Krishnamurthy Jayaraman

Crossflow of elastic liquids through arrays of cylinders

Abstract The flow of a dilute solution of polyisobutylene in polybutene transverse to unidirectional arrays of cylinders has been investigated at Reynolds numbers less than 0.1. Two different arrays were used—a triangular pitch array and a rectangular pitch array. Both arrays have a porosity of 0.704, the same bed length and comprise identical cylinders. Steady state permeation experiments were run over a range of superficial velocities in both arrays, to study the onset of departure from Darcys law. The rheology of the fluid was evaluated in shear before and after each set of runs. While departures from Darcys law occurred in both arrays at similar values of Deborah number, mechanical degradation of the polymer solution was much more severe with the triangular pitch array than with the rectangular pitch array. Specifically, after several runs through the triangular array the relaxation time was halved while the change in viscosity was relatively minor; this reveals loss of the high molecular weight tail in the original polymer. This degradation was irrecoverable; no recovery was noted after two weeks. Measurements of molecular weight distribution on the same samples in Odells laboratory confirm that the highest molecular weight components are degraded. Finite element simulations of Stokes flow were carried out for the two different geometries to determine extensional strain rates along the flow direction in several regions. This was followed by calculations of polymer chain deformation in these regions, with the nonlinear elastic dumbbell model. These calculations reveal that the maximum stretch rate in the triangular pitch array occurs along the streamline joining the stagnation points on adjacent cylinders; this leads to nearly complete extension of the polymer chain at a nominal Deborah number of 1 in the triangular array. However, in the rectangular pitch array, the maximum stretch rate occurs along streamlines considerably removed from the stagnation points, and the polymer chains are not extended along those streamlines up to a Deborah number of 1.

Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders

Abstract The kinematics of viscous and viscoelastic liquid flows transverse to periodic arrays of circular cylinders have been studied experimentally at Reynolds numbers ranging from 0.039 to 0.5. Streak photography was used to observe the flow of a dilute polyisobutylene solution in polybutene, through square and hexagonal arrays with a porosity of 70%. Unsteady flow patterns were observed at Deborah numbers above 0.5 for the hexagonal array and at Deborah numbers above 1.5 for the square array. In the case of the square array, the asymmetry of the particle paths was particularly striking. The flow resistance corresponding to each photograph has been recorded; progressively increasing flow resistance is seen to correspond to progressively increasing unsteadiness and asymmetry in the flow patterns. The velocity profiles along selected streamline segments of another concentrated solution of polyisobutylene in decalin flowing through the same arrays, were recorded with a laser Doppler velocimeter. The Reynolds number was less than 0.01 in all the runs. At Deborah numbers up to one within the square array, the average stretch rate between rows of cylinders, determined experimentally and normalized with the nominal strain rate, increases by up to 50%. At Deborah numbers of 1–2 within the hexagonal array, the average stretch rate measured between stagnation points is the same as the corresponding value for the Stokes field. The flow field becomes unsteady with this fluid also, at Deborah numbers where the fRe product increases for both arrays.

The effect of polymer extensibility on crossflow of polymer solutions through cylinder arrays

The effects of fluid rheology on the pressure drop in flow transverse to periodic arrays of circular cylinders (porosity=0.7) have been evaluated experimentally with several polyisobutylene solutions, at low Reynolds numbers. Care was taken to avoid degradation of the polymer during the permeation experiments. Specifically, the connection between extensional viscosity behavior and the flow resistance through the arrays has been evaluated experimentally with three dilute solutions of different molecular weight polyisobutylenes in polybutene at the same concentration. Fiber spinning of these solutions indicates that the apparent Trouton ratio of polymer contributions, at higher Deborah numbers, is proportional to the molecular weight. At Deborah numbers between 2 and 5, the (fRe) product attains a different asymptotic limit in each case. The high Deborah number limit of (fRe) is proportional to molecular weight, similar to the apparent Trouton ratios obtained from fiber spinning. In contrast, the fRe data for a strongly shear thinning solution of polyisobutylene in decalin do not show an upper limit even at a Deborah number of 8, based on a strain rate dependent relaxation time. Fluctuations in the downstream pressure are observed for the Boger liquids above the onset Deborah number, indicating the presence of an elastic instability. Hence, the assumption of a steady flow field appears to be untenable for computing the viscoelastic flow resistance in such media.

Creep recovery of random ethylene-octene copolymer melts with varying comonomer content

This paper presents an investigation of the effects of varying comonomer content from 20 to 38 wt % in random ethylene-octene copolymers made with a metallocene catalyst on the melt rheology including transients in shear creep recovery from high strains. The copolymer with 20% octene appeared to be the same as that reported to be long-chain branched in the literature and was used as a reference material. The materials were characterized in oscillatory shear and shear creep at stresses ranging from 5 to 30 000 Pa. Van Gurp-Palmen plots prepared from dynamic modulus data and zero-shear viscosity values from creep tests at very low stress confirmed that the reference material was long-chain branched and established that long-chain branching was absent from the copolymer with the highest comonomer content. The steady state recoverable shear compliance values for the three copolymers were very close. However, following large shear deformations brought about at higher strain rates, strain recovery was reduced most significantly for the copolymer with the highest comonomer content where long-chain branching was absent. The reduction in recovery at short times was also most significant for this copolymer.

Isostatic and Quasi-Isostatic Methods for Determining the Permeability of Organic Vapors Through Barrier Membranes

Two test methods have been developed which provide quantitative and reliable values for the rate of diffusion of organic vapors through polymer membranes. Method I is based on a quasi-isostatic procedure and utilizes gas chromatography analysis for quantifying the amount of organic vapor that has permeated through the membrane. The permeability of a number of permeant/polymer membrane combinations was determined by this method, with studies being carried out at constant temperature and with varying permeant concentrations. The effect of permeant concentration on the permeability rate, P, permeability constant, P, the apparent diffusion coefficient, D a , and the limiting diffusion coefficient, D 0 , was determined for the diffusion of toluene vapor through oriented polypropylene, Saran, and a Saran-coated oriented polypropylene structure. Method II involved an isostatic procedure, in which a constant and low concentration of permeant is flowed through the upper cell chamber of a permeability cell. Simultaneously, nitrogen carrier gas (N 2 ) of a known flow rate is continually passed through the lower cell chamber of the permeability cell and is conveyed to a gas chromatograph by means of a computer-aided gas sampling valve. The methods developed allow determination of the diffusion of organic aroma constituents through barrier membranes under defined conditions including (1) temperature, (2) permeant concentration, (3) membrane thickness, (4) polymer morphology (percent crystallinity), and, (5) polymer thermal mechanical history (that is, degree orientation), and they will have significant utility in evaluating plastic packaging material for food packaging, particularly as plastics are showing increased usefulness as packaging for fresh and processed food products.

Micelle growth and clustering in blends of polystyrene and styrene-butadiene diblock copolymer

Abstract This paper presents an investigation of the morphology of blends containing 5 wt% styrene-butadiene diblock copolymer in a high-molecular-weight polystyrene matrix. Different samples of these blends were prepared by melt compounding in an extruder and by solvent casting. Transmission electron microscopy was used to determine their morphology. The extruded blend contained well dispersed, disc-shaped micelles of the diblock. The morphology of the solvent-cast blend was strikingly different, with onion-skinned structures of diblock copolymer that spanned up to several micrometres. However, upon annealing at 200°C, the morphology of the extruded blend and of the solvent-cast blend evolved towards the same relaxed state. The micelles became more spherical, grew in size and slowly agglomerated into cluster formations. The kinetics of this evolution were observed for the extruded blend. Micelle growth and clustering rates at 200°C and also at 180°C were determined by characterizing their size, shape and spatial distribution. The micelles became more spherical quickly and formed clusters over a longer time period. The changes in micelle shape became apparent in blends annealed at 180°C for as little as 5 min. The micelle clustering, however, was only evident in the blends annealed at 200°C. The rate of clustering was quantified by plots of nearest-neighbour distributions at different times. Analysis of these plots indicates a diffusion mechanism for the clustering. The results seem to support theoretical assertions of Semenov on dynamics of block-copolymer micelles in a high-molecular-weight polymer matrix.

A Network Model for Melt Rheology of Block Copolymers

A kinetic network model is developed for the viscoelastic behavior of block copolymer melts with spherical microdomains. This model accounts for the variation in density of the matrix polymer segments from the domain boundary to the outer interphase boundary, with a non‐Gaussian segment distribution involving one new parameter. Rate terms consistent with this assumption are used to obtain expressions for the stress transients as well as steady‐state stress in uniaxial elongational flows. This model predicts an apparent yield stress at low strain rates, that is most sensitive to the new parameter a. Comparison of available data with model predictions indicates that increasing domain concentration is described by increasing values of a in the model.

Stability of polymerizing liquid flow in porous media

ABSTRACT This paper examines the flow stability of a polymerizing liquid in an anisotropic porous medium. The polymerization reaction leads to an increasing viscosity along the flow direction, particularly behind the advancing resin/air front, and may cause the miscible displacement process to become unstable and uneven. A linearized stability analysis of the flow within the filled region behind the liquid / air interface has been conducted. This reveals that under a moderate adverse viscosity gradient, the polymerization reaction has the potential for stabilizing the flow process by damping out disturbances of wavelengths above a critical size. Guidelines are provided for adjusting the composition of the reacting liquid and the anisotropic medium permeability to stabilize the flow process.

Impact of the NSF State/Industry/University Cooperative Research Center on low-cost, high-speed polymer composites processing on the research and educational programs at Michigan State University

Abstract The objectives of the National Science Foundation (NSF) State of Michigan/Industry/University Cooperative Research Center on low-cost, high-speed polymer composites processing at Michigan State University (MSU) are design, development and deployment of technology and knowledge-based systems that will reduce costs of polymer composites processing by (a) insuring faster processes, (b) reducing component costs, and (c) reducing implementation times of new composite designs. Significant accomplishments have been made in research, education and technology transfer in the areas of novel processing, liquid molding, thermoplastic processing, intelligent design and process modeling, and interphases and joining. The Centers primary educational activities were supported by the National Institute of Standards and Technology-Advanced Technology Program (NIST-ATP) with General Motors and General Electric, and the Technology Reinvestment Project (TRP) with the University of Delaware and the US Department of Defense. The Centers role in the four-year NIST-ATP was to disseminate injection-molded thermoplastics design methodologies to automotive, appliance, computer and other key US industries. The program enabled the Center to develop course material, a CD-ROM design manual, and workshop materials on state of the art thermoplastics design knowledge. To date, hundreds of individuals have participated in the workshops, and the material developed in this program is being integrated into undergraduate, graduate and continuing education offerings. The TRP program brought together the NSF Center at MSU and the composite materials center at the University of Delaware (UD) in a collaborative composite materials education and training effort for the Department of Defense and the durable goods industry. Educational developments included incorporation of knowledge derived from the TRP program into 49 new or existing engineering courses (23 at MSU and 26 at UD); six experiments for a new teaching laboratory; four workshops; four videotaped instructional modules (two each for liquid molding RTM technology and the injection molding technology); interactive WEB-based simulations and tutorials; and development of knowledge-based software.

Defects in Resin Transfer Molded Plaques Due to Resin Age Distribution During Mold Filling

Abstract This paper examines the development and consequence of flow structures and possible defects arising in multiple shot injection or multiple-gated injection of two-component resins mixed in-line into a mold with and without fiber preforms. This work may also be relevant to the packing stage. Experiments were run where a premixed batch of vinyl ester resin with peroxide and tracer dye, displaces another older batch of premixed resin in a mold. Polymerization of resin as it flows through the preform during the filling stage sets up an increasing viscosity profile along the fluid filled region and viscous fingering is observed as expected. The types of flow patterns associated with this phenomenon have been explored with random and woven fibrous media packed in a clear mold. The molded plaques were cut up and tested in 3-point bend so that the flexural moduli of specimens with various flow structures could be compared. The flow structures observed include fingers with rounded ends and fingers with multiple tips. Such flow structures lead to regions in the plaques where ‘packets’ of fluid with different extents of polymerization due to differences in age are juxtaposed prior to gelation of the resin. It was found that finger structures with several sharply defined interfaces tended to decrease the value of the flex modulus by up to 32 %, depending on the preform characteristics. Multiple finger tips with diffuse boundaries do not seem to be detrimental to the flex modulus, but multiple tips with sharp boundaries have lowered the flex modulus by 32%.