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Two-dimensional shear dispersion for skewed flows in narrow gaps between moving surfaces

Published online by Cambridge University Press:  26 April 2006

Ronald Smith
Ronald Smith
Affiliation:
Department of Mathematical Sciences, University of Technology, Loughborough LE11 3TU, UK
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Abstract

Flows transporting material between nearby moving surfaces are ubiquitous in machinery of all scales and with a variety of geometries. Here a general derivation is given of the effective two-dimensional mixing process in a narrow gap for a solute or miscible fluids. Explicit formulae are given for the shear dispersion tensor in laminar and turbulent (logarithmic velocity profile) flows. It is shown that if improved mixing is required, then the optimum direction for additional boundary motion or stress is at right angles to the primary flow direction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 211 - 228
Copyright
© 1990 Cambridge University Press

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References

Aris, R. 1956 On the dispersion of a solute in a fluid through a tube.. Proc. R. Soc. Lond. A 235, 67–77.Google Scholar
Bugliarello, G. & Jackson, E. D. 1964 Random walk study of convective diffusion. Engng Mech. Div. ASCE 90, 49–77.Google Scholar
Csanady, G. T. 1969 Diffusion in an Ekman layer. J. Atmos. Sci. 26, 414–475.Google Scholar
Elder, J. W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5, 544–560.Google Scholar
Fischer, H. B. 1978 On the tensor form of the bulk dispersion coefficient in a bounded skewed shear flow. J. Geophys. Res. 83, 2373–2375.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Tables of Integrals, Series and Products. Academic Press.
Hamrick, J. M. 1986 Long-term dispersion in unsteady skewed free surface flow. Estuarine, Coastal Shelf Sci. 23, 807–845.Google Scholar
Saffman, P. G. 1962 The effect of wind shear on horizontal spread from an instantaneous ground source. Q. J. R. Met. Soc. 88, 382–393.Google Scholar
Smith, F. B. 1965 The role of wind shear in horizontal diffusion of ambient particles. Q. J. R. Met. Soc. 91, 318–329.Google Scholar
Smith, R. 1979 Buoyancy effects upon lateral dispersion in open-channel flow. J. Fluid Mech. 90, 761–779.Google Scholar
Taylor, A. D. 1982 Puff growth in an Ekman layer. J. Atmos. Sci. 39, 837–850.Google Scholar
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube.. Proc. R. Soc. Lond. A 219, 186–203.Google Scholar