The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model

Mendoza, Carlos I.; Santamaría‐Holek, I.

doi:10.1063/1.3063120

Cited by 116 publications

(89 citation statements)

References 45 publications

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“…The effective viscosity of monodisperse suspensions has been described by many semiempirical models, including those of Mooney [Mooney, 1951], Krieger and Dougherty [Krieger and Dougherty, 1959], Maron and Pierce [Maron and Pierce, 1956] Quemada [Quemada, 1977], Zarraga and co-workers [Zarraga, Hill, and Leighton, 2000], and the recent model of Mendoza and Santamaria-Holek [Mendoza and Santamaria-Holek, 2009]. These models all include the maximum packing fraction f m as a parameter; f m is the volume fraction at which the system is presumed to jam and fluidity ceases.…”

Section: Introductionmentioning

confidence: 99%

Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions

Gamonpilas¹,

Morris²,

Denn³

2016

Journal of Rheology

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There was an error in data reduction, resulting in incorrect values for the normal stress differences N 1 and N 2 shown in Figs. 7-10, and the corrected figures are shown here. In particular, the algebraic sign of N 1 is changed, as are the relative magnitudes of N 1 and N 2 . The negative values of N 1 for these non-shear-thickening suspensions are larger in magnitude than those reported by other workers, but both N 1 and N 2 are in general agreement with the accelerated Stokesian Dynamics calculations of Sierou and Brady [1].FIG. 7. Normal stress differences N 1 and N 2 of monodisperse suspensions at volume fractions of 0.4 and 0.5 for both 10 and 52.6 µm particles as functions of (a) shear rate and (b) shear stress (Insets are the same data on a semilog scale). SYNOPSISWe have measured the viscometric functions of mono-and bimodal non-colloidal suspensions of PMMA spheres in a density-matched aqueous Newtonian suspending fluid using parallelplate and cone-and-plate rheometry for particle volume fractions in the range 0.20 to 0.50.Cone-and-plate normal stress measurements employed the method of Marsh and Pearson, in which there is a finite gap between the cone tip and the plate. The monodisperse suspensionsshowed an unexpected particle size dependence of the viscometric functions, with the viscosity increasing with decreasing particle size. Normal stresses were very small in magnitude and difficult to measure at volume fractions below 0.30. At higher concentrations, N 2 was negative and much larger in magnitude than N 1 , for which the algebraic sign was positive over most of the shear rate range for the monodisperse suspensions but indeterminate and possibly negative for the bimodal suspensions. The normal stresses were insensitive to bidispersity when plotted as functions of the shear stress at each volume fraction.

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Section: Introductionmentioning

confidence: 99%

Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions

Gamonpilas¹,

Morris²,

Denn³

2016

Journal of Rheology

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“…Table 2 shows 3 exponential and 9 power law models found in the literature in chronological order [22,[25][26][27][28][29][30][31][32][33][34]. Table 2.…”

Section: Models For Viscosity Prediction Of Feedstocks With Differentmentioning

confidence: 99%

Models to Predict the Viscosity of Metal Injection Molding Feedstock Materials as Function of Their Formulation

González-Gutiérrez

Đuretek

Kukla

et al. 2016

Metals

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Abstract:The viscosity of feedstock materials is directly related to its processability during injection molding; therefore, being able to predict the viscosity of feedstock materials based on the individual properties of their components can greatly facilitate the formulation of these materials to tailor properties to improve their processability. Many empirical and semi-empirical models are available in the literature that can be used to predict the viscosity of polymeric blends and concentrated suspensions as a function of their formulation; these models can partly be used also for metal injection molding binders and feedstock materials. Among all available models, we made a narrow selection and used only simple models that do not require knowledge of molecular weight or density and have parameters with physical background. In this paper, we investigated the applicability of several of these models for two types of feedstock materials each one with different binder composition and powder loading. For each material, an optimal model was found, but each model was different; therefore, there is not a universal model that fits both materials investigated, which puts under question the underlying physical meaning of these models.

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“…The experimental approach involving tapping or vibration to consolidate spheres to φ rcp is a highly repeatable experimental value hence it is widely accepted as a defined transition. In this work φ m for hard sphere suspensions is defined as being equivalent to the geometric maximum, φ rcp , an approach supported by theoretical and experimental literature (Quemada and Berli, 2002, Brady, 1993, Mendoza and Santamaria-Holek, 2009). …”

Section: Error Analysismentioning

confidence: 99%

“…The contribution to the error by incorrect choice of the C 2 term in Batchelor's equation was calculated for 5 % agarose microgels to be 10%. predictions, all of which contain the parameter φ m that corresponds to the point at which the viscosity diverges towards infinite values (equations 2.3 to 2.4 and 2.9 to 2.11) (Mendoza and Santamaria-Holek, 2009, Krieger, 1972, Quemada, 1977, Brady, 1993, Maron and Pierce, 1956. It is general practice to obtain φ m by fitting the model to experimental data, and hence the equations are used in an empirical manner despite theoretical foundations; this is a practice that may be unnecessary if information on the log mean square PSD (equation 2.24) is available, as will be shown.…”

Section: Error Analysismentioning

confidence: 99%

Rheology of soft particle suspensions

Shewan¹

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The purpose of this work is to investigate the effect of particle elasticity on suspension rheology and flow. Non-colloidal (~ 10 µm) spherical agarose microgels suspended in water are used as a model system. The advantage of these microgels is that they are manufactured to a specific elastic modulus, ranging from 8 to 300 kPa, determined from the modulus of an agarose gel disk. This is in contrast to routinely studied colloidal microgels where the particle modulus cannot be established. Colloidal microgel modulus and specific volume are variable as they are responsive to suspension conditions (such as, pH, temperature and osmotic pressure). Using experimental rheology, an investigation was carried out into the liquid and solid-like behaviour of agarose microgel suspensions. Suspension concentration regimes from dilute to densely packed were investigated to show explicitly the effect of particle modulus on rheology, which becomes increasingly more significant with increasing phase volume. In addition, particle modulus is shown to influence two shear flow characteristics -slip and shear thickening.To interpret suspension viscosity as a function of phase volume the model, developed by Maron and Pierce (1956) and popularised by Quemada (1977) (MPQ model), is applied. This model is based on a scaling relation of the pair distribution function and predicts the critical phase volume at which the viscosity tends to infinity, corresponding to when spherical particles are randomly close packed (φ rcp ).Commonly, it is used empirically by free fitting of experimental data to obtain the critical phase volume. In this work, a method has been developed to use the MPQ model in accordance with its theoretical basis by independently predicting φ rcp from the particle size distribution. It is shown that this theoretical form of the MPQ model, with no adjustable parameters, results in an accurate prediction (within experimental uncertainty, ± 5 %) of the viscosity-phase volume relationship for hard spheres. In addition, alterations in suspension microstructure (for example, through particle aggregation) or rheological artefacts (such as, particle migration) are readily identified by plotting the MPQ model in a linear form.In contrast to hard spheres, the phase volume of agarose microgels is difficult to define accurately. The approach typically used in literature, and used here, is to iii define the specific volume from dilute suspension viscosity. This approach can be corroborated using the theoretical viscosity-phase volume model validated with hard sphere suspensions. The specific volume of agarose microgels is easily defined at φ rcp using the particle size distribution. From this approach it is discovered that, in the viscous regime, below φ rcp , particle elasticity does not explicitly affect suspension viscosity. However, it is shown that particle elasticity has an indirect effect on viscosity at phase volumes between ~ 0.4 and φ rcp due to limited re-swelling during microgel preparation procedures.When microgels c...

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The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model

Cited by 116 publications

References 45 publications

Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions

Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions

Models to Predict the Viscosity of Metal Injection Molding Feedstock Materials as Function of Their Formulation

Rheology of soft particle suspensions

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