Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-19T22:54:39.114Z Has data issue: false hasContentIssue false

Time-dependent releases of solute in parallel flows

Published online by Cambridge University Press:  21 April 2006

Ronald Smith
Affiliation:
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW. UK

Abstract

A superposition of δ-function inputs is used to investigate the approach to the steady state, oscillatory discharges, and a Gaussian pulse for high-Péclet-number parallel shear flows. Illustrative results are given for open-channel flow with a logarithmic velocity profile.

Type
Research Article
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barton N. G. 1983 The dispersion of solute from time-dependent releases in parallel flow. J. Fluid Mech. 136, 243267.Google Scholar
Brinkman H. C. 1950 Heat effects in capillary flow: I. Appl. Sci. Res. A2, 120124.Google Scholar
Carrier G. F. 1956 On diffusive convection in tubes. O. Appt. Maths. 14, 108112.Google Scholar
Chatwin P. C. 1973 On the longitudinal dispersion of dye whose concentration varies harmonically with time. J. Fluid Mech. 58, 657667.Google Scholar
Chatwin P. C. 1980 Presentation of longitudinal dispersion data. J. Hydraul. Div. ASCE 106, 7183.Google Scholar
Erdelyi A., Magnus W., Oberhettinger, F. & Tricomi F. G. 1954 Tables of Integral Transforms. vol. II. McGraw-Hill.
Gill, W. N. & Sankarasubramanian R. 1972 Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow Proc. R. Soc. Lond. A 327, 191208.Google Scholar
Philip J. R. 1963a The theory of dispersal during laminar flow in tubes: I. Austral. J. Phys. 16, 287299.Google Scholar
Philip J. R. 1963b The theory of dispersal during laminar flow in tubes: II. Austral. J. Phys. 16, 300310.Google Scholar
Smith, R. 1985 Contaminant dispersion viewed from a fixed position. J. Fluid Mech. 152, 217233.Google Scholar
Taylor G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube Proc. Roy. Soc. Lond. A 219, 186203.Google Scholar
Tsai, Y. H. & Holley E. R. 1978 Temporal moments for longitudinal dispersion. J. Hydraul. Div. ASCE 104, 16171634.Google Scholar