Mooney Equation Research Articles

Determination of Some Hydrodynamic Parameters of Ovine Serum Albumin Solutions Using Viscometric Measurements

The influence of protein concentration and temperature on the viscosity of ovine serum albumin (OSA) solutions was studied. The Mooney equation and a modified Arrhenius formula were used to described the viscosity-concentration and viscosity-temperature dependence of the solutions, respectively. The effective specific volume, the activation energy and entropy of viscous flow for hydrated OSA were calculated. The axial ratio and the dimensions of the main semi-axes of hydrated OSA were established. At low concentration limit, the temperature dependence of the intrinsic viscosity and Huggins coefficient is presented. Comparison of some hydrodynamic parameters obtained for different proteins has been made.

A comparison of solution conformation and hydrodynamic properties of equine, porcine and rabbit serum albumin using viscometric measurements

This paper presents the results of viscosity determinations on aqueous solutions of equine, porcine and rabbit serum albumin over a wide range of concentrations and at temperatures ranging from 5 °C to (42–45) °C. The results are compared with human and bovine serum albumin previously studied. Viscosity–temperature dependence is discussed on the basis of the modified Arrhenius formula. The effective specific volume, the activation energy and entropy of viscous flow for all investigated albumins are compared. Viscosity–concentration dependence, in turn, is discussed on the basis of Mooney equation. Based on the assumption that theoretical and experimental values of Simha factor – at high temperature limit – are equal to each other, the hydrodynamic volume of the studied albumins has been calculated. The numerical values of a self-crowding factor were also obtained. At low concentration limit, the numerical values of the intrinsic viscosity and of Huggins coefficient were compared.

Rheological properties of a surfactant-induced gel for the lysozyme?sodium dodecyl sulfate?water system

Rheological properties of isotropic solutions and gel structures of lysozyme-sodium dodecyl sulfate mixtures in water are investigated. Isotropic solutions behave as Newtonian fluids with very low viscosity values. For the lysozyme solutions the intrinsic viscosity and the Huggins coefficient were calculated on the basis of the Mooney equation. Above a certain yield stress value, the viscosity of the gel samples decreases continuously in the whole range of the shear rate. Dynamic rheological experiments show weak gel behavior where the storage modulus and the loss modulus are almost parallel and are frequency-dependent. A belated gel stage with very slow kinetics has been characterized. There is a substantial enhancement of the gel strength by ageing since the belated gel stage manifests a higher yield stress value and a higher storage modulus than the initial gel stage. The gels are stable in the temperature range between 10 and 32degreesC. (Less)

On the hydrodynamics and temperature dependence of the solution conformation of human serum albumin from viscometry approach

The paper presents the results of viscosity determinations on aqueous solutions of human serum albumin (HSA) at a wide range of concentrations and at temperatures ranging from 5 to 45 °C. On the basis of a modified Arrhenius formula and Mooney's equation, the viscosity–temperature and viscosity–concentration dependence of the solutions are discussed. The effective specific volume, the activation energy and entropy of viscous flow for hydrated HSA were calculated. Different models of HSA molecule are discussed and the best one—from the hydrodynamic point of view—was established. At low concentration limit, such rheological quantities as the intrinsic viscosity and Huggins coefficient were obtained. Using the dimensionless parameter [ η] c, the existence of three characteristic ranges of concentrations: diluted, semi-diluted and concentrated, was shown.

Effect of filler fraction on strength, viscosity and porosity of experimental compomer materials

Objective. The primary goal is to develop a self-cured polyacid-modified resin composite with good mechanical and rheological properties. To achieve such a goal, the aim of this study is to determine how volume filler fraction (VFF) affects mechanical properties and viscosities of such materials containing different filler volumes. Methods. A series of self-cured polyacid-modified composites made from polyacid modified resins and TEGDMA, mixed with filler particles, were evaluated regarding compressive strength (CS), diametral compressive strength (DCS) and viscosity. The maximum filler content, which could be incorporated into the materials, was calculated from CS tests as well as from viscosity measurements using Mooney's equation. Porosity contents were also determined in an attempt to explain different failure behaviours. Results. The CS values peaked at 18.9 vol.% filler particles and declined afterwards for self-cured polyacid-modified resin composites cured in air. Using photopolymerisation and barium filler in the polyacid-modified resin composites resulted in the highest CS and DCS values. The viscosity increased continuously with increased VFF. VFF results determined experimentally and with Mooney's equation at shear rates of 0.01, 0.1, 1.0, and 10.0 s −1 revealed that the maximal filler fraction values were 54.9±1.8, 55.9±1.3, 56.3±0.9, and 56.8±0.8 vol.%, respectively. The largest porosity content occurred at a VFF value of 53 vol.% Conclusions. We conclude that an increase in filler fraction of the investigated experimental polyacid-modified resin composite materials above a certain value (20–30 vol.%) does not result in improved mechanical properties.

Multiaxial Deformations of End-linked Poly(dimethylsiloxane) Networks 5. Revisit to Mooney-Rivlin Approach to Strain Energy Density Function

We strictly assess the validity of the familiar Mooney-Rivlin approach to the strain energy density function (W) on the basis of the quasi-equilibrium uniaxial and biaxial deformation data of end-linked poly(dimethylsiloxane) networks prepared from the solutions with various precursor concentrations. The constants C1 and C2 in the Mooney equation (W = C1 (I1 − 3) + C2 (I2 − 3)) are obtained from the intercept and slope of the linear correlation in the Mooney-Rivlin plots for the uniaxial data, respectively. The biaxial stress-strain relations estimated by the Mooney equation are far from the real behavior for all samples. It is clearly demonstrated that the Mooney-Rivlin approach, which has still been employed due to the simplicity in many studies, is unsuccessful to deduce the form of W.

A methodology for the derivation of non-Darcian models for the flow of generalized Newtonian fluids in porous media

A methodology is presented for the development of analytic models that can suitably describe the flow of generalized Newtonian fluids in porous media. First, the volume averaging technique is employed for the derivation of generalized non-Darcian models concerning the creeping flow of inelastic non-Newtonian fluids in porous media. Two macroscopic properties are involved in these models: the effective permeability and average viscosity. The approximate Rabinowitch–Mooney equation is used to obtain analytical solutions for the flow of Meter and mixed Meter-and-power law fluid models through a pore of arbitrary cross-sectional shape. The analytical solutions are integrated into numerical simulators of the one-phase flow of the foregoing fluids in two-dimensional pore networks. The effective medium theory (EMT) is coupled with pore network simulations in order to replace the disordered porous medium with an effective medium that is described by two anisotropic hydraulic conductances and two effective hydraulic pore radii. Finally, closed expressions are developed to relate the superficial flow velocity with the pressure gradient and the macroscopic properties with the effective hydraulic pore radii, rheological parameters and pressure gradient. The new flow models predict satisfactorily numerical simulations of the flow of non-linear fluids in theoretical pore networks, and experiments of the flow of non-Newtonian oils in two-dimensional artificial glass-etched pore networks. Any observed discrepancies are attributed to the use of a small number of pore structure parameters for the homogenization of the porous medium, as well as to uncertainties embedded into the estimated values of rheological parameters.

Creeping flow of viscoelastic fluid through fixed beds of particles

A method is presented for the pressure drop calculation during the viscoelastic fluid (VEF) flow through fixed beds of particles. It is based on the application of the modified Rabinowitsch–Mooney equation together with the corresponding relations for consistency variables. The course of dependence of dimensionless quantity coming from the momentum balance and expressing the influence of elastic effects on the suitably defined elasticity number is determined experimentally. The satisfactory validity of the approach suggested has been verified for pseudoplastic viscoelastic fluids characterized by the power-law flow model.

Flow of viscoplastic fluids through fixed beds of particles: comparison of three approaches

Three approaches suggested for the purposes of calculation of pressure drop in flow of non-Newtonian fluids through fixed beds representing the capillary concept are compared, i.e. the Blake–Kozeny concept, the Kozeny–Carman concept, and the concept which solves the problem using the integral forms of the momentum balance, the equation of continuity of flow, and the Rabinowitsch–Mooney equation. The comparison with experimental results for viscoplastic fluids (VPF) characterized by the Herschel–Bulkley flow model given in literature leads to a conclusion that the most reliable results are obtained from the approach which used the correct integral forms of governing equations. Also discussed is the possibility of its application for the purposes of calculation of the pressure drop in flow of viscoelastic fluids through fixed beds.

Viscosity analysis of the temperature dependence of the solution conformation of ovalbumin

The viscosity of ovalbumin aqueous solutions was studied as a function of temperature and of protein concentration. Viscosity–temperature dependence was discussed on the basis of the modified Arrhenius formula at temperatures ranging from 5 to 55°C. The activation energy of viscous flow for hydrated and unhydrated ovalbumin was calculated. Viscosity–concentration dependence, in turn, was discussed on the basis of Mooney equation. It has been shown that the shape parameter S decreases with increasing temperature, and self-crowding factor K does not depend on temperature. At low concentration limit the numerical values of the intrinsic viscosity and of Huggins coefficient were calculated. A master curve relating the specific viscosity η sp to the reduced concentration c[η], over the whole range of temperature, was obtained and the three ranges of concentrations: diluted, semi-diluted and concentrated, are discussed. It has been proved that the Mark–Houvink–Kuhn–Sakurada (MHKS) exponent for ovalbumin does not depend on temperature.

Viscosity of magnetic particle suspensions

A rheological approach was used to study the effects of microstructure on the viscosity of magnetic particle suspensions as functions of concentration and shear rate. Empirical formulas derived from mean-field theory and the Mooney equation were used to relate viscosity with particle concentration for both rod- and plate-like particles. The Casson equation was employed to investigate the shear rate dependence of the viscosity.

Experimental examination of existing slurry models for coal softening and resolidification

Pelletised Goonyella coal was heated at a rate of 10Kmin−1 up to holding temperatures from 690 to 710K, while the apparent viscosity of the coal was measured by needle penetrometry and was found to change with time through a minimum viscosity of ca 106Pas. Existing slurry models, any of which predict the minimum viscosity at the maximum volume fraction of liquid without variation of its chemical composition, were adopted to analyse the change in the coal viscosity at a constant temperature of 690K. The assumption that softening coal behaves as a slurry was experimentally examined by analysing the viscosity of pelletised mixtures of semicoke as an inert solid and pyridine extract from the coal at temperatures over 500K where the extract behaved as a liquid. The results revealed that a model based on Mooney's equation can quantitatively describe the viscosity of the mixtures that varied with temperature and the fraction of the extract with an Einstein coefficient and critical mass fraction of solid of 5.9 and 0.77, respectively. Using these parameters and the viscosity of liquid given as that of the extract, Mooney's equation predicted the time-dependent change in the mass fraction of metaplast assumed to represent the liquid in the softening coal at 690K. The mass fractions of pyridine, quinoline and pyridine/CS2 extracts, which were obtained from the heat-treated and quenched coal pellets, were found to decrease monotonously with time and to be appreciably smaller than the predicted liquid fraction throughout the holding time. No significant changes with time of the chemical composition of the pyridine extracts were detected either. The solvent extracts were thus suggested to represent only a portion of the metaplast. Then the fraction of liquid in the coal, upon heating at 690K, was evaluated by means of an in-situ proton magnetic resonance (1H NMR) that can detect mobile hydrogen existing in the liquid phase distinguishing it from rigid hydrogen in the solid phase on the basis of molecular mobility. The observed fraction of mobile hydrogen was found to change in a manner similar to that for the predicted liquid fraction, although the former was slightly larger than the latter.

Drag and fall velocity of a spherical particle in generalized newtonian and viscoplastic fluids

An approach to the calculation of drag and fall velocity of a spherical particle in generalized Newtonian and viscoplastic fluids is suggested. It is based on the application of the modified Rabinowitsch–Mooney equation together with the corresponding relations for consistency variables. The usefulness of this approach has been verified for the Ellis and Bingham fluids. The solution has been used to suggest the corresponding relationships for the calculation of pressure drop in the flow of a viscoplastic fluid through a random fixed bed of particles.

Viscosity of magnetic particle suspension

The effect of microstructure on the viscosity of rheologically complex magnetic particle suspensions is investigated. The measurements of suspension viscosity are used to obtain the dependence of viscous energy dissipation on the microstructural states of magnetic particle dispersions as well as the microstructural effects which are related to magnetic particle orientation for both rod and plate-like particles. The empirical formulas from mean field theory and the Mooney equation, which are applicable for high concentrations of magnetic particles, are used to relate viscosity to particle concentration.

脱灰石炭造粒粒子の解砕による石炭‐重油‐水混合物の流動特性

The flow characteristics of coal-oil-water mixture (COW) was investigated. COW was prepared by a disintegration of deashed coal agglomerates, which were obtained by the oil agglomeration of coal. When the volume fraction of dispersed waterdrops in COW was smaller than 0.2, the dispersed waterdrops influenced the flow characteristics of COW to the same extent as the dispersed coal particles. COW behaved as Bingham fluid. Both the yield value and Bingham viscosity increased with increasing total disperse phase volume fraction in COW, and with decreasing temperature. The relative viscosity of COW was well correlated by the equation derived with reference to Mooney's equation.

Rheological study of magnetic particle suspensions

Viscometry was used to investigate the microstructural properties of various magnetic particle suspensions. Our study was focused primarily on the shape (acicular versus plate-like effects) of magnetic particles, magnetic particle and/or floc concentration, as well as the effects of shear rate. Mean field theory and the Mooney equation were adopted to estimate a maximum packing concentration of magnetic particles ( ∝) as well as the intrinsic viscosity ([ η]). The values of ∝ and [ η] for different suspensions were used to interpret the microstructure of magnetic particle suspensions. Further, the Casson equation was employed to investigate the dependence of shear rate on the viscosity.

Viscosity of base-treated asphaltene solutions

The viscosity behaviour of base-treated Ratawi asphaltene-toluene solutions was compared with that of untreated solutions. NaOH solutions (1, 3 and 6 M) were used to treat the asphaltene solutions by mechanical mixing followed by overnight two-phase equilibrium. The treatment noticeably affected the viscosity, particularly for asphaltene volume fractions ( ø) > 0.13. The simple Pal-Rhodes analysis indicated that the systems became very non-ideal, even at ø < 0.1, probably owing to the charges introduced into the asphaltene colloids. The Dougherty-Krieger formula failed to explain the data. The Mooney equation qualitatively characterized the particle polydispersity but not the interactions. The interaction was interpreted by a two-fluid model. The results showed that the interaction potential, V( r), between the asphaltene colloids was extensively modified, corresponding to a longer-range interaction potential, which leads to a much smaller maximum packing volume fraction ø m .

Rheological behaviour of surfactant-flocculated water-in-oil emulsions

The influence of surfactant concentration on the rheological properties of water-in-oil (macro)emulsions was investigated using a coaxial cylinder viscometer. The emulsions were prepared with petroleum oil, deionized water and sorbitan trioleate (a non-ionic, oil-soluble surfactant). The surfactant concentration was varied over a wide range from 1 to 50 wt.% based on the oil phase. The water concentration was varied from 0 to 75 vol.%. The emulsions produced at high surfactant concentrations were highly flocculated in nature; the flocculated emulsions exhibited non-Newtonian yield-pseudoplastic behaviour which was described adequately by the Casson model. The yield stress increased with both surfactant and water concentrations. The apparent and relative viscosities of the emulsions (at a given water concentration) increased with the surfactant concentration, However, the influence of surfactant concentration on the relative viscosities diminished with an increase in the shear stress. The relative viscosity versus dispersed phase concentration data for all the emulsions are described by a modified Mooney's equation.

A generalized model to predict the viscosity of solutions with suspended particles. I

AbstractSeveral suspension equations available in the literature have been found to have a common derivative form. This common derivative was found to be equivalent to a ratio of the intrinsic viscosity, [η], and a quantity, Vint, defined as the ldquo;relative suspension interaction volume” available for particle flow. Vint was, in general, found to be a relatively simple function of the suspension particle volume fraction, φ, the maximum particle packing fraction, φn, and a new variable, σ, defined as the particle interaction coefficient. Different forms of this common derivative were obtained by modifying VInt with a simple adjustment for the value for the interaction coefficient, σ. Integration of this generalized derivative yielded a generalized suspension viscosity equation that was found to predict the form of many suspension equations that have previously appeared in the literature. For example, by varying the interaction coefficient, σ, the Arrhenius equation resulted when σ = 0, the Kreiger‐Dougherty equation resulted when σ = 1, and when σ = 2, the Mooney equation resulted. Fractional values for the particle interaction coefficient were also found to be useful when optimizing the empirical fit of the literature data of Vand and Eiler. Additional insight from such a data fit can also be obtained from the magnitude of both the particle interaction coefficient, σ, and the packing fraction, φn. © 1993 John Wiley &amp; Sons, Inc.

Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta'') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 microm as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 microm mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, eta = eta(0) exp[K gamma(.)(-beta)phi(c)(1 - K'' sigmaphi(c) /D)] was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field.