A simple semiempirical model for the effective viscosity of multicomponent suspensions

Mendoza, Carlos I.

doi:10.1007/s00397-017-1011-6

Cited by 10 publications

(8 citation statements)

References 52 publications

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“…Models have been developed previously to predict the viscosity of suspensions of multimodal particles, for example in references Mendoza (2017) in Mwasame et al (2016b). However these models are mathematically complex and do not describe accurately our experimental results.…”

Section: A Semi-empirical Predictive Modelmentioning

confidence: 99%

Viscosity of protein-stabilized emulsions: Contributions of components and development of a semipredictive model

Roullet

Clegg

Frith

2019

Journal of Rheology

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Protein-stabilised emulsions can be seen as mixtures of unadsorbed proteins and of protein-stabilised droplets. To identify the contributions of these two components to the overall viscosity of sodium caseinate o/w emulsions, the rheological behaviour of pure suspensions of proteins and droplets were characterised, and their properties used to model the behaviour of their mixtures. These materials are conveniently studied in the framework developed for soft colloids. Here, the use of viscosity models for the two types of pure suspensions facilitates the development of a semi-empirical model that relates the viscosity of protein-stabilised emulsions to their composition.

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Section: A Semi-empirical Predictive Modelmentioning

confidence: 99%

Viscosity of protein-stabilized emulsions: Contributions of components and development of a semipredictive model

Roullet

Clegg

Frith

2019

Journal of Rheology

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“…Curiously, when the starting function is itself a truncated series, one or more of the Padé approximants may approximate the full series more closely than the truncated series from whence it came. Fluid physicists [11,12,13,14,15,16,17,18,19,20,21,22] and, in particular, rheologists [23,24,25,26,27,28,29,30,31,32,33,34] have exploited this useful property of Padé approximants for various purposes. In this paper, we shall exploit this useful property for the prediction or interpretation of the normal stress difference responses of polymeric liquids in large-amplitude oscillatory shear flow (LAOS).…”

Section: Tablesmentioning

confidence: 99%

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

et al. 2018

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Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. Specifically, we examine replacing the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We begin by extending the Goddard integral expansion (GIE) from its third [J Non-Newt Fluid Mech 166, 1081 (2011)] to its fifth order term in the shear rate amplitude. We then explore the Padé approximants for this extension. We uncover the best approximant, the [3,4] approximant, and compare this with both the GIE and the exact solution [Macromol Theory Simul 24, 352 (2015)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map its onto Pipkin space. We find the [3,4] approximant to be a simple accurate expression for the normal stress differences in LAOS. Our applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene, and on dissolved polyisobutylene in isobutylene oligomer.

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“…Over the years, research involving the blending of different pseudo-spherical particle sizes to maximize the packing fraction has been addressed to optimize several physical properties including viscosity [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ], modulus [ 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ], and impact [ 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ]. The importance of the packing fraction for a property such as viscosity can easily be evaluated by addressing one of the more general models to characterize viscosity, such as the following generalized viscosity model [ 7 , 8 , 9 , 10 ]:

where …”

Section: Introductionmentioning

confidence: 99%

Practical Limits for Two Fundamental Approaches to Designing Particle Size Distributions to Address a Specific Physical Property like Viscosity

Sudduth¹

2021

Polymers

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It has previously been shown that optimum particle size distributions with a maximum packing fraction can be achieved from a straight line plot of the accumulated sum of particle volume fractions versus the square root of particle size. This study addresses practical limits for two dominant fundamental approaches to designing particle size distributions to address the effect on a specific physical property such as viscosity. The two fundamental approaches to obtain such a straight line would include: the first design approach would be generated utilizing the same initial particle size, Dmin, but by using different ultimate particle sizes, Dmax. The second design approach would be generated where each distribution starts with the same initial particle size, Dmin, and ends with the same ultimate particle size, Dmax. The first design approach is particularly useful to identify the possible slopes available based on the smallest and largest particle sizes available. The second design approach can be utilized to identify the preferred ratio between particles, Z, and the number of different particle sizes, n, to be utilized in the final particle blend. The extensive empirical experimental evaluations of particle size distributions generated by McGeary were then utilized to confirm the limits.

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A simple semiempirical model for the effective viscosity of multicomponent suspensions

Cited by 10 publications

References 52 publications

Viscosity of protein-stabilized emulsions: Contributions of components and development of a semipredictive model

Viscosity of protein-stabilized emulsions: Contributions of components and development of a semipredictive model

Padé approximant for normal stress differences in large-amplitude oscillatory shear flow

Practical Limits for Two Fundamental Approaches to Designing Particle Size Distributions to Address a Specific Physical Property like Viscosity

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