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Journal of RheologyVolume 48, Issue 4 (Jul-Aug 2004) |
Contents
Influence of dispersed-phase elasticity on steady-state deformation and breakup of droplets in simple shearing flow of immiscible polymer blendsWanchai Lerdwijitjaruda), Anuvat Sinvatb), and Ronald G. Larsonc,d) a) Department of Materials Science and
Engineering b) Petroleum and Petrochemical College c) Department of Chemical Engineering AbstractThe effect of dispersed-phase elasticity on steady-state deformation and breakup of isolated droplets for polybutadiene/poly(dimethyl siloxane) blends in simple shearing flow is investigated systematically for values of the dispersed-phase Weissenberg number (Wid) ranging up to around 3, where the Weissenberg number is defined as the ratio of the first normal stress difference to twice the shear stress at the imposed shear rate. The dependence on droplet elasticity of steady-state morphology for 10%- dispersed phase blends is also studied. The polybutadiene droplet phase is an elastic “Boger” fluid prepared by dissolving a high-molecular-weight polybutadiene into a low-molecular-weight Newtonian polybutadiene melt. To isolate the contribution of droplet elasticity, all experiments were done at a fixed viscosity ratio of around unity, achieved by adjusting the temperature appropriately for each blend. When the droplet elasticity increases, the steady-state deformation of isolated droplets decreases for fixed capillary number. The critical capillary number for breakup (Cacrit) increases linearly with the Weissenberg number of the droplet phase (Wid) up to a value of Wid of around unity. When Wid is greater than unity, Cacrit seems to approach an asymptotic value of 0.95 for high values of Wid. For 10%-dispersed phase blends, the steady-state capillary number (Cass) calculated from a volume-averaged droplet diameter is less than the Cacrit for isolated droplets for the same blend. Cass increases monotomcally with the first normal stress difference of the droplet phase (N1d). Droplet widening in the vorticity direction is not observed even at droplet Weissenberg numbers much in excess of those for which widening is observed in blends of melts, suggesting that widening is strongly influenced by factors other than the first normal stress difference, such as shear thinning or second normal stress differences. d) Corresponding author. Stability analysis of injection molding flowsArjen C.B. Bogaerds, Martien A. Hulsen, Gerrit W. M. Peters, and Frank P. T. Baaijens Materials Technology (http://www.mate.tue.nl/) AbstractWe numerically investigate the stability problem of the injection molding process. It was indicated by Bulters and Schepens [Bulters M. and A. Schepens, “The origin of the surface defect ‘slip-stick’ on injection moulded products.”, Paper IL 3-2 in Proceedings of the 16th Annual Meeting of the Polymer Processing Society, Shang-hai (China), pp. 144-145] that surface defects of injection molded products may be attributed to a flow instability near the free surface during the filling stage of the mold. We examine the stability of this flow using the eXtended Pom-Pom (XPP) constitutive equations. The model allows for controlling the degree of strain hardening of the fluids without affecting the shear behavior considerably. To study the linear stability characteristics of the injection molding process we use a transient finite element algorithm that is able to efficiently handle time dependent viscoelastic flow problems and includes a free surface description to take perturbations of the computational domain into account. It is shown that the fountain flow, which is a model flow for the injection molding process, is subject to a viscoelastic instability. If the various rheologies are compared, we observe that the onset of unstable flow can be delayed by increasing the degree of strain hardening of the fluid (by increasing the number of arms in the Pom-Pom model). The most unstable disturbance which is obtained after exponential growth is a swirling flow near the fountain flow surface which is consistent with the experimental findings. Rheo-NMR of emulsion systemsK. G. Hollingsworth and M. L. Johnsa) Department of Chemical Engineering AbstractThis paper uses the technique of rheo-NMR (reviewed by Callaghan: Rep. Prog. Phys., 62, 599-670 (1999)) to perform a systematic study of emulsion rheology. Rheo-NMR uses NMR velocimetry to produce velocity maps, from which it is possible to quantify rheological parameters, with apparent wall slip being measured directly. The study is initially conducted on silicone oil-in-water emulsions. Xanthan gum, an important emulsion thickener and stabiliser in the food industry, is then investigated. Finally the technique is applied to a commercial mayonnaise, which is a complex product comprising a concentrated oil in water emulsion with various thickeners and stabilisers in the continuous phase. Rheological parameters (based on either a power-law fluid or a Hershel-Bulkley analysis) and apparent slip characteristics are extracted from the velocity maps for these materials, across a wide range of shear rates. Comparison with conventional rheological measurement and analysis is presented; reasonably good agreement is produced between the two methods. a) Corresponding author: Tel: +44 1223 334767; Fax: +44 1223 334796; E-mail address: mlj2l@cheng.cam.ac.uk Director reorientation of a side-chain liquid crystalline polymer under extensional flowRyan J. Cormiera), Claudia Schmidtb), and Paul T. Callaghana) a) MacDiarmid Institute for Advanced Materials
and Nanotechnology b) Fakultät für Naturwissenschaften AbstractWhen a nematic liquid crystal is subject to deformational flow, rotational torques arising from the Leslie viscosities lead to director realignment. In the case when a magnetic field is present these torques compete with the alignment torque associated with magnetic anisotropy. Under purely extensional flow, this competition results in a sudden director flip at a critical rate of strain given by ec-dot = caB02/m0|a3 + a2| where ca is the anisotropy of the magnetic susceptibility per unit volume of the liquid crystalline polymer, and a2 and a3 are viscosity coefficients arising from the anisotropic (or viscous) part of the stress tensor in the Leslie-Ericksen velocity equation. Using a four roll mill placed in the 7 T magnet of an NMR spectrometer, we have observed the orientation of the director, as a function of strain rate, for a flow aligning liquid crystalline polymer consisting of a polysiloxane backbone and mesogenic 4-methoxyphenyl-4'-butenyloxybenzoate side chains, the temperature being 348 K, just a few degrees below the nematic to isotropic transition. Director orientations were obtained using 2H NMR spectral splittings from a probe molecule species comprising < 10% methy1-(sulfoxide)-d6. A distinct director flip is observed at a value of strain rate measured by NMR velocimetry to be 0.037 s-1. From this value we determine |a2 + a3|/ca ~ 107 x 107 Pa s. Thickening effect in soluble hydrogen-bonding interpolymer complexes. Influence of pH and molecular parametersF. Bossarda,c) , M. Sotiropouloub), and G. Staikosb) a) Institute of Chemical Engineering and High
Temperature Chemical Processes b) Department of Chemical Engineering AbstractLinear and non-linear viscoelastic properties of poly(acrylic acid) (PAA) and poly(acrylic acid-co-2-acrylamido-2-methylpropane sulfonic acid)-graft-poly(N,N dimethylacrylamide) (P(AA-co-AMPSA)-g-PDMAM) mixtures have been investigated as a function of pH, the PDMAM content of the graft copolymer and the molecular weight of PAA. At pH < 3.75, strong hydrogen-bonding interpolymer complexation between PAA and PDMAM side chains in semidilute solution leads to the formation of a transient network, as the considerable increase in viscosity indicates. The sol/gel transition observed at pH = 2.0 by increasing the graft copolymer composition in PDMAM is explained by a substantial increase in the number of the junctions (stickers) resulting from the PDMAAM/PAA hydrogen bonding complexation. Moreover, the thickening effect observed is further strengthened by increasing the molecular weight of PAA, due to the inter-connection of more copolymer chains. c) Author to whom correspondence should be addressed; e-mail: bossard@iceht.forth.gr A semi-empirical approach for modeling charged soft microgel particlesTan B. H.b), Tam K. C.a,b,c), Lam Y. C.a,b), and Tan C. B.c) a) Singapore-MIT Alliance c) Dow Chemicals Pacific (Singapore) Pte Ltd AbstractWe describe a unified semi-empirical approach for predicting the viscosity of dilute and concentrated hard and soft sphere systems. A variable specific volume, k was introduced to convert the mass concentration to effective volume fraction. With increasing particle concentration, the concentration of free counter-ions in the solution can be large enough to induce an osmotic de-swelling of soft particles, resulting in the particle shrinkage. The viscosity data for four different microgel systems at different neutralization degree showed excellent agreement with the modified Krieger-Dougherty model. c) Corresponding author; e-mail: mkctam@ntu.edu.sg Broad frequency range characterization of molten polymersChunxia Hea,c), Paula Wood-Adamsb), and John M. Dealya,d) a) Department of Chemical Engineering b) Department of Mechanical and Industrial
Engineering AbstractWe report a technique for obtaining the continuous retardation spectrum or relaxation spectrum over a very broad range of relaxation times. The major challenge is to obtain reliable data at the long-time end of the spectrum. It is often not practical to use low-frequency oscillatory shear to obtain the necessary data because of the very long time required for the measurements. Polyoleflns pose special problems in long-time characterization, because time-temperature superposition is not very useful. Information about the long-time behavior can be obtained by means of creep experiments, but now another problem arises. If we use a stress sufficiently large to yield precise data, the strain may go beyond the limit of linear viscoelastic behavior before steady state is achieved. This problem can be addressed by eliminating the stress well before nonlinearity becomes a problem and tracking the resulting recovery. Using a method proposed by Meissner, the combined creep and recovery data can be used to construct the entire creep curve. The final challenge is to combine the data from the oscillatory shear and creep experiments to obtain a composite linear spectrum. We propose a new method for accomplishing this. Retardation spectra are inferred from both sets of data and compared to reveal the range of times over which both techniques provide reliable data and the range in which each technique is uniquely reliable. The two spectra can then be combined to form a composite spectrum, which can be used to calculate any linear material function. This procedure is demonstrated for two branched polypropylenes whose terminal zones could not be accessed by means of oscillatory shear. For each of these materials, we found that the spectra obtained by the two experimental techniques superposed perfectly within the region of overlapping experimental windows, making it possible to construct a reliable composite spectrum valid over a wide range of times. The composite continuous spectrum contains more detailed information about molecular structure than rheological properties, such as the complex modulus, that are derived from the spectrum by integration. c)
Present address: Department of Chemical Engineering, MIT, Cambridge, MA A model for post-flow induced crystallization: General equations and predictionsR. Zheng and P. K. Kennedy Moldflow Pty Ltd AbstractThe aim of this work is to model the flow-enhanced crystallization and the flow-induced morphological changes of semi-crystalline materials during and after shearing flow. A FENE-P dumbbell model and a rigid dumbbell model are used to describe the molecular chain conformation and the orientation evolution for the amorphous phase and the semi-crystalline phase, respectively. The effect of flow on crystallization is considered by relating excess free energy and flow-induced orientation to crystallization kinetics. The crystallization of the material couples back to influence the solidification rheology of the crystallizing system. An isotactic polypropylene is used as an example to illustrate model predictions. We predict a pronounced effect of short-term shear treatments in accelerating nucleation and changing rheological behavior. Results are compared with available experimental data. Monte Carlo simulation of steady extensional flowsc)Xianfeng Lia) and Morton M. Dennb,d) a) Department of Physiology & Biophysics b) Benjamin Levich Institute for Physico-Chemical
Hydrodynamics AbstractAn efficient nonequilibrium Monte Carlo method using the Bond Fluctuation Model is used to simulate uniaxial and planar extension of dilute polymer solutions. The time scale is obtained from the stress relaxation of a fully stretched chain and can be related to the longest relaxation time of a real molecule, while the length scale is taken to be the statistical Kuhn segment length. The method leads to t1 ~ N2.16 and D ~ N-1.02 for a freely draining chain with an excluded volume constraint, where t1, N, and D are the longest relaxation time, chain length, and diffusion coefficient, respectively. The finite extensibility of the bond causes extension thinning following the coil-stretch transition. The Monte Carlo predictions for the transient extension of isolated DNA molecules in a planar extensional flow agree reasonably well with published experimental measurements and Brownian dynamics simulations. “Molecular individualism” is observed in the unraveling of the polymer chain. c) The editorial process for this manuscript
was carried out by Editorial Board member Ronald Larson. The effect of long branches on the rheology of polypropylenec)A. D. Gotsisa,d), B. L. F. Zeevenhovena), and C. Tsenogloub) a) Delft University of Technology b) National Technical University of Athens AbstractIn order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts, using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this improves considerably the melt strength of the modified polymer. The zero shear viscosity and the elasticity as measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe the strain hardening of viscosity in the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening and melt strength are all related to the degree of long chain branching. c) Dedicated to W. W. Graessley on occasion
of his 70th birthday Large shear deformation of particle gels studied by Brownian Dynamics simulationsA. A. Rzepielaa), J. H. J. van Opheusdena,c) and T. van Vlietb) a) Mathematical and Statistical Methods Group b) Food Physics Group AbstractBrownian Dynamics (BD) simulations have been performed to study structure and rheology of particle gels under large shear deformation. The model incorporates soft spherical particles, and reversible flexible bond formation. Two different methods of shear deformation are discussed, namely affine and non-affine deformation, the second being novel in simulation studies of gels. Also two dynamic descriptions of the model are presented, with and without inertia effects. Non-affine deformation resulted in a slower increase of the stress at small deformation than affine deformation. At large deformation both models gave similar stress responses, although the inertia model resulted in lower stresses. The particle gels, regardless of the model used, were observed to fracture into lumps that compactified due to local reorganization. A reversible yielding transition, as observed in polymer gels, was not found. Fractal properties of the gels were irreversibly lost at large deformation. c) Author to whom all correspondence should be addressed. E-mail: Joost.vanOpheusden@wur.nl Visualization of individual DNA molecules in a small-scale coating flowRajat Duggal and Matteo Pasqualia) Department of Chemical Engineering AbstractIndividual DNA molecules in an ultradilute solution were observed with a fluorescence microscope, as they flow between a scaled-down rotating roll and a stationary glass knife. The roll picks up a thin layer of liquid from a pool and drags it to the knife, establishing a bead delimited by two menisci. At low roll speed the flow is premetered and recirculations are present. The DNA experiences a nearly rectilinear shear flow at the minimum gap position where there is a zero velocity surface. We report the mean and the distribution of fractional extension of DNA molecules here and show that the mean fractional extension asymptotes to 0.5, in agreement with the results of Smith et al. (1999). Interestingly, no polymer distortion is observed at the two menisci. At high roll speed, capillarity is not strong enough to drive a back flow; the big recirculation under the coverslip breaks into two smaller recirculations and two separation surfaces arise, upstream and downstream of the location of the minimum gap. At the upstream separation surface, most DNA molecules are extended parallel to the knife as they traverse the field of view. We report the distribution of DNA extension and shape in this flow region. Slow, nodular recirculations are present under the upstream and downstream free surfaces. Notably, most DNA molecules stretch axially as they move in these slow recirculating regions. a) Corresponding author; e-mail: mp@rice.edu |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 15 August 2004 |