Rheology of silicon carbide/vinyl ester nanocomposites

Silicon carbide (SiC) nanoparticles with no surface treatment raise the viscosity of a vinyl ester resin much more intensely than micrometer‐size SiC particles. An effective dispersant generally causes a reduction in the resin viscosity attributed to its surface‐active properties and thereby increases the maximum fraction of particles that can be introduced. This article assesses the rheological behavior of SiC‐nanoparticle‐filled vinyl ester resin systems with the Bingham, power‐law, Herschel–Bulkley, and Casson models. The maximum particle loading corresponding to infinite viscosity has been determined to be a 0.1 volume fraction with the (1 ? η_r^?1/2)–? dependence (where η_r is the relative viscosity and ? is the particle volume fraction). The optimum fractional weight percentage of the dispersants (wt % dispersant/wt % SiC) is around 40% for 30‐nm SiC nanoparticles, which is much higher than 1–3% for micrometer‐size particles. SiC nanoparticles at a concentration of 9.2 wt % (0.03 volume fraction) cause a fourfold increase in the resin viscosity. The addition of a dispersant at the optimum dosage lowers the viscosity of SiC/vinyl ester suspensions by 50%. The reduction in the viscosity is substantial to improve the processability of SiC/vinyl ester nanocomposites. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 4365–4371, 2006     

Viscosity of polydimethylsiloxane gum: Shear and temperature dependence from dynamic and capillary rheometry

The rheology of Dow Corning polydimethylsiloxane gum (PDMS/silicone gum) was studied over a time range of 10^?2 to 10⁵ s^?1 and a temperature range of 23–150°C using both capillary and dynamic rheometry. A low shear Newtonian region is observed at room temperature below 0.01 rad/s (increasing to 0.1 rad/s at 150°C) for which an Arrhenius activation energy for a viscous flow of 13.3 kJ/mol was determined. The Cox–Merz rule for merging of shear and complex viscosities is found to be valid up to 10 s^?1. Viscosity is found to be independent of temperature above 100 s^?1, where terminal power‐law flow is encountered. This is exhibited in the dynamic data as equal plateau moduli for the various temperature curves. Gross wall slippage is seen in capillary flows above approximately 100 s^?1, corresponding to a stress value of 70–100 kPa. Slip‐stick (spurt) flow is not observed. The viscosity data are best fitted by the Carreau–Yasuda model with a fitting parameter a of 0.7, a power‐law index n of 0.05 (low because of slip effect), and a zero shear viscosity of 32 kPa s at 23°C. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2533–2540, 2002     

Water‐soluble polymers. LXXXIII. Correlation of experimentally determined drag reduction efficiency and extensional viscosity of high molecular weight polymers in dilute aqueous solution

The extensional viscosity for aqueous solutions of high molecular weight poly(acrylamide) copolymers and poly(ethylene oxide) homopolymers was measured using a laboratory‐designed screen extensional rheometer. A Bingham model was developed to estimate the average local polymer coil extensional viscosity (η_coil). A strong correlation was found between the measured η_coil values and the polymer extensional viscosity predicted by a bead‐spring model. The dilute aqueous solution drag reduction was measured with a rotating disk instrument under conditions minimizing the effects of shear degradation. Extensional viscosity and drag reduction measurements were performed in deionized water and in 0.514M sodium chloride. The relative drag reduction efficiency values (Δ) in both solvents were found to strongly correlate with measured η_coil values. This is the first report of the accurate prediction of drag reduction behavior for a wide range of polymer types in various solvents from the independently measured molecular parameters η_coil and [η]C. The often‐used relative drag reduction efficiency expressed as the product of [η]C and Δ can now be replaced by the absolute drag reduction efficiency [η]Cη_coil. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1222–1231, 2001     

Compatibility,steady and dynamic rheological behaviors of polylactide/poly(ethylene glycol) blends

Understanding the rheological behavior of plasticized polylactide (PLA) contributed to the optimization of processing conditions and revealed the microstructure–property relationships. In this study, the morphological, thermal, steady and dynamic rheological properties of the PLA/poly(ethylene glycol) (PEG) blends were investigated by scanning electron microscope, differential scanning calorimeter, and capillary and dynamic rheometers, respectively. The results illuminated that the melt shear flow basically fitted the power law, whereas the temperature dependence of the apparent shear viscosity (η_a) or complex viscosity (η*) followed the Arrhenius equation. Both the neat PLA and PLA/PEG blends exhibited shear‐thinning behavior. Because the incorporation of PEG reduced the intermolecular forces and improved the mobility of the PLA chains, the η_a, η*, and storage and loss moduli of the PLA/PEG blends decreased. The PEG content (W_PEG) ranged from 0 to 10 wt %, both η_a and η* decreased significantly. However, the decrements of η_a and η* became unremarkable when W_PEG exceeded 10 wt %. The reason was attributed to the occurrence of phase separation, which resulted in the decrease in the plasticization and lubrication efficiencies. This study demonstrated that the addition of the right amount of PEG obviously improved the flow properties of PLA. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42919.     

Simplified theory for linear rheology of monodisperse linear polymers

A new version of the tube theory based on the de Gennes–Doi–Edwards reptation concept (reported in Likhtman and McLeish's work published in 2002) is evaluated, modified to allow for simplified computations, and used to study the relationship between zero‐shear viscosity and molecular weight for monodisperse entangled linear homopolymers. The Likhtman–McLeish model combines self‐consistent theories for contour length fluctuations and constraint release with reptation theory for monodisperse linear polymers. Because of the nature of the Rubinstein and Colby approach used for the treatment of constraint release, the related term is probabilistic and requires stochastic simulations for the calculation of the relaxation modulus G(t). This makes the Likhtman–McLeish model computationally difficult to use. In this work we solve this problem by generating an approximate closed‐form solution for the stochastic term. Then analytical integration of the relaxation modulus function G(t) provides an expression for the zero‐shear viscosity (η₀). Results of the computations of the zero‐shear viscosity and of the slope of η₀ versus molecular weight are compared with available experimental data for monodisperse entangled linear polystyrene and polyethylene (hydrogenated polybutadiene). The model is a major improvement over previous theoretical models, even if there is still some disagreement between the predictions and experimental data of the slope of η₀ versus molecular weight. The possibility of inferring monomer chemistry–dependent parameters from the zero‐shear viscosity remains a difficult task because of the introduction of a constraint‐release parameter. Nevertheless, the model is a useful tool for the prediction of linear viscoelasticity data. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 569–586, 2004     

Correlations between the Shape of Viscosity Functions and the Molecular Structure of Long‐Chain Branched Polyethylenes

The viscosity functions of long‐chain branched metallocene‐catalyzed ethene homopolymers and copolymers (LCB‐mPE) were described by an extended Carreau‐Yasuda model. The two characteristic relaxation times, λ₁ and λ₂, and the slope of the viscosity function between these two characteristic relaxation times can be correlated to the zero shear‐rate viscosity, η₀, and the molar mass . The characteristic relaxation times, λ₁ and λ₂ (describing the main curvatures of the viscosity function) exhibit a power law dependency on the molar mass, . The parameterization of the viscosity function can be used for a molecular characterization and flow simulations of various kinds.

     

Three‐Dimensional Simulation of Bubble Formation Through a Microchannel T‐Junction

Three‐dimensional simulations of bubble formation in Newtonian and non‐Newtonian fluids through a microchannel T‐junction are conducted by the volume‐of‐fluid method. For Newtonian fluids, the critical capillary number Ca for the transition of the bubble breakup mechanism is dependent on the velocity ratio between the two phases and the microchannel dimension. For the power law fluid, the bubble diameter decreases and the generation frequency increases with higher viscosity parameter K and power law index n. For a Bingham fluid, the viscous force plays a more important role in microbubble formation. Due to the yield stress τ_y, a high‐viscous region is developed in the central area of the channel and bubbles deform to a flat ellipsoid shape in this region. The bubble diameter and generation frequency are almost independent of K.     

Effect of concentration on apparent viscosity of a globular protein solution

The viscosity of a globular protein solution as a function of concentration was studied with a cone and plate viscometef (Ferranti-Shirley Viscometer System) using, β-lactoglobulin as a model. An aqueous buffer solution (pH 7, ionic strength 0.04) containing up to 40 percent protein was subjected to rates of shear between 800 and 17,000 sec^?1. Specific viscosity of β-lactoglobulin up to 10 weight percent was proportional to the weight concentration of protein in solution such that: η_s = η₀ [ 1+0.8 (weight percent concentration)] where η₀ and η_s are viscosity coefficients for the pure solvent and the solution, respectively. For 3-40 weight percent, a linear relation of shear rate and shear stress was observed at high shear rates. Linearity began at 3500, 4300, 6800, and 7000 see^?1 for 10, 20, 30 and 40 weight percent concentrations respectively. The apparent viscosity was lower below these critical shear rates.     

The effect of mesh refinement on the computation of entrance effects for shear-thinning fluids

The effect of mesh refinement on the finite element computation of velocity and pressure is assessed for the creeping flow of a power law fluid and a Carreau fluid through an axisymmetric sudden contraction. The emphasis is placed on the determination of the entrance pressure correction n_ent. The augmented Lagrangian formalism is used and the discretization of the variational problem is based on the Crouzeix-Raviart triangular element. For power-law fluids, it is found that fine meshes yield values of n_ent which are significantly lower than those obtained in previous numerical studies, especially for high shear-thinning fluids. A similar trend is observed in the Carreau model.     

Melt shear viscosity of PP/Al(OH)3/Mg(OH)2 flame retardant composites at high extrusion rates

The melt apparent shear viscosity (η_a) of polypropylene (PP) composites filled with aluminum hydroxide [Al(OH)₃] and magnesium hydroxide [Mg(OH)₂] was measured by means of a capillary rheometer under experimental conditions of temperature ranging from 180 to 200°C and apparent shear rate varying from 10 to 2 × 10³ s⁻¹, to identify the effects of the filler particle content and size on the melt viscosity. The results showed that the melt shear flow of the composites obeyed the power law and presented pseudoplastic behavior. The dependence of η_a on temperature was consistent with the Arrhenius equation. The sensitivity of η_a for the composite melts to temperature was greater than that of the unfilled PP, and weakened with increasing apparent shear rate. The η_a increased linearly with an increase of the weigh fraction of the flame retardant, especially in the low apparent shear rate region. The η_a of the composites decreased slightly with an increase of particle size of flame retardant. Moreover, the variation for the η_a with particle size of flame retardant was much less than with apparent shear rate under these test conditions. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

VISCOSITY OF BIOMATERIALS

Viscosity data for honey, corn oil, mayonnaise, yogourt, blood and banana puree have been analyzed using two Theological models: the Herschel-Bulkley model and a proposed model. The proposed model contains three parameters: a yield stress, a parameter having the units of time and a parameter having the units of viscosity.

The model parameters were obtained by non-linear regression and the proposed model was shown to compare favorably with the Herschel-Bulkley equation.

An Arrhenius-type of correlation could be verified between the viscosity of banana puree and the inverse of the temperature. Also, the time parameter (t₁) of the proposed model could be correlated with the temperature and the parameter η₁.

It is asserted that the proposed model should replace advantageously the commonly used Casson expression.     

Rheological characterization of carbon black/polystyrene solution systems

Steady‐shear measurements of suspensions of carbon blacks (CB) in polystyrene (PS)/di‐(butyl phthalate) (DBP) solution were investigated as a function of volume fraction (?) of CB to clarify the effect of the primary particle size and the structure of CB aggregates on the rheological properties. The suspensions show a typical shear‐thinning behavior in the range of a shear rate studied. The Casson model was applied to evaluate the viscosity at infinite of shear rate η_∞ and the yield stress σ_y for the suspensions. Relative viscosity η_∞/η_m, (η_m: medium viscosity) thus obtained was compared to the high‐frequency viscosity for the ideal hard‐sphere silica suspensions to evaluate the effective volume fraction ?_eff of CB aggregates. The ?_eff value was larger for the higher‐structure CB with higher DBP absorption value, irrespective of the primary particle size. The yield stress σ_y had almost the same ?_eff dependence for neutral furnace CB/(PS/DBP) suspensions, although it was larger for acetylene black (AcB)/(PS/DBP) suspensions. These results demonstrated that the effective volume fraction is the most important quantity to characterize the CB aggregates on the rheological properties. It was also found that the correction of the medium viscosity changes due to polymer adsorption on the CB surface is important since neutral furnace CB adsorbs PS polymers but AcB hardly adsorbs PS polymers in the solution. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Formation of dispersed phase in incompatible polymer blends: Interfacial and rheological effects

The formation of dispersed phase in blends of incompatible polymers during melt extrusion with a co-rotating twin screw extruder was studied, using nylon and polyester as the matrix and ethylene-propylene rubbers as the dispersed phase. A master curve is obtained, i.e., Gηmα/γ = 4p^±0.84, where G is the shear rate, γ the particle diameter, η the interfacial tension, η_m the matrix viscosity, η_d the dispersed-drop viscosity, and p = η_d/η_m. The plus (+) sign applies for p > 1, and the minus (?) sign for p < 1. Thus, the dispersed-drop size is directly proportional to the interfacial tension and the ±0.84 power of viscosity ratio. The dispersed drops are the smaller, when the interfacial tension is the lower and the viscosity ratio is the closer to unity. The interfacial tension is largely controlled by the polarities of the two phases, and can be varied over several orders of magnitude by using appropriate dispersants.     

EXACT ANALYSIS OF UNSTEADY CONVECTIVE DIFFUSION IN A SIMPLIFIED CROSS MODEL FLUID

The article presents the effect of non-Newtonian viscosity on the longitudinal dispersion of tracer molecules released in an incompressible viscous non-Newtonian fluid (known as the simplified Cross model fluid) under the action of a constant pressure gradient. The Gill and Sankarasubramanian model is used to solve the unsteady convection diffusion equation for all time periods. An exact expression is obtained for the longitudinal convection coefficient K ₁(η?), which shows the effect of the non-Newtonian parameter η? on the centerline coefficient. It is seen that the value of the K ₁(η?) for η? > 1 is always smaller than the corresponding value for a Newtonian fluid. Also, the longitudinal dispersion coefficient of the solute K ₂(τ, η?) is determined exactly. The results show that the K ₂(τ, η?) asymptotically reaches a stationary state after a certain time. The effect of the η? on the most dominant dispersion coefficient is clearly depicted. Finally, the axial distribution of the average concentration θ _m of the solute over the channel cross section is determined at a fixed instant after the solute injection for several values of the η?. The results for “pure convection” are also reported     

A single-mode rheological model for steady flows of polymer melts

The steady shear viscosity (η_s), the steady first normal stress coefficient (Ψ₁), the steady second normal stress coefficient (Ψ₂), and extensional viscosity (η_e) are four important parameters for polymer melts during polymer processing. In this article, we propose a stress and rate-dependent function to describe creation and destruction of polymer junctions. Moreover, we also introduce a movement expression to describe nonaffine movement of network junctions. Based on network theory, a nonaffine single-mode rheological model is presented for the steady flow of polymeric melts, and the equations of η_s, Ψ₁, Ψ₂, and η_e are derived from the model accordingly. Furthermore the dependences of η_s and η_e on model parameters are discussed for the model. Without a complex statistical simulation, the single-mode model with four parameters yields good quantitative predictions of the steady shear and extensional flows for two low density polyethylene melts reported from previous literature in very wide range of deformation rates. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Synthesis of polyurethane acrylates by hydrogenated castor oil and dimer‐based polyester diol and study on pressure‐sensitive adhesive

Synthesis of polyurethane acrylate (PUA) and preparation of the UV‐cured pressure‐sensitive adhesives (PSA) are reported. Molecular weight (M_w) (by gel permeation chromatography) and viscosity (η*) of PUA were measured. Characterization of PUA and PSA before and after UV‐curing was made by FTIR. Increase of the hydroxyls from hydrogenated castor oil/hydroxyls from dimer‐based polyester diol (OH_HCO/OH_Diol) ratio decreased the M_w and η* value of PUA. Dynamic viscoelastic properties (by dynamic rheological spectrometer) and performance of the UV‐cured PSA were also studied. Increase of the OH_HCO/OH_Diol ratio increased the storage modulus (G′), the loss modulus (G″), and complex viscosity (Eta*) of the UV‐cured PSA, which, in turn, enhanced holding power and shear adhesion failure temperature (SAFT) and yet decreased peeling strength. Substitution of OB for DBTDL depressed the M_w and η* value of PUA, while the G″ and Eta* values of the UV‐cured PSA were elevated, which, in turn, increased the holding power and SAFT and yet depressed the peeling strength. Elevation of the tackifying resin content depressed the G′, G″, and Eta* values of the cured PSA and yet increased glass transition temperatures (T_g) of PSA, measured by differential scanning calorimetry. Peeling strength of PSA elevated as increasing the tackifying resin, while the holding power and SAFT fell. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1814–1821, 2005     

Rheological properties of the blends of polychloroprene with poly[ethylene(vinyl acetate)]

Blends of poly[ethylene(vinylacetate)] (EVAc-45; 45% VAc content) and polychloroprene (CR) have been studied with respect to capillary and dynamic flow. It is found that EVAc-45, CR, and their blends are shear thinning (pseudoplastic) in nature. Though shear viscosity (η_a) and dynamic out-of-phase viscosity (η′_E) obeys power law, dynamic elongational viscosity (η′_E) does not follow it due to the synchronization of molecular vibration with the applied frequency at around 11 Hz. Both η_a and η′_E of the blends show positive deviation with respect to their additive values. The relative positive deviation (RPD) in shear flow increases with increasing temperature and shear rate. In the case of dynamic flow, RPD increases with increasing temperature but exhibits a decreasing trend with increasing frequency. RPD can be fitted well into a fifth-order equation with a weight fraction of CR (W_CR) in EVAc-45—CR blends. From rheological point of view, this relative positive deviation indicates blend compatibility between EVAc-45 and CR. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1759–1765, 1997     

The rheology and mold flow of polyester sheet molding compound

Flow properties of sheet molding compounds (SMC) were measured by several rhemeters. Shear viscosities of SMC paste can be fitted by the Carreau viscosity equation and reduced to a single master curve by plotting the reduced shear viscosity (η/η₀) against reduced shear rate (\documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} η₀/T). The deformation fo glass filled compounds under extensional forces. When the shear forced was applied, the compound defomed like a deck of cards being slid. It behaved essentially like a laminate of many layers. On the other hand, SMC compounds elongated much less before sample failure occurred under the extensional flow. The extensional viscosity was much higher than the shear viscosity. This phenomenon was explained by a solid composite theory and theories developed from local shear flows between adjacent fibers. The flow of SMC compounds during molding showed that the surface layers flowed further than the inner layers when the mold surfaces were hot. This casued inner plies to show through at the surface and resulting in some wavy glass orientation. This phenomenon was explained equalitatively by a heat penetration model.     

Rheological characterization of concentrated cellulose solutions in 1‐allyl‐3‐methylimidazolium chloride

The rheological properties of high concentrated wood pulp cellulose 1‐allyl‐3‐methy‐limidazolium Chloride ([Amim]Cl) solutions were investigated by using steady shear and dynamic viscoelastic measurement in a large range of concentrations (10–25 wt %). The measurement reveals that cellulose may slightly degrade at 110°C in [Amim]Cl and the Cox–Merz rule is valid for 10 wt % cellulose solution. All of the cellulose solutions showed a shear thinning behavior over the shear rate at temperature from 80 to 120°C. The zero shear viscosity (η_o) was obtained by using the simplified Cross model to fit experimental data. The η_o values were used for detailed viscosity‐concentration and activation energy analysis. The exponent in the viscosity‐concentration power law was found to be 3.63 at 80°C, which is comparable with cellulose dissolved in other solvents, and to be 5.14 at 120°C. The activation energy of the cellulose solution dropped from 70.41 to 30.54 kJ/mol with an increase of concentration from 10 to 25 wt %. The effects of temperature and concentration on the storage modulus (G′), the loss modulus (G″) and the first normal stress difference (N₁) were also analyzed in this study. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Rheological behavior of N,N‐dimethyl acrylamide–acrylamido methylpropane sulphonate copolymer

Copolymer of N,N‐dimethylacrylamide (NNDAM) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (NaAMPS) have been prepared by free‐radical copolymerization and characterized with the help of molecular weight, molecular weight distribution, intrinsic viscosity, and monomer ratio in the copolymer. The solution behavior of a copolymer containing 26.62 wt % NaAMPS is studied in different solvents, namely, water (W), dimethyl sulfoxide (DMSO), ethylene glycol (EG), and ethanol (EtOH). The reduced viscosity of the copolymer is highly dependent on the ionic strength of the copolymer solution. The reduced viscosity decreases as a function of solvent selection in the order W > DMSO > EtOH > EG. The shapes of the η_sp / C vs. C plots indicate the polyelectrolyte behavior of the copolymer, except for the case of EG solutions, where nonpolyelectrolyte behavior is observed. However, at a certain degree of ionization attained by adding W as cosolvent, the copolymer begins to demonstrate polyelectrolyte behavior. For this copolymer, there exists a minimum concentration of brine (NaCl, CaCl₂, etc.) above which solution viscosity is not further reduced. The copolymer solution behaves as a power law fluid, and exhibits time‐dependent thixotropic behavior. The copolymer cannot regain its solution viscosity when allowed to shear at a constant rate for long period of time. The reduced viscosities of copolymer solutions increase with increasing temperature in W and DMSO, yet decreases with increasing temperature in EG. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1521–1529, 2002