The Local Volume-Averaged Equations of Motion for a Suspension of Non-Neutrally Buoyant Spheres

Jiang, Tsung-Shann; Kim, Michael; Kremesec, V.J.; Slattery, John C.

doi:10.1080/00986448708911813

Cited by 17 publications

(20 citation statements)

References 31 publications

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“…Reviews of local volume averaging are available elsewhere (Slattery, 1981;Alemfin et al, 1988;Jiang et al, 1986). We will confine ourselves here to stating the notation and equations in terms of which we will be describing this problem.…”

Section: Local Volume Averagingmentioning

confidence: 99%

A linear stability analysis for immiscible displacements

Alem�n

Slattery

1988

Transp Porous Med

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A linear stability analysis has been performed for an immiscible displacement of a nonwetting phase by a wetting phase in a semi-infinite system of finite width and thickness. It is found that instabilities become a more severe problem as the capillary number based upon the characteristic thickness of the system increases. A displacement can always be stabilized, if the capillary number is sufficiently small. As the aspect ratio (ratio of thickness to width) decreases for a fixed capillary number, the potential for unstable behavior increases. All of this means that a displacement in the laboratory is likely to be more stable than a similar displacement in the field. Since the solution to the base state assumes the analytical solution of Yortsos and Fokas (1983), the effect of the mobiiity ratio could not be examined.

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Section: Local Volume Averagingmentioning

confidence: 99%

A linear stability analysis for immiscible displacements

Alem�n

Slattery

1988

Transp Porous Med

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“…This approach has been succe.ssfully illustrated in the context of momentum transfer problems (Lin and Slattery, 1982;Jiang et al, 1987;Alemhn and Slattery, 1988) but, as yet, no similar treatment has been given for dispersion.…”

Section: Introductionmentioning

confidence: 99%

A new description for dispersion

Chang

Slattery

1988

Transp Porous Med

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Chang and Slattery (1986) introduced a simplified model for dispersion that contains only two empirical parameters, both of which can be determined in one-dimensional experiments. The traditional model for dispersion (Nikolaevskii, 1959;Scheidegger, 1961;de Josselin de Jong and Bossen, 1961;Bear, 1961a;Peaceman, 1966;Bear, 1972) has three empirical parameters, two of which can be measured in one-dimensional experiments while the third, the transverse dispersivity, must be measured in experiments in which a two-dimensional concentration profile develops. For the common one-dimensional experiment in which the signs of the concentration gradient and of the velocity field are different, the simplified model and the traditional model give identical results. For a one-dimensional experiment in which the signs of the concentration gradient and of the velocity field are at least sometimes the same and for two-and three-dimensional flows, the simplified model of Chang and Slanery (1986) gives results that can differ from those predicted using the traditional model.Only the experimental data of Bear (1961b) and of Yule and Gardner (1978) are sufficiently complete to permit a comparison of the two models. Considering the quality of the experimental data, we can not distinguish between the predicted profiles based upon the simplified model and those based upon the traditional model.

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“…They all concluded that the suspension behaved like an incompressible Newtonian fluid in all flow fields. Jiang et al (1987) have developed the local volume averages of the equations of motion as well as the appropriate boundary conditions for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. As did Einstein (1906Einstein ( , 1956 and others (Landau and Lifshitz, 1959;Batchelor, 1970;Jeffrey and Acrivos, 1976), in their analysis of the single sphere problem they neglected particle interactions.…”

Section: Introductionmentioning

confidence: 99%

“…Since we are dealing with a suspension in which the positions of the spheres are unknown functions of time, we choose to work in terms of the local volume-averaged forms of these relations. Reviews of local volume averaging are available elsewhere (Slattery, 1981;Jiang et al, 1987;Aleman et al, 1988).…”

Section: Introductionmentioning

confidence: 99%

“…

The theory developed by Jiang et al (1987) for a flowing suspension of neutrally buoyant spheres in an incompressible Newtonian fluid is further tested for a limiting case of the Couette viscometer, for a limiting case of the cone-plate viscometer, and for the parallel-plate viscometer. Compared with the available data for the Couette viscometer, the average errors are less than 2.6% for y <0.10, 4.2% for y < 0.15, and 5.5% for y < 0.20.

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confidence: 99%

See 1 more Smart Citation

Flows of Neutrally Buoyant Suspensions in Several Viscometers

Kim

Jiang

et al. 1988

Chemical Engineering Communications

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The theory developed by Jiang et al. (1987) for a flowing suspension of neutrally buoyant spheres in an incompressible Newtonian fluid is further tested for a limiting case of the Couette viscometer, for a limiting case of the cone-plate viscometer, and for the parallel-plate viscometer. Compared with the available data for the Couette viscometer, the average errors are less than 2.6% for y <0.10, 4.2% for y < 0.15, and 5.5% for y < 0.20. The predictions of its limiting case for very dilute suspensions are capable of representing these data with errors less than 4% for y < 0.08. KEYWORDS Suspension Apparent viscosity Effective viscosity Couette viscometerCone-plate viscometer Parallel-plate viscometer.

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The Local Volume-Averaged Equations of Motion for a Suspension of Non-Neutrally Buoyant Spheres

Cited by 17 publications

References 31 publications

A linear stability analysis for immiscible displacements

A linear stability analysis for immiscible displacements

A new description for dispersion

Flows of Neutrally Buoyant Suspensions in Several Viscometers

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