Normal Stress Difference Coefficient Research Articles

Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part 1: Effect of the polymer concentration

We study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function β, on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We compare the bulk rheology using immersed boundary simulations at Φ=2.5% and 5% to body-fitted single-particle simulations and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of β considered. However, as β decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect stretched polymers away from the particle surface. At low β, the polymer stress is diffuse, where the distribution of the particle induced fluid stress (PIFS) caused by the stretched polymers is spread out in the simulation domain rather than concentrated near the particle surface. Therefore in multiparticle simulations, the polymer stress can be significantly affected by particle-particle interactions. The stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower PIFS than that of the single-particle simulation. In addition, at increased volume fractions and low values of β, the polymer stress distribution on the particle surface shifts so as to increase the magnitude of the polymer stress moments, resulting in a shear-thickening stresslet contribution to the viscosity that is not seen in single particle or high β simulations. This result indicates that for suspensions in highly viscoelastic suspending fluids that are characterized by a low β parameter, hydrodynamic interactions are significant even at modest particle concentrations and fully resolved multiparticle simulations are necessary to understand the rheological behavior.

Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part II: Effect of a shear thinning suspending fluid

The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of β (solvent viscosity ratio) and finite values of α (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of β and finite values of α have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.

Rod-climbing rheometry revisited.

The rod-climbing or "Weissenberg" effect in which the free surface of a complex fluid climbs a thin rotating rod is a popular and convincing experiment demonstrating the existence of elasticity in polymeric fluids. The interface shape and steady-state climbing height depend on the rotation rate, fluid elasticity (through the presence of normal stresses), surface tension, and inertia. By solving the equations of motion in the low rotation rate limit for a second-order fluid, a mathematical relationship between the interface deflection and the fluid material functions, specifically the first and second normal stress differences, emerges. This relationship has been used in the past to measure the climbing constant, a combination of the first (Ψ1,0) and second (Ψ2,0) normal stress difference coefficients from experimental observations of rod-climbing in the low shear rate limit. However, a quantitative reconciliation of such observations with the capabilities of modern-day torsional rheometers is lacking. To this end, we combine rod-climbing experiments with both small amplitude oscillatory shear (SAOS) flow measurements and steady shear measurements of the first normal stress difference from commercial rheometers to quantify the values of both Ψ1,0 and Ψ2,0 for a series of polymer solutions. Furthermore, by retaining the oft-neglected inertial terms, we show that the "climbing constant"  = 0.5Ψ1,0 + 2Ψ2,0 can be measured even when the fluids, in fact, experience rod descending. A climbing condition derived by considering the competition between elasticity and inertial effects accurately predicts whether a fluid will undergo rod-climbing or rod-descending. Our results suggest a more general description, "rotating rod rheometry" instead of "rod-climbing rheometry", to be more apt and less restrictive. The analysis and observations presented in this study establish rotating rod rheometry combined with SAOS measurements as a prime candidate for measuring normal stress differences in complex fluids at low shear rates that are often below commercial rheometers' sensitivity limits.

Rheological characterization of complex fluids through a table-top 3D printer

3D printing is changing the way we conceive, design, and build 3D objects in mechanical, biomedical, aerospace, construction, automotive and maritime industries. In the current work, the nonlinear rheological behaviour of polymer melts is measured through a table-top 3D printer (3D RheoPrinter) that, smartly modified, allows inline investigation of viscosity, extrudate swell and melt fracture. By using a piezoresistive mini-transducer, the innovative system is designed to be applicable to all Fused Deposition Modelling (FDM) 3D printers by a simple and cost-effective modification of a state-of-art nozzle. The measurements of the nonlinear rheological behaviour are compared with traditional, rotational rheology. Two biodegradable polymers, i.e. polylactic acid and polycaprolactone, are investigated as model systems to test the 3D RheoPrinter. The results of the shear viscosity and the first normal stress difference coefficient, as function of shear rate, show a good agreement between the 3D RheoPrinter and rotational rheometer with an error of about 6% for a confidence interval of 96%. Moreover, the 3D RheoPrinter can still be used as 3D printer. In the last part of this work, it is presented a printing test for building 3D structures in which the results show controllable resolution by means of the measured rheological information such as the extrudate swell. The vision of this work is that an inline rheological characterization, possible with the developed 3D RheoPrinter, can enable automatic process optimization and quality assurance to the 3D printing community. The social and scientific impacts of this work are maximized by the cost-efficiency and simplicity of the design that makes it within reach of the general public. The 3D RheoPrinter opens for a rheological experimentation to a broad audience and it offers important insights to bring FDM to the next level of resolution.

A new slit‐radial die for simultaneously measuring steady state shear viscosity and first normal stress difference of viscoelastic liquids via capillary rheometry

AbstractA new slit‐radial die capable of simultaneously obtaining steady state shear viscosity and the average first normal stress difference coefficient via capillary rheometry has been developed. The steady state shear viscosity and average first normal stress difference coefficient are calculated in the slit part and radial part of the die, respectively. The steady state shear viscosity from the slit part of the slit‐radial die is compared to shear viscosities obtained from a capillary die and also the magnitude of the complex viscosity obtained from oscillatory shear experiment. The average value of first normal stress difference coefficient which is calculated in the radial part of the slit‐radial die is compared to first normal stress difference coefficient obtained from transient shear experiment in a cone‐plate geometry and the molecular stress function model predictions. The effect of variation of power law fitting parameters (consistency index, k and power law index, n) on average value of the first normal stress difference coefficient obtained from the radial part of the slit‐radial die is discussed. As this die has the shape of the city map of Karlsruhe it is named as Karlsruhe die.

Polymer branching and first normal stress differences in small‐amplitude oscillatory shear flow

AbstractGeneral rigid bead‐rod theory explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead‐rod theory, we relate the normal stress differences of polymeric liquids to the branch position on a backbone branched macromolecule. In this work, we explore the first normal stress differences coefficients of different axisymmetric polymer configurations. When non‐dimensionalized with the zero‐shear first normal stress difference coefficient, the normal stress differences depend solely on the dimensionless frequency. In this work, in this way, we compare and contrast the normal stress differences of macromolecular chains that are branched. We explore the effects of branch position, length, functionality, spacing, and multiplicity, along a straight chain, in addition to rings and star‐shaped macromolecules in small‐amplitude oscillatory shear flow.

Research of Polymer Melt Stability by Vibrating Based on Synergetics

A self-developed experimental facility by the national engineering research center of novel equipment for polymer processing, named as a coaxial barrel dynamic rheometer, is used to test the Weissenberg number and the first and the second normal stress difference coefficient for polymer melt and the effect of vibration parameters on them in vibration shear field. At the same time, it can be used the synergetics analysis method into explain the effects of elasticity stability of polymer melts. The testing principle of the rheometer is to transform the shear power of a motor and extrusion pressure in shear field to melt viscosity. The shear field can simulate orthogonal superposed vibratory flow, boundary vibrating pressure flow, and their combined flow. By comparing equation predictions with experimental results, a satisfied-qualitatively and reasonable-quantitatively predictive ability is shown, which verifies the work of mathematical derivations.

Mechanism of shear thickening in suspensions of rigid spheres in Boger fluids. Part II: Suspensions at finite concentration

The steady shear rheology of nondilute suspensions of noncolloidal, rigid spheres in highly elastic, constant viscosity fluids is studied via numerical simulation using three-dimensional, finite-volume methods and via experiments using cone-and-plate measurements. In the numerical study, we use an immersed boundary method to simulate an ensemble of particles as a function of time until they achieve steady average bulk properties, and the simulations include fully resolved particle-scale hydrodynamics and fluid stresses. The simulations show that for low volume fraction, nondilute suspensions, the viscosity thickens at high shear and this effect can be fully determined by considering a single particle’s interactions with the suspending fluid. In fact, we show that experimentally measured viscosities of suspensions up to ϕ∼0.25, where ϕ is the volume fraction of particles, can be characterized by a shift factor that determines the zero-shear viscosity and a master curve that describes the viscosity thickening. The master curve is determined by single particle–fluid interactions that depend critically on the extensional properties of the suspending fluid. Thus, the “per particle” thickening contribution to the viscosity, at large values of the Weissenberg number, is not dependent on particle–particle interactions when plotted versus the suspension stress. This “master curve” for the thickening of the shear viscosity is not only demonstrated in the simulations, but also we show that it is consistent with all available experimental data including our own. We show that the first normal stress difference coefficient can be described similarly by a shift factor and a master curve. Our numerical simulations do not quantitatively reproduce the experimental data and in general underpredict the experimentally measured shear-thickening of the rheological properties. We suggest, and provide supporting evidence, that this can be explained by the inability of the constitutive model employed in the simulations to adequately describe the extensional properties of the suspending fluid.

Steady-shear rheological properties for suspensions of axisymmetric particles in second-order fluids

Following Leal who gave the motion of a slender axisymmetric rod in a second-order fluid, we derived a complete rheological constitutive equation for dilute and semidilute slender rod suspensions in a viscoelastic solvent based on a cell model. Numerical solutions for the Fokker–Planck equation are obtained for simple shear flows at low and large Peclet numbers using a finite volume method, hence avoiding the need for closure approximations. The second normal stress difference coefficient of the solvent plays a non-negligible role in the particle contribution to the stress as well as on the rod orientation dynamics: a spread of the particle orientation in the flow-vorticity plane and an enhancement of the alignment along the vorticity direction are predicted when increasing the second normal stress difference coefficient. Brunn extended the Leal analysis to dumbbells and tri-dumbbells, for which both normal stress difference coefficients have to be considered. The original Pipkin diagram is finally modified to help guide the choice of relevant constitutive equations for particles in viscoelastic fluids.

Rheology of cubic particles suspended in a Newtonian fluid.

Many real-world industrial processes involve non-spherical particles suspended in a fluid medium. Knowledge of the flow behavior of these suspensions is essential for optimizing their transport properties and designing processing equipment. In the present work, we explore and report on the rheology of concentrated suspensions of cubic-shaped colloidal particles under steady and dynamic shear flow. These suspensions exhibit a rich non-Newtonian rheology that includes shear thickening and normal stress differences at high shear stresses. Scalings are proposed to connect the material properties of these suspensions of cubic particle to those measured for suspensions of spherical particles. Negative first normal stress differences indicate that lubrication hydrodynamic forces dominate the stress in the shear-thickened state. Accounting for the increased lubrication hydrodynamic interactions between the flat surfaces of the cubic particles allows for a quantitative comparison of the deviatoric stress in the shear-thickened state to that of spherical particles. New semi-empirical models for the viscosity and normal stress difference coefficients are presented for the shear-thickened state. The results of this study indicate that cubic particles offer new and unique opportunities to formulate colloidal dispersions for field-responsive materials.

Microstructure and rheology of soft to rigid shear-thickening colloidal suspensions

The shear rate-dependent rheological properties of soft to rigid colloidal suspensions are studied using computational models. We show that a contact force defined based on an elasto-hydrodynamic deformation theory captures an important rheological behavior of colloidal suspensions: While near hard-sphere particles exhibit a strong and continuous shear thickening the evolves to a constant viscosity state, soft suspensions undergo a second shear-thinning regime at high Peclet numbers when the hydrodynamic stresses become larger than the modulus of the colloidal particles. We measure N1 and N2 to be large and negative in the shear-thickening regime; however, for soft spheres at the onset of second shear-thinning N2 reduces in magnitude and eventually becomes positive. We show that for near hard-sphere suspensions, colloidal pressure, shear stress, and normal stress difference coefficients tend to diverge near the maximum packing fraction while P>σ>N1>N2.

Material properties of the shear-thickened state in concentrated near hard-sphere colloidal dispersions

Reversible shear thickening is common in concentrated dispersions of Brownian hard-spheres at high-shear rates. We confirm the existence of a well-defined colloidal shear-thickened state through experimental measurements of the shear stress and the first and second normal stress differences in the shear-thickened state as a function of the particle volume fraction for a model dispersion of near hard-spheres. The shear stress and normal stress differences are observed to grow linearly with the shear rate in the shear-thickened state and both normal stress differences are observed to be negative. Our experimental results show the shear-thickened state of colloidal dispersions can be described by three material properties—the shear viscosity and first and second normal stress difference coefficients—that are a function of the volume fraction. All three material properties are found to diverge with a power law scaling as (1−ϕϕmax)−2 close to maximum packing, ϕmax, which is found to be 0.54 ± 0.01. We find ηr,sts > ϒ2,sts > ϒ1,sts. These results are consistent with theoretical predictions for shear thickening by hydrocluster formation and quantitatively comparable to Stokesian Dynamics simulations. We further postulate and show that these material properties are consistent with those measured for non-Brownian suspensions.

Experiments research of polymer solution viscoelasticity

The rheological characteristic of polymer solution directly influences the oil displacement efficiency in the process of polymer flooding, and it is necessary that rheological characteristics of polymer solution used in polymer flooding are researched. Loss modulus and storage modulus of polymer solution with different mass concentration and relative molecular mass are studied and the relationship between them is analyzed through steady and dynamic shear experiments. The first normal stress difference at low angular rate is calculated based on loss modulus and storage modulus, and combined with the first normal stress difference obtained by steady shear flow experiments at high shear rate. The first normal stress differences at a wider range of shear rate can be obtained and the relationship between the first normal stress difference and shear rate is set up. The results show that the relationship established between the first normal stress difference and shear rate at wide range shear rate is feasible. The higher the mass concentration or the relative molecular mass of polymer solution is, the higher the first normal stress difference coefficient is.

Principles of polymer processing

1. History, Structural Formulation of the Field Through Elementary Steps, and Future Perspectives. 1.1 Historical Notes. 1.2 Current Polymer Processing Practice. 1.3 Analysis of Polymer Processing in Terms of Elementary Steps and Shaping Methods. 1.4 Future Perspectives: From Polymer Processing to Macromolecular Engineering. 2. The Balance Equations and Newtonian Fluid Dynamics. 2.1 Introduction. 2.2 The Balance Equations. 2.3 Reynolds Transport Theorem. 2.4 The Macroscopic Mass Balance and the Equation of Continuity. 2.5 The Macroscopic Linear Momentum Balance and the Equation of Motion. 2.6 The Stress Tensor. 2.7 The Rate of Strain Tensor. 2.8 Newtonian Fluids. 2.9 The Macroscopic Energy Balance and the Bernoulli and Thermal Energy Equations. 2.10 Mass Transport in Binary Mixtures and the Diffusion Equation. 2.11 Mathematical Modeling, Common Boundary Conditions, Common Simplifying Assumptions, and the Lubrication Approximation. 3. Polymer Rheology and Non-Newtonian Fluid Mechanics. 3.1 Rheological Behavior, Rheometry, and Rheological Material Functions of Polymer Melts. 3.2 Experimental Determination of the Viscosity and Normal Stress Difference Coefficients. 3.3 Polymer Melt Constitutive Equations Based on Continuum Mechanics. 3.4 Polymer Melt Constitutive Equations Based on Molecular Theories. 4. The Handling and Transporting of Polymer Particulate Solids. 4.1 Some Unique Properties of Particulate Solids. 4.2 Agglomeration. 4.3 Pressure Distribution in Bins and Hoppers. 4.4 Flow and Flow Instabilities in Hoppers. 4.5 Compaction. 4.6 Flow in Closed Conduits. 4.7 Mechanical Displacement Flow. 4.8 Steady Mechanical Displacement Flow Aided by Drag. 4.9 Steady Drag-induced Flow in Straight Channels. 4.10 The Discrete Element Method. 5. Melting. 5.1 Classification and Discussion of Melting Mechanisms. 5.2 Geometry, Boundary Conditions, and Physical Properties in Melting. 5.3 Conduction Melting without Melt Removal. 5.4 Moving Heat Sources. 5.5 Sintering. 5.6 Conduction Melting with Forced Melt Removal. 5.7 Drag-induced Melt Removal. 5.8 Pressure-induced Melt Removal. 5.9 Deformation Melting. 6. Pressurization and Pumping. 6.1 Classification of Pressurization Methods. 6.2 Synthesis of Pumping Machines from Basic Principles. 6.3 The Single Screw Extruder Pump. 6.4 Knife and Roll Coating, Calenders, and Roll Mills. 6.5 The Normal Stress Pump. 6.6 The Co-rotating Disk Pump. 6.7 Positive Displacement Pumps. 6.8 Twin Screw Extruder Pumps. 7. Mixing. 7.1 Basic Concepts and Mixing Mechanisms. 7.2 Mixing Equipment and Operations of Multicomponent and Multiphase Systems. 7.3 Distribution Functions. 7.4 Characterization of Mixtures. 7.5 Computational Analysis. 8. Devolatilization. 8.1 Introduction. 8.2 Devolatilization Equipment. 8.3 Devolatilization Mechanisms. 8.4 Thermodynamic Considerations of Devolatilization. 8.5 Diffusivity of Low Molecular Weight Components in Molten Polymers. 8.6 Boiling Phenomena: Nucleation. 8.7 Boiling-Foaming Mechanisms of Polymeric Melts. 8.8 Ultrasound-enhanced Devolatilization. 8.9 Bubble Growth. 8.10 Bubble Dynamics and Mass Transfer in Shear Flow. 8.11 Scanning Electron Microscopy Studies of Polymer Melt Devolatilization. 9. Single Rotor Machines. 9.1 Modeling of Processing Machines Using Elementary Steps. 9.2 The Single Screw Melt Extrusion Process. 9.3 The Single Screw Plasticating Extrusion Process. 9.4 The Co-rotating Disk Plasticating Processor. 10. Twin Screw and Twin Rotor Processing Equipment. 10.1 Types of Twin Screw and Twin Rotor-based Machines. 10.2 Counterrotating Twin Screw and Twin Rotor Machines. 10.3 Co-rotating, Fully Intermeshing Twin Screw Extruders. 11. Reactive Polymer Processing and Compounding. 11.1 Classes of Polymer Chain Modification Reactions, Carried out in Reactive Polymer Processing Equipment. 11.2 Reactor Classification. 11.3 Mixing Considerations in Multicomponent Miscible Reactive Polymer Processing Systems. 11.4 Reactive Processing of Multicomponent Immiscible and Compatibilized Immiscible Polymer Systems. 11.5 Polymer Compounding. 12. Die Forming. 12.1 Capillary Flow. 12.2 Elastic Effects in Capillary Flows. 12.3 Sheet Forming and Film Casting. 12.4 Tube, Blown Film, and Parison Forming. 12.5 Wire Coating. 12.6 Profile Extrusion. 13. Molding. 13.1 Injection Molding. 13.2 Reactive Injection Molding. 13.3 Compression Molding. 14. Stretch Shaping. 14.1 Fiber Spinning. 14.2 Film Blowing. 14.3 Blow Molding. 15. Calendering. 15.1 The Calendering Process. 15.2 Mathematical Modeling of Calendering. 15.3 Analysis of Calendering Using FEM. Appendix A: Rheological and Thermophysical Properties of Polymers. Appendix B: Conversion Tables to the International System of Units (SI). Appendix C: Notation. Author Index. Subject Index.

Rheo-optical measurements of the first and third normal stresses of homopolymer poly(vinyl methyl ether) melt

Normal stresses play a key role in polymer processing, yet accurate measurements are still challenging. Simultaneous rheo-optical measurements are conducted on a poly(vinyl methyl ether) homopolymer melt over a wide range of temperatures and oscillatory shear frequencies, in an effort to measure the normal stresses, by using quantitative flow birefringence measurements. The stress optical rule holds well for this polymer as expected, with the value of the stress optic coefficient of (6.38±0.19)×10−11 cm2/dyn at 30°C. The first and third normal stress difference coefficients\(\psi ^{ * }_{1} ,\psi ^{ * }_{3} \), calculated using a single memory constitutive equation applied to the stress and birefringence data, are in excellent agreement. The ratio of the measured third and first normal stress difference coefficients, (1−β)=0.71±0.05, agrees well with the result of the Doi–Edwards model with independent alignment approximation (β=0.28). The measurement of normal stress difference coefficients with such small deviations proves the robust nature of the improved rheo-optical instrument and its ability to measure complete stress tensor.

Rod‐climbing characteristics of α‐Fe2O3 suspended polyisobutylene/polybutene solution

AbstractFrom rod‐climbing rheometer measurements, we systematically investigated the normal stress values of suspended particles in polymeric liquids at low shear rates using the second‐order fluid constitutional relationship. The climbing constants β of the suspended α‐Fe2O3 particles in polyisobutylene/polybutene solutions, which exhibit Boger fluid characteristics (highly elastic, but no shear‐thinning), were estimated from the rod‐climbing experiment, showing that β increased with polymer concentration and polymer molecular weight. The first normal stress difference coefficient of the suspended α‐Fe2O3 in polymeric liquids obtained from the rod‐climbing rheometer was well correlated with the rheological properties measured by rotational rheometers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1548–1552, 2004

Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenes

The effects of sparse (<1 branch per chain) long-chain branching (LCB), molecular weight (MW), and molecular weight distribution on the shear rheological properties of commercial polyethylenes are often convoluted. In this paper a method for separating the effects of sparse LCB in metallocene-catalyzed polyethylenes (mPE) from those of molecular weight and its distribution based on time–molecular weight superposition is proposed. Four metallocene polyethylenes with degrees of long-chain branching [i.e., M of the arm (Ma) is greater than that for the onset of entanglements, Mc] as determined from dilute solution measurements ranging from zero (linear) to 0.79 LCB/104 CH2, along with a conventional Ziegler–Natta polymerized linear low-density polyethylene (LDPE), and a tubular free-radical polymerized LDPE are investigated. In general, it is observed that sparse LCB (for levels < 1.0 LCB/104 CH2) increases the zero shear viscosity, η0 (e.g., by a factor of 7) and decreases, but even to a greater degree, the critical shear rate (γ̇c) for the onset of shear thinning (e.g., by a factor of 100). The breadth of the molecular weight distribution just affects γ̇c but not η0 for the range of data used in this study. Furthermore, the dynamic storage modulus G′ shows similar enhancement at low frequencies as viscosity does, while the primary normal stress difference coefficient, Ψ1,0, exhibits a greater dependence on long-chain branching than that predicted from the zero-shear viscosity enhancement. The results for the mPEs are consistent with recent molecular theories for randomly branched molecules in that it is the spacing between branch points and not the number of branches at a point that is important. Furthermore, the results are consistent with the idea that the branches are located on the longest chains, and hence, have the greatest effects on the longest relaxation modes.

Viscometric functions for Hookean dumbbells with excluded volume and hydrodynamic interactions

The rheological properties of a dilute solution of polymers in a good solvent are predicted by incorporating excluded volume effects and hydrodynamic interactions into a Hookean dumbbell model. We use a narrow Gaussian repulsive potential between the beads of the dumbbell to model the effect of excluded volume. The linear viscoelastic relaxation modulus is estimated using Brownian dynamics simulations and a Green–Kubo relation. When excluded volume interactions dominate, a stretched-exponential function is shown to better describe the decay of the relaxation modulus with time, than a simple exponential decay. Although the excluded volume and hydrodynamic interactions are nonlinear phenomena, Brownian dynamics simulations show that their influence on viscosity and first normal stress difference coefficient is approximately additive. This linear coupling, however, is not true for the second normal stress difference coefficient. Results of Brownian dynamics simulations also show enhanced shear thinning as th...

1228 球とばねによる赤血球のモデル化と血液の定ずり流動解析

The blood flow in large arteries is commonly analyzed by means of the constitutive equations. However, it is not appropriate to use constitutive equations for small arteries because of the heterogeneity of the blood. In this paper, a new method to model an erythrocyte by using beads and springs is proposed as an alternative to analyze the blood flow. The behavior of a single erythrocyte is computed under a constant shear field. The rotating attitude of an erythrocyte, shear viscosity, normal stress difference coefficient and stress thinning are discussed. The results show that the bead-spring model appropriately can simulate the tank tread motion of an erythrocyte under a high shear field and stress thinning. It is therefore considered that the bead-spring erythrocyte model is able to consistently express blood characteristics.

Modeling of an Erythrocyte by Beads and Springs and the Numerical Analysis of Blood Flow under the Constant Shear Field.

The blood flow in large arteries is commonly analyzed by means of the constitutive equations. However, it is not appropriate to use constitutive equations for small arteries because of the heterogeneity of the blood. In this paper, a new method to model an erythrocyte by using beads and springs is proposed as an alternative to analyze the blood flow. The behavior of a single erythrocyte is computed under a constant shear field. The rotating attitude of an erythrocyte, shear viscosity, normal stress difference coefficient and stress thinning are discussed. The results show that the bead-spring model appropriately can simulate the tank tread motion of an erythrocyte under a high shear field and stress thinning. It is therefore considered that the bead-spring erythrocyte model is able to consistently express blood characteristics.