Dean vortices with wall flux in a curved channel membrane system.: 6. Two dimensional magnetic resonance imaging of the velocity field in a curved impermeable slit

Abstract

Nuclear magnetic resonance flow imaging (MRFI) was used to measure fluid flow noninvasively in a curved 180° slit with impermeable walls. The flow rates were kept constant at 0.5, 1.0, 1.75 and 2 times the critical Dean number ( De c). Above the critical Dean number, the laminar flow changed to unstable viscous flow resulting in rotating spiral vortices (called Dean vortices). The NMR results (wavenumber a=2.3) are in reasonable agreement with Finlay et al.'s theoretical predictions [J. Fluid Mech., 194 (1988) 417] in which the a varied from 2.4 to 2.7 for 1.5 De c to 2.0 De c. It is these vortices that can be used to depolarize the solute build-up near the membrane-solution interface. Also, we determined the distance the vortices persisted and how vortex strength decreased along the flat slit. It suggests the possibility that new membane modules can be designed with curved entrances (to produce vortices) and flat sections (to maximize packing considerations and reduce complexity).