K. H. Jensen ,T. Bohr and H. Bruus
Journal of Fluid Mechanics, 2010.
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.