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Self-consistent unstirred layers in osmotically driven flows

Published online by Cambridge University Press:  27 September 2010

K. H. JENSEN ,
T. BOHR  and
H. BRUUS
K. H. JENSEN*
Affiliation:
Center for Fluid Dynamics, Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech Building 345 East, DK-2800 Kongens Lyngby, Denmark
T. BOHR
Affiliation:
Center for Fluid Dynamics, Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark
H. BRUUS
Affiliation:
Center for Fluid Dynamics, Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech Building 345 East, DK-2800 Kongens Lyngby, Denmark
*
†Email address for correspondence: kaare.hartvig.jensen@nanotech.dtu.dk
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Abstract

It has long been recognized that the osmotic transport characteristics of membranes may be strongly influenced by the presence of unstirred concentration boundary layers adjacent to the membrane. Previous experimental as well as theoretical works have mainly focused on the case where the solutions on both sides of the membrane remain well mixed due to an external stirring mechanism. We investigate the effects of concentration boundary layers on the efficiency of osmotic pumping processes in the absence of external stirring, i.e. when all advection is provided by the osmosis itself. This case is relevant in the study of intracellular flows, e.g. in plants. For such systems, we show that no well-defined boundary-layer thickness exists and that the reduction in concentration can be estimated by a surprisingly simple mathematical relation across a wide range of geometries and Péclet numbers.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Convection: Convection Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 197 - 208
Copyright
Copyright © Cambridge University Press 2010

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References

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