 9.4 times, respectively. Additionally, the ERE manufactured samples maintained ultra-transparency and high heat resistance, making them suitable for food packaging, biomedicine, and other related fields. This methodology provides an efficient industrial-scale approach for manufacturing neat, biodegradable PLA with outstanding mechanical performance and ultra-transparency.

Influence of PMMA brushes grafted from GO on rheological properties of PMMA/SAN immiscible blend in shear and elongation flow

In real technological processes, both shear and elongational flow is present. The material properties may differ significantly under both types of flow. Hence, they both define the final morphology and thus properties of the materials. In this work, the morphology of immiscible blends containing polymer hybrid particles was related to extensional rheological properties for the first time. The effect of various lengths of polymer brushes grafted from graphene oxide particles (GO) surface was investigated. As a polymer matrix the immiscible blend of poly(methyl methacrylate)/styrene-co-acrylonitrile (PMMA/SAN) was used. Thus the poly(methyl methacrylate) (PMMA) brushes grafted from GO (GO-g-PMMA) with various number average molar masses (Mn) of PMMA brushes with respect to chain entanglement limit of freely dispersed PMMA were prepared. The extensional rheological properties were affected by Mn of PMMA brushes, while the rheological properties in shear were unchanged. Transmission electron microscopy revealed the compatibilization effect for short densely grafted brushes with Mn of 10,300 g/mol, as smaller domains were observed. On the contrary, the higher Mn PMMA brushes facilitated coalescence. With increasing length of brushes, the elongational viscosity at low elongation rates (∼< 0.1 s−1) decreased, which facilitated the coalescence. The increase of viscosity at higher elongation rates (∼> 0.1 s−1) was not sufficient enough to cause fiber breakup and thus elongated domains were formed.

Elongational properties of liquids in contraction flow

Flows through contraction geometries (contraction flows) are found in many fields involving fluids, but they are poorly understood because they have two inseparable aspects as a whole: shear flow and elongational flow. In this paper, we focus on the center line of the contraction flow where the shear component vanishes because of the symmetry of the flow field and clarify elongational properties of liquids using the data obtained to date. First, we show images of contraction flows of water and dilute polymer solutions, and then, the continuity equation is used to obtain expressions for the center-line velocity. The expressions represent either the exponential contraction flow (ECF) or linear contraction flow (LCF) and agree well with experimental results obtained to date. It is suggested that the Deborah number plays an important role in deciding ECF or LCF. For dilute solutions of polyethylene oxide and polyacrylamide, the ratio of the elongational viscosity (μe) to the shear viscosity (μs) is found to be high, of the order of 104 and 103, respectively. On the other hand, molten polyethylene and 5.0-wt. % polyisobutylene in hydrocarbon tetradecane have greatly different values of μe and μs, but their values of μe/μs do not differ much from four. We propose a novel relaxation velocity number (RV) and find that the exponent ai of the ECF velocity-profile is correlated with log10RV for water, polymer solutions, and molten polyethylene. Furthermore, the expressions agree with experimental data for wet spinning. We propose a novel spinning model for the contraction flow of polymer solutions.

Generation of Tough Poly(glycolic acid) (PGA)/Poly(butylene succinate-co-butylene adipate) (PBSA) Films with High Gas Barrier Performance through In situ Nanofibrillation of PBSA under an Elongational Flow Field

Generation of Tough Poly(glycolic acid) (PGA)/Poly(butylene succinate-co-butylene adipate) (PBSA) Films with High Gas Barrier Performance through In situ Nanofibrillation of PBSA under an Elongational Flow Field

Atomistic Simulation of Flow-Induced Microphase Separation and Crystallization of an Entangled Polyethylene Melt Undergoing Uniaxial Elongational Flow and the Role of Kuhn Segment Extension.

Atomistic simulations of the linear, entangled polyethylene C1000H2002 melt undergoing steady-state and startup conditions of uniaxial elongational flow (UEF) over a wide range of flow strength were performed using a united-atom model for the atomic interactions between the methylene groups constituting the polymer macromolecules. Rheological, topological, and microstructural properties of these nonequilibrium viscoelastic materials were computed as functions of strain rate, focusing on regions of flow strength where flow-induced phase separation and flow-induced crystallization were evident. Results of the UEF simulations were compared with those of prior simulations of planar elongational flow, which revealed that uniaxial and planar flows exhibited essentially a universal behavior, although over strain rate ranges that were not completely equivalent. At intermediate flow strength, a purely configurational microphase separation was evident that manifested as a bicontinuous phase composed of regions of highly stretched molecules that enmeshed spheroidal domains of relatively coiled chains. At high flow strength, a flow-induced crystallization (FIC) occurred, producing a semicrystalline material possessing a high degree of crystallinity and primarily a monoclinic lattice structure. This FIC phase formed at a temperature (450 K) high above the quiescent melting point (≈400 K) and remained stable after cessation of flow for temperature at or below 435 K. Careful examination of the Kuhn segments constituting the polymer chains revealed that the FIC phase only formed once the Kuhn segments had become essentially fully extended under the UEF flow field. Thermodynamic properties such as the heat of fusion and heat capacity were estimated from the simulations and found to compare favorably with experimental values.

Design of thermal conductive polymer composites with precisely controlling graphene nanoplatelets at the interface of polypropylene and high melt strength polypropylene via elongation flow

AbstractThe migration and selective localization of graphene nanoplatelets (GNPs) in a polypropylene/high melt strength polypropylene (PP/HMSPP) blend under elongational and shear forces are studied. The effects of elongational flow upon the elongational rheology, X‐ray diffraction patterns, thermal properties, and mechanical properties are investigated. The results show that the elongational viscosity and melt strength of HMSPP are higher than those of PP under elongational flow, whereby HMSPP shows elongational strain hardening behavior, and the migrating of GNPs from the PP to the HMSPP phase is hindered. As a result, the GNPs are constrained to remain at the interface between the two phases. In addition, the elongational force can exfoliate GNPs more effectively, and the orientation of GNPs along the phase interface will reduce the migration rate of GNPs at the interface, while precisely controlling the location of the GNPs at the phase interface. Thus, more thermal conductivity pathways are constructed and, hence, the thermal conductivity of the PP/HMSPP/GNPs composite prepared under elongational flow is higher than that prepared under shear flow. The present work provides a new method for the preparation of highly thermally conductive polymer composites.

Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method.

We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler etal. [V. Kantsler etal., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.

Effect of polymer viscosity and viscoelasticity on tooth cooling and aerosolization during dental procedures

Cooling liquids used in ultrasonic scalers are aerosolized into droplets. Larger droplets splatter over dental practitioners and patients, and small aerosols become airborne, posing a health threat to people in the surrounding area if a patient is infected by viral or bacterial infections. Polyacrylic acid (PAA), polyethylene glycol (PEG), and polyvinylpyrrolidone (PVP) can efficiently cool teeth and suppress aerosolization owing to their rheological properties, with PAA being the superior viscoelastic suppressant. Although the solutions of PEG and PVP studied here are also efficient in suppressing aerosol formation, their high viscosity may hinder their supply to the dental tools because of high viscous dissipation. The rheological behavior of PAA, PEG, and PVP is studied in the uniaxial elongational flow in self-thinning capillary threads. Then, the behavior of these solutions in an ultrasonic scaler in dental practice is explored. In particular, the aerosolization phenomena and the corresponding aerosol size distributions and droplet trajectories are studied and compared. The tooth temperature is found to be similar to that of water when these polymer solutions are used. The dispersion of the aerosolized droplets is qualitatively demonstrated by performing scaling using model teeth on a phantom mannequin face.