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Non-Newtonian secretion flow in tubes

Published online by Cambridge University Press:  29 March 2006

J. M. Fitz-Gerald
J. M. Fitz-Gerald
Affiliation:
Department of Mathematics, University of Queensland, Brisbane, Australia
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Abstract

A model is developed for the phenomenon of non-Newtonian secretion in tubes. The motivation for this study is the problem of glandular secretion, particularly in the pancreas. Power-law fluids are considered in some detail, as being biologically appropriate. It is found that for a power-law fluid whose exponent is less than unity (the biological case) two types of flow occur. For a sufficiently high secretion pressure, all of the tube is used for secretion, and a nonlinear pressure profile results. Numerical solutions are obtained for the pressure and rate of efflux. When the secretion pressure parameter falls below a certain critical value, the upper end of the tube begins to be choked off, only part of the tube being used for secretion. This phenomenon does not occur for exponents greater than or equal to unity. Physiological implications are considered, and a qualitative discussion given for the case of non-power-law fluids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 3 , 25 November 1974 , pp. 529 - 539
Copyright
© 1974 Cambridge University Press

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References

Bird, R. B. 1956 A.I.Ch.E. J. 2, 428.
Heike, J. 1973 Thesis, University of Queensland.
Heike, J. & Fitz-Gerald, J. M. 1974 Biorheology, to appear.
Metzner, A. B. & Reed, J. C. 1955 A.I.Ch.E. J. 1, 434.