 |
 |
|
|
 |
Journal of RheologyVolume 44, Issue 3 (May-June 2000) |
Contents
Brownian dynamics simulation of hard-sphere colloidal dispersionsDavid R. Foss and John F. Brady AbstractThe rheology of hard-sphere suspensions in the absence of hydrodynamic interactions is examined by Brownian Dynamics. Simulations are performed over a wide range of volume fraction, φ, and Péclet number, Pe = [γ-dot]a2/D, where [γ-dot] is the shear rate and D = kT/6πηa is the Stokes-Einstein diffusivity of an isolated spherical particle of radius a and thermal energy kT in a fluid of viscosity η. At low Pe, the viscosity decreases as Pe increases - the suspension shear thins. The first normal stress difference is positive, while the second normal stress difference is negative. Each normal stress difference vanishes at very low Pe and increases in magnitude to an extremum at Pe » 3. The suspension pressure is proportional to kT and is found to grow as Pe2 from its equilibrium value. Long-time self-diffusivities scale as D and grow as Pe is increased in this regime. At Pe » 100, the suspension undergoes a disorder-order transition to a microstructure of hexagonally-packed strings aligned in the flow direction, which is accompanied by precipitous drops in the viscosity, pressure and longtime self-diffusivities. At high Pe, all components of the stress tensor scale as η [γ-dot] and the diffusivities scale as [γ-dot]a2. Viscosity data for a wide range of φ and Pe are collapsed using scaling theories. Validation and application of a novel elongational device for polymer solutionsM. Stelter1, G. Brenn1, A. L. Yarin2, R. P. Singh3, and F. Durst1 1Lehrstuhl für Strömungsmechanik 2Faculty of Mechanical Engineering 3Materials
Science Centre, Indian Institute of Technology AbstractA novel elongational device is used to investigate the capillary thinning process of threads of dilute and semi-dilute aqueous polymer solutions. It is shown that the end regions of the threads do not play an essential role in the thinning process, so that a simple theory describing the self-thinning of the liquid thread is appropriate to describe the experiments with polymer solutions carried out with this device. Aqueous solutions of four different polymers (all polyacrylamide-based) are studied using the elongational device. It is shown that the elasticity of the polymers is dominated by polyacrylamide chains and that the effect of branching and topological structure of macromolecules is negligible. The time dependent decrease of the thread diameter can be divided into two stages. The first, viscoelastic one where macromolecular coils are stretched by the elongational flow, and the quasi-Newtonian one, where full stretching has already been achieved resulting in a very high but constant elongational viscosity. At the first stage the rheological behavior of the solutions studied is characterized by a constant relaxation time, whereas at the second one by a constant elongational viscosity. For polymer macromolecules of a relatively low stability, mechanical degradation of the molecules is found during their stretching in a self-thinning capillary thread. Investigating the morphology/rheology interrelationships in immiscible polymer blendsP. Martin, P. J. Carreau, and B.D. Favis R. Jérôme AbstractMorphological changes in immiscible polymer blends have been studied in shear flow using an original method based on quenching following deformation of molten samples. Relaxation effects were expected to be negligible during cooling and, hence, the real shear-induced blend microstructure could be analyzed. The method has been successfully applied to follow morphological changes of immiscible blends composed of polystyrene (PS) and relatively high amounts of high-density polyethylene (HDPE) during creep experiments. The final steady-state morphology appeared to be intimately related to the applied shear stress and total deformation. Coalescence as well as large deformation and orientation of the dispersed phase particles have been observed depending on the flow conditions. The variations with time of the blend rheological properties and morphological observations are in qualitative agreement. Bulk polymerisation of e-Caprolactone rheological predictive lawsJérôme Gimenez, Philippe Cassagnau, and Alain Michel AbstractThe rheological behavior during bulk polymerization of ε-Caprolactone with titanium tetrapropoxide as initiator was studied in connection with the kinetics of the reaction (conversion rate and molecular weight variations). The viscoelastic properties of the melt polycaprolactone performed by this reactive system was reasonably predicted using phenomenological models such as Yasuda-Carreau or relaxation spectrum models, and a molecular dynamic model based on a blending law of relaxation function. The evolution of these viscoelastic properties during bulk polymerization was calculated from the combination of these viscoelastic models with the kinetic laws of the system. Taking into account the dilution effect caused by the presence of monomer, a global rheological predictive model was then achieved. It was shown to give a reasonable depiction of the viscoelastic properties (½η*(t)½, G'(t) and G"('t)) whatever the processing conditions are (temperature, frequency, initiator concentration). Surface mobility and slip of polybutadiene melts in shear flow*Geoffrey M. Wise1, Morton M. Denn2,
and Alexis T. Bell Jimmy W. Mays, Kunlun Hong, and Hermis Iatrou3 1Present address: Procter and Gamble, 8256
Union Center Blvd 2Corresponding author. E-mail: denn@levdec.engr.ccny.cuny.edu 3Present
address: Department of Chemistry, University of Athens AbstractSurface mobility and wall slip of entangled polybutadiene melts were studied with attenuated-total-reflectance infrared spectroscopy at stresses characteristic of the sharkskin, spurt, and melt-fracture regimes. Small-scale slip, accompanied by an apparent decrease in transverse mobility, occurs in the sharkskin regime, but at a stress above the visual onset of sharkskin in capillary viscometry. Simulations cannot distinguish between a cohesive mechanism and a lubrication mechanism that might follow from a stress-induced phase transition, but an adhesive failure seems to be excluded. The near-surface length scale is of the order of four to six times the equilibrium root-mean-square end-to-end distance, and the estimated slip velocity is insensitive to molecular weight. Strong slip occurs in the spurt regime, either at the wall or within one radius-of-gyration. Substantial apparent slip occurs with a fluorocarbon surface, but the mechanism does not appear to be an adhesive failure; there seems to be a substantial decrease in the friction coefficient of chains over a distance of order 300 nm or more from the fluorocarbon surface, and the transverse chain mobility in this region appears to be enhanced rather than retarded. Overall, the results of this study indicate that the influence of the wall extends farther into the sheared melt than would be expected from the chain dimensions, except in the case of strong slip. *The editorial process for this manuscript was carried out by Editorial Board member Jean-Michel Piau. Simple shearing flow of dry soap foams with TCP structureDouglas A. Reinelt Andrew M. Kraynik AbstractThe microrheology of dry soap foams subjected to quasistatic, simple shearing flow is analyzed. Two different monodisperse foams with tetrahedrally close-packed (TCP) structure are examined: Weaire-Phelan (A15) and Friauf-Laves (C15). The elastic-plastic response is evaluated by using the Surface Evolver to calculate foam structures that minimize total surface area at each value of strain. The foam geometry and macroscopic stress are piecewise continuous functions of strain. The stress scales as T/V1/3 where T is surface tension and V is cell volume. Each discontinuity corresponds to large changes in foam geometry and topology that restore equilibrium to unstable configurations that violate Plateau's laws. The instabilities occur when the length of an edge on a polyhedral foam cell vanishes. The length can tend to zero smoothly or abruptly with strain. The abrupt case occurs when a small increase in strain changes the energy profile in the neighborhood of a foam structure from a local minimum to a saddle point, which can lead to symmetry-breaking bifurcations. In general, the new structure associated with each stable solution branch results from an avalanche of local topology changes called T1 transitions. Each T1 cascade produces different cell neighbors, reduces surface energy, and provides an irreversible, film-level mechanism for plastic yield behavior. Stress-strain curves and average stresses are evaluated by examining foam orientations that admit strain-periodic behavior. For some orientations, the deformation cycle includes Kelvin cells instead of the original TCP structure; but the foam does not remain perfectly ordered. Bifurcations during subsequent T1 cascades lead to disorder and can even cause strain localization. How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometerGareth H. McKinley and Anubhav Tripathi AbstractThe liquid filament microrheometer originally described by Bazilevsky et al. (1990) provides a simple way of extracting material parameters for Newtonian and viscoelastic fluids from measurements of the capillary breakup of a thin fluid thread. However, there is an unresolved discrepancy in the value of the Newtonian viscosity obtained from the experimental data when using the existing theoretical analysis. We demonstrate how to correctly analyze measurements of the midpoint radius and present a simple formula that enables one to obtain quantitative values for the Newtonian viscosity for a range of viscous fluids. The validity of this correction is supported by numerical simulations and experiments with a number of viscous Newtonian fluids. In addition we analyze the role of gravitational body forces on modifying the dynamics of capillary thinning of a Newtonian liquid filament. Finally, we show how such capillary breakup devices may be used to make quantitative time-resolved measurements of changes in the viscosity of hygroscopic materials or fluids with a volatile solvent component that are exposed to an ambient atmosphere. Dynamic mechanical properties of gelling colloidal disksStéphane Cocard, Jean François
Tassin, Taco Nicolai AbstractThe viscoelastic properties of gelling Laponite clay suspensions were studied by measuring the time evolution of the frequency dependent shear modulus. At a well defined gel time the loss and storage modulus have a power law frequency dependence with the same exponent Δ=0.55. The exponent is compared with theoretical predictions for fully flexible and locally rigid gels. After the gel point the shear modulus continues to evolve and a stable state was not reached in the experiments. The loss modulus of the gel increases with decreasing frequency at low frequencies indicating the presence of slow relaxation processes. The rate of gelation increases strongly with increasing ionic strength. Temperature dependent instabilities in the capillary flow of a metallocene LLDPE meltJosé Pérez-González1,2,
Lourdes de Vargas2, Vladimír Pavlínekl, 1Technical University of
Brno, Faculty of Technology in Zlín 2 Departamento de Física,
Escuela Superior de Física y Matemáticas *Corresponding author. E-mail: saha@zlin.vutbr.cz AbstractThe capillary flow behavior of a metallocene linear low density polyethylene (mLLDPE) was studied in a wide temperature range. The critical shear stress for the onset of the unstable spurt flow was found to be dependent on temperature in a non-linear fashion and it showed a minimum value at a critical temperature, at which unusually long period pressure oscillations were observed. For temperatures above the critical one, the observed decrease of the critical shear stress with decreasing temperature is explained on the basis of an increase in the distance between entanglements. At temperatures below the critical one, the increase in the critical shear stress and the eventual suppression of pressure oscillations as the temperature is further decreased are suggested to be the result of a flow-induced phase change that ends on complete crystallization and suppression of flow. The flow-induced crystallization phenomenon and the extrudate quality were dependent on the contraction ratio. Elimination of surface extrudate distortions took place at low temperatures when using a contraction ratio of 30; this fact can be attributed to the flow-induced phase change. Finally, a decrease in the activation energy for flow or "easy flow" was observed at temperatures below the critical one. Such "easy flow" is perhaps the precursor of the "temperature window" of low flow resistance reported by Keller and co-workers. The rheology of systems containing rigid spheres suspended in both viscous and viscoelastic media, studied by Stokesian Dynamics simulationsH. M. Schaink1, J. J. M. Slot2, R. J. J. Jongschaap1, and J. Mellema1 1 J. M. Burgers Centre, Rheology Group,
Faculty of Applied Physics 2 Department for Physical, Analytical and
Computational Chemistry AbstractAn extensive Stokesian Dynamics study is presented of the rheological behavior of suspensions of rigid spheres subjected to an oscillating shear strain. Two types of suspensions are considered: 1) rigid spheres in a viscous medium, and 2) rigid spheres in a viscoelastic medium. For this last system we need to extend the Stokesian Dynamics method, which was originally developed by Brady and Bossis for particles suspended in a viscous medium. The derivation of the necessary equations for these extended Stokesian Dynamics simulations is given. In this derivation we use the well known correspondence principle and apply it to the set of equations for the hydrodynamic forces and stresslets that are valid for spheres suspended in a viscous medium. Then using Fourier transformation we obtain differential equations for these forces and stresslets in the viscoelastic case. The contribution of the Brownian motion of the spheres to the bulk stress is found to be independent of the viscoelastic properties of the suspending medium. As an example of a viscoelastic medium we have chosen the Maxwell fluid. In our computer simulations we have calculated both elastic and viscous moduli and compared these results with experimental data. For the case of spheres suspended in a viscous medium we find that the elastic modulus reaches a plateau at high frequencies. Finally we present a simple analytical model which reproduces accurately the hydrodynamic contribution to the viscosity of spheres suspended in a Maxwell medium. This model is used to interpret the experimental results of Aral and Kaylon (Aral and Kaylon, 1997) that were obtained at Peclet numbers currently inaccessible to Stokesian Dynamics simulations. Predictive model of the turbulent flow of dilute gas-particulate suspension in a vertical pipeYuri A. Sergeev* and David C. Swailes *Corresponding Author. E-mail: yuri.sergeev@ncl.ac.uk AbstractA Chapman-Enskog closure approximation for the third order fluctuating velocity correlations in the particle phase of a turbulent dilute gas-particulate suspension is used to formulate the closed system of equations and boundary conditions for fully developed flow of dilute but densely loaded suspension of 'high-inertia' particles in a vertical pipe. The particle size and concentration are assumed to be sufficiently small so that direct interparticle interactions (e.g. collisions) can be neglected, and the main mechanism inducing particle velocity fluctuations is the interaction between particles and turbulent flow. The case of moderate gas pressure gradient is studied thus modeling a number of practical applications (e.g. riser flow). The resulting set of continuum equations, consisting of mass and momentum conservation and Reynolds stress equations for the particulate phase is free of empirical parameters. Although in a general case the effective stress in the particulate phase is anisotropic, the criterion is obtained showing that in a wide range of parameters typical for applications this anisotropy may be neglected, so that the equations for the individual diagonal components of the Reynolds stress tensor may be reduced to just one conservation equation for the particle fluctuation energy. The numerical solution shows the bifurcation of flow properties at a certain gas pressure gradient, thus providing an explicit criterion (i.e. a critical pressure gradient for the given total mass flux of solid particles) for upward particulate flow. The profiles of particle volume fraction and velocity are calculated, the former demonstrating the phenomenon of particle segregation towards the wall. A generalization of the model for the nearly developed flow is discussed, and an estimate is derived for the vertical distance required for the flow to become fully developed. Viscosity of polymer/solvent systems: Quantitative description on the basis of molecular surfacesMatthias Schnell and Bernhard A. Wolf * *E-mail: Bernhard.Wolf@Uni-Mainz.de AbstractA model for the description of the viscosity of polymer/solvent systems made up of homologues, developed earlier, is generalized to normal polymer solvent mixtures. It is based on three premises: (i) the dissipation of energy takes place at the molecular interfaces, (ii) the friction between solvent and solute varies with composition due to a change in the flow mechanism (drainage of coils), and (iii) the specific coil volume generally also depends on polymer concentration. The resulting simple expression contains four system-specific parameters: a geometric factor γ, which accounts for the differences of the surface to volume ratios of the components; a viscometric interaction parameter α, which measures the friction between solute and solvent in the case of fully draining polymer coils, [η], the specific hydrodynamic volume of the polymer at infinite dilution (intrinsic viscosity), and [η]Θ, the specific hydrodynamic volume under theta conditions. The suitability of this model is demonstrated by means of extensive experimental data reported in the literature for the systems diethyl phthalate/poly(vinyl acetate) and diethyl phthalate/poly(methyl acrylate). It appears worthwhile to mention that the evaluation yields [η] and [η]Θ, even in absence of information within the relevant composition range, and that there exists a linear correlation between γ and α. |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |