Diffusion in a Power-Law fluid: a mathematical study

Harlacher, Eugene A.; Engel, A. J.

doi:10.1016/0009-2509(70)85100-4

Chemical Engineering Science

1970

DOI: 10.1016/0009-2509(70)85100-4

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Diffusion in a Power-Law fluid: a mathematical study

Eugene A. Harlacher

A. J. Engel

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1975

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Cited by 7 publications

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“…Erdogan (1967) applied Taylor-Aris dispersion theory to non-Newtonian fluids which obey the Casson constitutive equation and compared his results with those of Fan and co- workers (1965,1966). Harlacher and Engel (1970) predicted the steady-state concentration distribution resulting from a step change at some point along the axis for laminar flow tube flow of power-law fluids. However, Gill and Sankarasubramanian (1972) have shown that Harlacher and Engel's results are useful only for relatively large distances from the continuous source.…”

mentioning

confidence: 99%

Dispersion in the Laminar Flow of Power-Law Fluids through Straight Tubes

Booras¹,

Krantz²

1976

Ind. Eng. Chem. Fund.

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The generalized dispersion model of Gill and Sankarasubramanian is applied to the laminar tube flow of powerlaw fluids. The time-independent dispersion coefficient, when appropriately nondimensionalized, is within ±2% of the Newtonian dispersion coefficient for the range of flow behavior indices 0.5 < < 1.2. In all cases the time-dependent dispersion coefficient is within 95% of its time-independent value at a dimensionless time of = 0.30. The Taylor-Aris dispersion theory results appear to apply with negligible error when r > 0.60. This analysis suggests that the widely used generalized dispersion model may not be applicable at very small , at least for high Peclet number flows.Dispersion theory is concerned with the dispersal of a solute in a flowing fluid due to the combined action of a nonuniform velocity profile, molecular diffusion, and eddy diffusion in turbulent flows. Numerous papers have discussed dispersion in a variety of laminar and turbulent flows since Sir Geoffrey Taylor (1953) and Aris (1956) published the first papers on the subject. However, most papers have been confined to dispersion in Newtonian fluids.Developments in the areas of polymer processing, biomedical engineering, and biochemical processing have contributed to the ever-increasing interest in the flow and properties of non-Newtonian fluids. Typical occurrences of this dispersion phenomenon in applications involving non-Newtonian fluids include the behavior of dyes in injection molding processes, the determination of the residence time of tracer solutes injected into the bloodstream, the transport of slurries and polymer solutions, and the design of flow reactors for biological systems.Relatively few papers have considered dispersion in non-Newtonian fluids. Taylor-Aris dispersion theory has been extended to the laminar tube flow of power-law, Bingham plastic, and Ellis fluids by Fan and co-workers (1965,1966). Erdogan (1967) applied Taylor-Aris dispersion theory to non-Newtonian fluids which obey the Casson constitutive equation and compared his results with those of Fan and co- workers (1965,1966). Harlacher and Engel (1970) predicted the steady-state concentration distribution resulting from a step change at some point along the axis for laminar flow tube flow of power-law fluids. However, Gill and Sankarasubramanian (1972) have shown that Harlacher and Engel's results are useful only for relatively large distances from the continuous source. Taylor-Aris dispersion theory has been extended to the turbulent tube flow of power-law fluids by Wasan and Dayan (1970) and Krantz and Wasan (1974). This brief review indicates that all analyses of dispersion in non-Newtonian fluids have followed Taylor-Aris dispersion theory. Ananthakrishnan et al. (1965) have shown that Taylor-Aris dispersion theory for Newtonian fluids applies only for sufficiently large values of the dimensionless time r ( =

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mentioning

confidence: 99%

Dispersion in the Laminar Flow of Power-Law Fluids through Straight Tubes

Booras¹,

Krantz²

1976

Ind. Eng. Chem. Fund.

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Convective diffusion from a non-uniformly distributed source in flowing blood

Mashelkar

Venkatsubramanian

1975

Appl. Sci. Res.

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A flow method for measuring difusion coefficients in power law fluids

Deo

Vasudeva

1977

Chemical Engineering Science

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Diffusion in a Power-Law fluid: a mathematical study

Cited by 7 publications

References 4 publications

Dispersion in the Laminar Flow of Power-Law Fluids through Straight Tubes

Dispersion in the Laminar Flow of Power-Law Fluids through Straight Tubes

Convective diffusion from a non-uniformly distributed source in flowing blood

A flow method for measuring difusion coefficients in power law fluids

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