The Viscosity of Concentrated Suspensions and Solutions
TL;DR: In this paper, an expression for the viscosity of solutions and suspensions of finite concentration is derived by considering the effect of the addition of one solute-molecule to an existing solution, which is considered as a continuous medium.
Abstract: An expression for the viscosity of solutions and suspensions of finite concentration is derived by considering the effect of the addition of one solute‐molecule to an existing solution, which is considered as a continuous medium.
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TL;DR: In this article, the authors considered seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid and concluded that only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids.
Abstract: Nanofluids are engineered colloids made of a base fluid and nanoparticles (1-100 nm) Nanofluids have higher thermal conductivity' and single-phase heat transfer coefficients than their base fluids In particular the heat transfer coefficient increases appear to go beyond the mere thermal-conductivity effect, and cannot be predicted by traditional pure-fluid correlations such as Dittus-Boelter's In the nanofluid literature this behavior is generally attributed to thermal dispersion and intensified turbulence, brought about by nanoparticle motion To test the validity of this assumption, we have considered seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid These are inertia, Brownian diffusion, thermophoresis, diffusioplwresis, Magnus effect, fluid drainage, and gravity We concluded that, of these seven, only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids Based on this finding, we developed a two-component four-equation nonhomogeneous equilibrium model for mass, momentum, and heat transport in nanofluids A nondimensional analysis of the equations suggests that energy transfer by nanoparticle dispersion is negligible, and thus cannot explain the abnormal heat transfer coefficient increases Furthermore, a comparison of the nanoparticle and turbulent eddy time and length scales clearly indicates that the nanoparticles move homogeneously with the fluid in the presence of turbulent eddies so an effect on turbulence intensity is also doubtful Thus, we propose an alternative explanation for the abnormal heat transfer coefficient increases: the nanofluid properties may vary significantly within the boundary layer because of the effect of the temperature gradient and thermophoresis For a heated fluid, these effects can result in a significant decrease of viscosity within the boundary layer, thus leading to heat transfer enhancement A correlation structure that captures these effects is proposed
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TL;DR: In this article, a model is developed to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion, where the transport equations are solved numerically using the finite-volume approach along with the alternating direct implicit procedure.
2,560 citations
Cites methods from "The Viscosity of Concentrated Suspe..."
...The effective viscosity of a fluid of viscosity lf containing a dilute suspension of small rigid spherical particles is given by Brinkman [15] as...
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...The effective viscosity of a fluid of viscosity lf containing a dilute suspension of small rigid spherical particles is given by Brinkman [15] as leff ¼ lf ð1 /Þ2:5 ð7Þ The heat capacitance of the nanofluid can be presented as ðqcpÞnf ¼ ð1 /ÞðqcpÞf þ /ðqcpÞs ð8Þ The effective stagnant thermal conductivity of the solid– liquid mixture was introduced by Wasp [11] as follows ðkeffÞstagnant kf ¼ ks þ 2kf 2/ðkf ksÞ ks þ 2kf þ /ðkf ksÞ ð9Þ This equation is applicable for the two-phase mixture containing micro-sized particles....
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TL;DR: In this article, the authors proposed two different approaches for deriving heat transfer correlation of the nanofluid, and investigated the mechanism of heat transfer enhancement of the nano-fluid.
2,355 citations
TL;DR: In this article, the authors investigated the behavior of nanofluids inside a two-sided lid-driven differentially heated square cavity to gain insight into convective recirculation and flow processes induced by a nano-fluid.
1,797 citations
TL;DR: In this paper, the authors used the finite volume technique to solve the governing equations of heat transfer and fluid flow due to buoyancy forces in a partially heated enclosure using nanofluids.
1,783 citations
Additional excerpts
...…of the nanofluid can be approximated as viscosity of a base fluid lf containing dilute suspension of fine spherical particles and is given by Brinkman (1952): lnf ¼ lf ð1 uÞ2:5 ð8Þ The radial and tangential velocities are given by the following relations respectively, u ¼ ow oy0 ; ð9Þ v ¼…...
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References
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4,775 citations
TL;DR: In this article, Bredee and de Booys and von Houwink and Klaassens vorgeschlagenen Formeln zur Beschreibung der Viskositat disperser Systeme werden verglichen with Bestimmungen, with runden, nichtverformbaren Teilchen, normal von Emulsionen hochviskoser Kohlenwasserstoffe.
Abstract: Die von Bredee und de Booys und von Houwink und Klaassens vorgeschlagenen Formeln zur Beschreibung der Viskositat disperser Systeme werden verglichen mit Bestimmungen der Viskositat von Dispersionen mit runden, nichtverformbaren Teilchen, deren Gesamtvolumen bekannt war, normal von Emulsionen hochviskoser Kohlenwasserstoffe. Von diesen Formeln gab die 6. Potenzgleichung von Bredee und de Booys
$$\eta r = \left( {1 + \frac{{2,5C_v }}{{6(1 - C_v )}}} \right)^6$$
den besten Anschlus an die experimentell gefundenen Werte; fUr sehr konzentrierte Systeme,Cv>0,65, ergibt sie jedoch zu niedrige Werte.
441 citations
TL;DR: In this article, a Wandeinflus auf eine Kugel in einer reinen Dilatationsstromung und ganz grob is described, e.g., in a translatorisch bewegte kugel im Einklang with den Versuchen von H. Przibram.
Abstract: In dieser Mitteilung wird angegeben:
1.
Der Wandeinflus auf eine rotierende Kugel. Dieser erweist sich kleiner als fur eine translatorisch bewegte Kugel im Einklang mit den Versuchen von H. Przibram.
2.
Der Wandeinflus auf eine Kugel in einer reinen Dilatationsstromung und ganz grob — eine Wandeinfluskorrektur zum Einstein'schen Viskositatsgesetz
3.
Die Wechselwirkung zweier rotierender Kugeln.
4.
Die Methode zur Erfassung desjenigen Einflusses auf die Viskositat (II), der von der (hydrodynamischen) Wechselwirkung der suspendierten Kugeln herruhrt. Die vollstandige Formel wird in der 8. Mitteilung publiziert.
257 citations
TL;DR: The theory of the concentration dependence of the viscosities of solutions is developed for the dumbbell, rigid rod, and flexible chain macromolecules in this paper, where both the intramolecular hydrodynamic interactions between the monomer units of the same molecule and the intermolecular interactions between different molecules are considered.
Abstract: The theory of the concentration dependence of the viscosities of solutions is developed for the dumbbell, rigid rod, and flexible chain macromolecules. Both the intramolecular hydrodynamic interactions between the monomer units of the same molecule and the intermolecular interactions between monomer units of different molecules are considered. The methods of Riseman and Kirkwood are applied throughout. The numerical result of the calculation for the dumbbell shaped molecule is compared with that obtained by Simha.
55 citations
13 citations