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On the mixing of a low Reynolds number biological jet with a quiescent outer bathing solution

Published online by Cambridge University Press:  29 March 2006

J. Richard Goldgraben  and
Sheldon Weinbaum
J. Richard Goldgraben
Affiliation:
Polytechnic Institute of Brooklyn, New York
Sheldon Weinbaum
Affiliation:
City College of the City University, New York
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Abstract

Existing analyses of the very low Reynolds number Stokes jet, e.g. Birkhoff & Zarantonello (1957) and Förste (1963), have been confined to a single-component fluid satisfying the usual zero-slip boundary conditions at a solid surface. In contrast, the low Reynolds number biological jets which emerge from the pores and channels at the secreting surfaces of numerous human, animal and insect organs entail the movement of water and solute subject to novel boundary conditions that arise from the local osmotic driving forces at the secreting surfaces. These boundary conditions introduce a nonlinear coupling between the fluid momentum and solute conservation equations. This paper first discusses the fundamental dimensionless groups and length scales that characterize these biological jet flows and then examines in detail, using the technique of matched inner and outer expansions, one flow situation important in epithelial membrane transport, namely, the two-dimensional mixing of an inhomogeneous jet with a quiescent outer bathing solution which is bounded by a semi-permeable mem brane in the plane of the exit. The paper concludes with a discussion of other physiologically relevant problems which arise from different orderings of the length scales, and different overall geometrical configurations and flow conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 159 - 175
Copyright
© 1973 Cambridge University Press

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References

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