The Relationship between the Apparent Viscosity and the Void Fraction in Two-Phase Flow

Hinata, Shigeru; Ohki, Morimatsu

doi:10.1299/jsme1958.14.951

Cited by 7 publications

(3 citation statements)

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“…This study proposes a viscosity estimation formula, similar to the formulas reported by Frankel and Acrivos, 22) Han and King, 23) and Hinata et al, 24) that is applicable to a gas-liquid-coexisting fluid in which bubbles are dispersed in a liquid. A viscosity estimation formula using the capillary number, Ca, 25,26) has also been proposed.…”

Section: Empirical Modelling Of Simulated Foaming Slagmentioning

confidence: 68%

Viscosity Evaluation of Simulated Foaming Slag via Interfacial Reaction at Room Temperature

Hatano

Hayashi²,

Saito

et al. 2021

ISIJ Int.

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CaO-based slag used in hot metal pretreatment and converters in steelmaking processes typically contains dispersed gas phases. This is called foaming slag, which is known to degrade the quality of slag. The rheological behavior of this slag is dependent on the dispersed part of the gas phase. This gas is generated by the chemical reaction between the hot metal and the slag. In this study, simulated foaming slag was prepared by reacting sodium hydrogen carbonate and oxalic acid in glycerol, which disperses carbon dioxide. Next, we systematically investigated the effects of the volume fraction of the dispersed gas phase and the proportion of glycerol on the viscosity and bubble diameter. According to the model used in this study, the bubbles were smaller than those in the model in which the gas was directly dispersed. The bubble size increased as the gas phase ratio and liquid viscosity increased, likely because the bubble growth is promoted by increase in the gas phase ratio and liquid phase viscosity, and the frequency with which the bubbles contact one other. The increase of the gas phase ratio at low liquid-phase viscosity and low shear rate caused an increase in both apparent viscosity and relative viscosity, which was obtained by dividing the apparent viscosity by liquid-phase viscosity. However, these increases in viscosity were not observed at a high shear rate. This is likely because the mechanism of bubble diffusion and flow is affected by the liquid-phase viscosity and shear rate. We found that the model in this study exemplified a Herschel-Bulkley fluid. In addition, we proposed an equation for measuring viscosity from the gas phase ratio.

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Section: Empirical Modelling Of Simulated Foaming Slagmentioning

confidence: 68%

Viscosity Evaluation of Simulated Foaming Slag via Interfacial Reaction at Room Temperature

Hatano

Hayashi²,

Saito

et al. 2021

ISIJ Int.

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“…It is perhaps slightly surprising that the presence of gas bubbles (endowed with zero viscosity) should increase the equivalent viscosity of the suspension, but that is in fact the result. Experimental verification of this result is provided by Hinata andOhki (1971). Medvedev (1982) suggests that p* = p/(l-n ) is a better correlation of the Hinata and Okhi data, which do extend into values of n large enough that the Taylor result does not hold.…”

Section: Discussionmentioning

confidence: 81%

Slit devolatilization of polymers

Maffettone

Astarita

Cori³

et al. 1991

AIChE Journal

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“…It was nearly half a century later that expansion to higher volume fractions of the secondary phase gained the attention of numerous researchers. [16][17][18][19][20][21][22][23][24][25] Of these, the Einstein-Roscoe relationship shown in (Eq. (8)) 26) is considered to be one of the most applicable models.…”

Section: Empirical Modeling Of Slag Foam Viscositymentioning

confidence: 99%

Rheological Behavior and Empirical Model of Simulated Foaming Slag

et al. 2014

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The slags and fluxes found in modern steelmaking convertors all contain finely dispersed gas phases, which are generated by the refining reaction used to decarburize the molten iron. The frothing effect that is often generated as a result of these gasses can often prove to be a fatal obstacle in the efficient operation of the converter. In the present study, a simulated slag foam was produced by dispersing N2 bubbles in silicone oil. The effect of varying the volume fraction and bubble size of the dispersed gas phase, the shear rate, and the viscosity of the liquid phase, was then systematically investigated by measuring the viscosity of the N2 bubble dispersed silicone oil with a rotating viscometer. This found that the relative viscosity is increased as the volume fraction of the gas phase is increased, ultimately transitioning from a Newtonian to pseudo-plastic fluid at higher gas phase rates. In addition, an empirical model for the viscosity of the slag foam was developed by modifying the Einstein-Roscoe equation, with this model capable of reproducing the variation in relative viscosity with various gas phase rates, shear rates, and bubble sizes.

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The Relationship between the Apparent Viscosity and the Void Fraction in Two-Phase Flow

Cited by 7 publications

References 0 publications

Viscosity Evaluation of Simulated Foaming Slag via Interfacial Reaction at Room Temperature

Viscosity Evaluation of Simulated Foaming Slag via Interfacial Reaction at Room Temperature

Slit devolatilization of polymers

Rheological Behavior and Empirical Model of Simulated Foaming Slag

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