Summary
The dispersion of a solute in non-Newtonian fluids flowing through channels and pipes has been studied by taking into account the homogeneous first-order chemical reaction. It is shown that for the same mean velocity of the flow the equivalent dispersion coefficient decreases as the rate of the chemical reaction increases. This decrease is enhanced due to non-Newtonian nature of the fluid.
Zusammenfassung
Die Verteilung eines gelösten Stoffes in nicht-newtonschen Flüssigkeiten, die durch Kanäle und Rohre fließen, wird unter Zugrundelegung einer homogenen chemischen Reaktion erster Ordnung untersucht. Es wird gezeigt, daß bei gleicher mittlerer Strömungsgeschwindigkeit der äquivalente Verteilungskoeffizient abnimmt, wenn die Reaktionsgeschwindigkeit zunimmt. Diese Abnahme wird bei nicht-newtonschen Flüssigkeiten noch verstärkt.
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Abbreviations
- c :
-
concentration of the solute in the fluid
- \(\frac{{dP}}{{dz}}\) :
-
pressure gradient
- D :
-
molecular diffusion coefficient
- D * :
-
equivalent dispersion coefficient
- J * :
-
flux used in Fick's law of diffusion
- K :
-
homogeneous chemical reaction rate constant
- L :
-
typical length of the system
- m :
-
consistency of the power law fluid
- n :
-
flow behaviour index (power law index)
- p :
-
index for systems
- \(\bar Q\) :
-
average flux of the solute across a section of the duct
- R :
-
radius of the tube and half thickness of the channel
- (r,z):
-
coordinate system
- t :
-
time
- v :
-
velocity component of the fluid alongz-direction
- \(\bar \upsilon \) :
-
mean velocity of the fluid alongz-direction
- τ :
-
shear stress
- τ 0 :
-
yield stress
- µ :
-
consistency of the fluid (in Bingham and Casson models)
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Shukla, J.B., Parihar, R.S. & Rao, B.R.P. Dispersion in non-Newtonian fluids: Effects of chemical reaction. Rheol Acta 18, 740–748 (1979). https://doi.org/10.1007/BF01533349
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DOI: https://doi.org/10.1007/BF01533349