Mooney Equation Research Articles

Rheological study of mixed cyclopentane + CO2 hydrate slurry in a dynamic loop for refrigeration systems

The use of CO2 hydrates as phase change materials is promising for secondary loop refrigeration, as these compounds present adjustable dissociation temperature that can be higher than 273.15 K and have high enthalpy of dissociation. In the present work, by using various promoters, cyclopentane (CP) in this study, the formation pressure of hydrates may be significantly lowered than CO2 hydrates. For their application as a secondary refrigerant, the rheological properties of mixed CP + CO2 hydrate slurry need to be controlled. The flow properties of CP and mixed CP + CO2 hydrate slurries were studied in a dynamic flow loop at different cyclopentane contents ranging from 3 wt% to 15 wt%, using a capillary viscometer based on Rabinowitch and Mooney equation. Rheological parameters (viscosity, flow behavior…) related to these two slurries were compared. The experimental results demonstrate that CP and mixed CP + CO2 hydrates slurries exhibit a shear thinning behavior and the viscosity values vary between 3 and 12 mPa.s-1 at [100–1000 s−1] for CP hydrates slurries and between 2 and 10 mPa s−1 at [100–1200 s−1] for CP + CO2 hydrates slurries. CP hydrate and CP + CO2 hydrate slurry viscosity is close to that of TBPB hydrate and lower than that of CO2 hydrate. Moreover, mixed CP + CO2 have shown a time-evolution of the rheological behavior.

On the prediction of suspension viscosity, grain morphology, and agitation power in SPVC reactors

AbstractThe role of primary and secondary stabilizers in the suspension polymerization of VCM and their effect on grain morphology (i.e., particle size distribution, grain porosity, and bulk density) is critically discussed. Using the modified Mooney equation, the time‐varying viscosity of the suspension in an SPVC reactor is calculated in terms of the volume fraction of the dispersed monomer/polymer phase, the ratio of the viscosity of the dispersed phase over the viscosity of the continuous aqueous phase, and the maximum packing volume fraction of SPVC grains. A population balance equation is numerically solved to calculate the dynamic evolution of particle size distribution (PSD) in an industrial batch suspension VCM polymerization reactor. A porosity model is postulated to calculate the dynamic evolution of the PVC grain porosity with respect to monomer conversion and the extent of primary particle fusion. Finally, the underlying theory regarding the calculation of the required agitation power in SPVC reactors is detailed. It is shown that the time‐varying viscosity of the suspension can be calculated and the PVC grain morphology (i.e., extent of particle agglomeration) can be accessed via the on‐line estimation of the effective volume fraction of the dispersed phase using on‐line power agitation measurements obtained from an industrial‐scale SPVC reactor.

Flow characteristics of hydrofluorocarbon gas hydrate slurries under various conditions in a loop tube

Gas hydrate slurries, which are prepared using solid hydrates and water, are effective secondary refrigerants with a high latent heat of fusion and could be used to reduce global warming. The effective application of these slurries requires knowledge of their flow characteristics in good and poor flow states. In the present work, the flow properties of R-134a and R-32 gas hydrate slurries circulating in a loop tube were investigated using the Rabinowitsch–Mooney equation to estimate the flow characteristics. When undergoing laminar flow, the slurries in a good flow state were pseudoplastic fluids. However, under conditions that induced poor flow, the slurries behaved as dilatant fluids. The relative viscosities of the slurries were estimated using Happel’s equation according to the apparent particle hold-up. In turbulent flow, both slurries in good flow state acted as pseudoplastic fluids and maintained good flow characteristics.

Accurate Approximate Methods for the Fully Developed Flow of Shear-Thinning Fluids in Ducts of Noncircular Cross Section

The fully developed laminar flow of Non-Newtonian fluids in ducts has broad application in engineering. The power-law viscosity model is utilized most often in the engineering literature, but it is deficient for many fluids as it does not admit limiting Newtonian viscosities at low and high shear rates. The goal of this work is to demonstrate two approximate but accurate and efficient methods for computing the pressure gradient in ducts of noncircular cross section for shear-thinning fluids following a general viscosity curve. Both methods predict the pressure gradient to better than 1% as established by full numerical solutions for ten cross-sectional shapes, a result representing an order-of-magnitude improvement over previous approximate methods. In the first method, an approach recently proposed and demonstrated to be accurate for a circular duct is shown to be equally applicable to noncircular ducts. In the second method, a widely used approach for noncircular ducts based on a generalization of the Rabinowitsch–Mooney equation is improved through an alternate evaluation of its parameters. Both methods require one-time numerical solutions of the power-law viscosity model for a duct shape of interest, and the necessary results are tabulated for the ten cross-sectional shapes analyzed. It is additionally demonstrated that the pressure-gradient error of the second method is approximately halved by simply replacing the hydraulic diameter with a viscous diameter obtained from the Hagen–Poiseuille equation.

Segmental dynamics and linear rheology of nearly athermal all-polystyrene nanocomposites

Nanoparticles impact on segmental dynamics and rheology of polymers while the mechanisms are far from being clarified. Herein nearly athermal nanocomposites composed of crosslinked polystyrene (cPS) nanoparticles dispersed in linear polystyrene were investigated. The crosslinking degree and thus rigidity of cPS nanoparticles of the same size are found to play an important role in affecting the segmental relaxation and rheology of the nanocomposites. While scarcely crosslinked nanoparticles depress glass transition temperature and accelerate segmental relaxation of the matrix markedly, these effects become negligible for highly crosslinked nanoparticles. On the contrary, the reinforcement becomes increasingly large with increasing crosslinking degree of cPS nanoparticles. Increasing the content of the highly crosslinked nanoparticles may cause a transition from Vogel-Fulcher-Tammann to Arrhenius-like temperature-dependence of segmental relaxation for the frustration of intermolecular coupling. The improvement of reinforcement factor with increasing nanoparticle crosslinking degree is well explained by a modified Mooney equation and is associated to the enlarged local strain and retarded terminal relaxation of the matrix.

A new model of thermodynamics. Extension of chemical thermodynamics to complex materials of cellular structure

This paper presents a structural model of complex materials that are partly or entirely of cellular structure, and a new model of thermodynamics, which can be applied to the processes taking place in complex materials. Since the complex materials always contain cellular fraction, the supposition of cellular equilibrium is real. The complex materials are characterized by polyagent behaviour. Therefore, new concepts such as principal variables, redundancy, macroscopic/microscopic uncertainty are defined, moreover, the application of chemical thermodynamics is limited to micro processes only, and the free energy (F) and the free enthalpy (G) function cannot be generally applied to calculations concerning the bulk amount. Temperature as only a local intensive variable can be discussed. The first law of thermodynamics is expressed in the traditional way. The second law applied to the processes taking place both in open and in adiabatically closed systems is formulated as in words as an equation of stability, completed by the relations to first and second differential of entropy. In connection with the second law the Damköhler balance equation system, the Rabinowitsch–Mooney equation, and the application of dimensional analysis are presented. Only the apparent thermal capacities can be used for complex materials in general. The data of specific thermal capacity of complex materials in the proximity of absolute zero temperature are not sufficient for drawing conclusions on their entropy. The concept ‘shelf-life’ is essential in food science and practice, a Monte-Carlo method is presented for its calculation.

Methacrylamide grafted elastomer composites reinforced with biobased particles

Modulus of rubber can be improved with grafting of unsaturated monomers. To increase the modulus of bio-based rubber composites, methacrylamide was grafted onto natural rubber composites reinforced with bio-based hydrophilic particles. Rubber particles in water were modified with methacrylamide using redox free radical initiator. Modified rubber composites have higher crosslinking density, bound rubber, and modulus than the unmodified rubber composites. Without methacrylamide, initiator modified rubber composites have poor tensile strength and elongation. The modified rubber has a greater stress relaxation rate than the unmodified rubber because of interactions between methacrylamide grafts. Relaxation behaviors of modified and unmodified rubber composites are similar because the effect of filler dominates the dissociation process. The rapid increase of reinforcement factors with filler content can be described by the modified Mooney equation. At small strain, the reinforcement factors for both modified and unmodified rubber composites indicate the association of poly(methacrylamide) grafts is the main contribution to the increase of modulus in the modified rubber composites.

Variational approach for the flow of Ree–Eyring and Casson fluids in pipes

The flow of Ree–Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally obtained solutions are compared to the analytical solutions derived from the Weissenberg–Rabinowitsch–Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.

Rheology and Fluid Dynamic of Egg White: Effect of Thixotropy on Engineering Design

AbstractThe wide application of egg products by food industries reinforces the importance of dealing with egg white properties, such as thermophysical ones, for correct processing and equipment design. Therefore, rheological properties, density and pressure drops were studied from 0.5 to 53.4C, as well as their influence on the energy pump required in a hypothetical pipeline configuration. Egg white presented Power–Law behavior, with thixotropy. Consistency coefficient and apparent viscosity were estimated by an Arrhenius‐type equation for downward and upward curves. Densities were obtained as a linear function of temperature. Fanning friction factors could be calculated and correlated with generalized Reynolds number. The use of Rabinowitsch–Mooney equation resulted in good similarity with the rheological behavior obtained using the rheometer. Different cases of pipeline simulation showed a deviation of until 2.8% in the required energy pump.Practical ApplicationsEgg white is a very useful product of food industry, but its processing requires the knowledge of some thermophysical properties. Among them, there are rheological properties and flow behavior which could present thixotropy. Studying how transport properties are affected by shear rate is valid for the correct equipment design. In order to evaluate this behavior deviation on industrial plant designs, thixotropy and friction factors of egg white are discussed in this work through the aid of a hypothetical pipeline. Rheograms obtained from pressure drops (along a pipe) and shear stress (by rheometer) were compared to provide information about the similarity between different ways for data acquisition.

Intermolecular Interactions and the Viscosity of Highly Concentrated Monoclonal Antibody Solutions.

The large increase in viscosity of highly concentrated monoclonal antibody solutions can be challenging for downstream processing, drug formulation, and delivery steps. The objective of this work was to examine the viscosity of highly concentrated solutions of a high purity IgG1 monoclonal antibody over a wide range of protein concentrations, solution pH, ionic strength, and in the presence / absence of different excipients. Experiments were performed with an IgG1 monoclonal antibody provided by Amgen. The steady-state viscosity was evaluated using a Rheometrics strain-controlled rotational rheometer with a concentric cylinder geometry. The viscosity data were well-described by the Mooney equation. The data were analyzed in terms of the antibody virial coefficients obtained from osmotic pressure data evaluated under the same conditions. The viscosity coefficient in the absence of excipients was well correlated with the third osmotic virial coefficient, which has a negative value (corresponding to short range attractive interactions) at the pH and ionic strength examined in this work. These results provide important insights into the effects of intermolecular protein-protein interactions on the behavior of highly concentrated antibody solutions.

Applicability of blocking laws in non-Newtonian fluid membrane filtration

The blocking laws for constant flux non-Newtonian fluid filtration were derived by means of the Rabinowitsch–Mooney equation in the form of different first-order derivative expressions of pressure change over filtered volume dP/dV. The modified blocking laws were found theoretically sound as the modified equations reduced to those of classical blocking laws if the value of flow behavior index of Newtonian fluid was inserted. Dead end, constant flux microfiltration experiments of kaolin, titanium oxide (TiO2), and sodium carboxymethyl cellulose at different concentrations (0.25–2% w/v) and at different fluxes (80 and 120 L/m2/h) were conducted to investigate the impact of non-Newtonian fluid behavior due to particle dispersion in water and soluble material on membrane filtration. It was found that the rheology of the fluid changed due to material retention on the membrane which led to conclusion that the model was not fully confirmed and, thus, its applicability might be insufficient to elucidate fouling mechanisms in constant flux, non-Newtonian fluid filtration.

Determination of the flow curve of complex fluids using the Rabinowitsch–Mooney equation in sensorless microrheometer

In this work, we present a way to make rheological measurements on a microfluidic chip. The originality of our approach relies on the determination of the flow curve of a fluid using the Rabinowitsch–Mooney equation. For this purpose, we use a parallel flow between a reference fluid and a studied fluid to measure the pressure drop inside the channel. Using a Newtonian fluid of known viscosity, knowing the flow rates of the two liquids and measuring the geometrical features of the two-phase flow allows determining the pressure drop in the channel. The Rabinowitsch–Mooney equation is used to calculate the local shear rate and shear stress at the wall for the studied sample. We validate our method for several complex fluids.

Development of a Model Foamy Viscous Fluid

The objective is to develop a model viscous foamy fluid, i.e. below the very wet limit, the rheological and stability properties of which can be tuned. First, the method used for the preparation of foamy fluids is detailed, including process and formulation. Then, experimental results highlight that stable foamy fluids with a monomodal bubble size distribution can be prepared with a void fraction between 25% and 50% (v/v). Their viscoelastic properties under flow and low-strain oscillatory conditions are shown to result from the interplay between the formulation of the continuous phase, void fraction and bubble size. Their apparent viscosity can be described using the Cross equation and zero-shear Newtonian viscosity may be predicted by a Mooney equation up to a void fraction about 40%. The Cox-Merz and the Laun’s rules apply when the capillary number Ca is lower than 0.1. The upper limit of the zero-shear plateau region decreases when void fraction increases or bubble size decreases. In the shear-thinning region, shear stress varies with Ca1/2 , as in wet foams with immobile surfaces. Finally, foamy fluids can be sheared up to Ca about 0.1 without impairing their microstructure. Their stability at rest achieves several hours and increases with void fraction due to compact packing constraints. These constitute, therefore, versatile model fluids to investigate the behaviour of foamy fluids below the very wet limit in process conditions.

Cyanate ester–alumina nanoparticle suspensions: Effect of alumina concentration on viscosity and cure behavior

AbstractThe effect of alumina nanoparticles on the viscosity and curing behavior of a bisphenol E cyanate ester monomer suspension was investigated by rheometry and differential scanning calorimetry. The viscosity was found to increase with solids content and was fit well by the Mooney equation. Cure experiments indicate that alumina particles catalyze the curing of the suspensions. The viscosity reduction achieved at high particle loadings by the addition of benzoic acid was also investigated by nuclear magnetic resonance. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

Effects of nanotalc inclusion on mechanical, microstructural, melt shear rheological, and crystallization behavior of polyamide 6‐based binary and ternary nanocomposites

AbstractThe objective of the study is to investigate the effect of inclusion of nanotalc on the strength properties of polyamide 6 (PA6)‐based binary and ternary nanocomposites. Binary nanocomposites were prepared by melt compounding of PA6 with varying content of nanotalc (1, 2, and 4 wt%). Ternary nanocomposites were prepared by melt compounding of compatibilized blend of PA 6 and ethylene‐co‐butyl acrylate (EBA elastomer) with varying content of nanotalc (1, 2, and 4 wt%). Both the binary and ternary nanocomposites registered a very high improvement in the strength/stiffness‐related properties at lower filler loading of 1 wt%. Phase morphology of the composites studied by SEM, TEM, and XRD revealed the formation of extended brane‐like structures and delaminated talc layers in the binary nanocomposites. The modulus predicted by Halpin‐Tsai and Mooney equation suggests that the composites retained a very good aspect ratio after melt mixing. Orientation effects of nanotalc enhanced the melt flow behavior in the composites. POLYM. ENG. SCI., 50:1978–1993, 2010. © 2010 Society of Plastics Engineers

DYNAMIC VISCOELASTIC BEHAVIOR OF GRAPHITE FILLED HIGH DENSITY POLYETHYLENE COMPOSITES AND MODIFICATION OF MOONEY EQUATION

A study of viscoelastic properties of graphite(GP) filled high density polyethylene composites was carried out.The Mooney equation was modified to evaluate the formation and development of agglomerate structure for high filled suspension system.The apparent filler concentration(φ) was substituted by the effective volume fraction,φ_(eff).It is believed that in the case of high filler concentrations the viscoelastic properties of the composites are mainly related with φ_(eff).Here,we define φ_(eff)=fφ,in which f(f≥1) is the experiential factor of effective volume,corresponding to the microstructure with different relaxation time in HDPE/GP system.In the low φ region,the viscoelastic properties of the composites can be described by the original Mooney equation,while the viscoelastic properties of the high loading composites can be described by the modified Mooney equation considering the effective filler volume in the case of ω=0.1 rad/s,experientially postulate f=1.55.

Reversible thermal gelation of soft semi‐crystalline polyethylene microparticles with surface interactions in squalane

AbstractThe effect of temperature on the steady‐shear viscosity of a soft semi‐crystalline crosslinked‐polyethylene microparticle suspension in squalane was studied using rotational rheometry. The results show a sharp increase in the viscosity of the system occurring at about 86°C. The magnitude of this spike is dependent on the concentration of the suspension and is reproducible over multiple heating and cooling cycles. This phenomenon has been attributed to the melting of the crystalline regions within the particles, causing them to swell by soaking up squalane. The Mooney equation was used to model the viscosity data based on swelling data obtained from separate experiments. The results showed that the model is inadequate for describing the observed phenomenon, suggesting the possibility of additional interactions existing among the particles. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers

Modeling rheological properties of low-in-fat o/w emulsions stabilized with xanthan/guar mixtures

Abstract The incorporation of hydrocolloids is a suitable alternative to stabilize low-in-fat o/w emulsions against creaming. The effect of composition on rheological properties and stability of low-in-fat o/w emulsions formulated using xanthan/guar gum mixtures in an acidic aqueous solution containing 2% NaCl was studied. A central composite design involving oil fraction and gum content was used. Frequency sweeps showed that both G′ and G″ increased with oil content. However, the viscoelastic behavior was mainly governed by the hydrocolloid content. The shear-thinning behavior of both aqueous dispersions (continuous phases) and emulsions was successfully modeled with Ellis equation. Mooney equation was used to obtain the shape factor and maximum packaging volume fraction. Zero shear viscosity was also predicted based on emulsion composition by response surface methodology. Droplet size distribution was measured by light scattering; microscopic observations revealed a flocculated system. Visual inspections of the formulated emulsions showed that they remained stable after eight months.

Mechanics of Polymer−Clay Nanocomposites

The mechanics of nanocomposites is critical in the design of nanomaterials with desirable properties. In this paper, the mechanics of polymer−clay nanocomposites is studied using a designed polymer and solution nanocomposite synthesis. A copolymer latex, with function groups that strongly interact with the surface of the clay nanoplatelet and glass-transition temperature lower than room temperature, was synthesized. Uniformly dispersed nanocomposites were then generated using water as the intercalation agent through the solution process. The chain mobility in the nanocomposites is greatly reduced as studied by dynamic mechanical thermal analysis (DMTA) and dielectric thermal analysis (DETA). The modulus of the composite increases significantly. The modulus enhancement strongly relates to the volume of the added clay as well as the volume of the constrained polymer. This modulus enhancement follows a power law with the content of the clay and is modeled well by Mooney's equation for this soft-polymer-based...

Effect of hexafluoropropylene oxide plasma polymer particle coatings on the rheological properties of boron nitride/poly(dimethylsiloxane) composites

This work explores the use of conformal nanoscale plasma coatings on the surface of boron nitride (BN) powders to control the rheological properties of BN/poly(dimethylsiloxane) (PDMS) composites. BN particles are conformally coated with hexafluoropropylene oxide (HFPO) in a tumbling RF-plasma reactor. Following the HFPO plasma treatment, XPS evidence indicates the presence of thin coating on the surface of the particles having a F:C ratio of 1.77. Filled BN/PDMS composites are investigated using oscillatory shear rheometry in the concentration range of 0.09–0.41 vol% ( ϕ). The addition of the plasma treated BN particles to the PDMS matrix reduces the complex viscosity by 40–60% when compared with equally loaded control samples across a broad concentration range. The frequency dependence of the maximum packing fraction ( ϕ m = 0.38 – 0.42 ) is also observed for both treated and untreated particles. The maximum packing fraction does not appear to be significantly affected by the conformal plasma polymer treatment. The investigation has shown that the relative dynamic viscosity of the BN/PDMS can be described by the modified Mooney equation.