Agnès Montillet

Experimental characterization of flow regimes in various porous media—II: Transition to turbulent regime

Abstract This work deals with hydrodynamics in porous media beyond the end of the stable laminar regime, at higher Reynolds numbers. Local measurements of current fluctuations were carried out with electrochemical probes located at different positions in the porous media. Owing to the use of the electrochemical transfer function, the spectrum of velocity gradient fluctuations at the micro-electrodes and the velocity gradient fluctuating rate were determined. In packed beds of particles, a stabilization of this fluctuation rate was observed at most electrodes in the Reynolds number range covered. It is shown that this stabilization corresponds to a locally turbulent flow. In reticulated media, no such stabilization was observed. The characteristic length scales of the flow, i.e. the order of magnitude of the flow eddies dimensions, were evaluated from the autocorrelation function of the velocity gradient fluctuations calculated from the spectrum. They were compared to the pore diameter calculated from the capillary model proposed by Comiti and Renaud [(1989), Chem Engng Sci. 44, 1539 –1545]. The stable values of the length scales obtained for high Reynolds numbers confirm the turbulent nature of the flow regime. The flow regime transition is gradual from laminar to turbulent in the entire bed, it is characterized with the pore Reynolds number, Re p , based on the employed capillary model: in packed beds presenting an isotropy in the plane perpendicular to the main direction of the fluid flow, the laminar regime ends at Re p =180 whereas a value of Re p =900 corresponds to the stabilization of the velocity gradient fluctuating rate at 90% of the electrodes. Calculations, based on a pressure drop model related to the capillary representation, show that the percentage of inertial effect on the pressure drop is then about 90% at this Reynolds number in these packed beds.

Experimental characterisation of flow regimes in various porous media—I: Limit of laminar flow regime

This work is part of a global study of flow regimes in porous media beyond Darcy regime. In view of determining the end of stable laminar regime in various porous media such as beds packed with spheres, stratified media and reticulated media, electrochemical micro-probes are inserted inside the medium and at the wall of test sections. Local instantaneous measurements of the limiting current intensity are implemented. Spectral analysis of the signal fluctuations enables an accurate determination of the end of stable laminar regime in the studied media. The comparison between internal measurements and those implemented at the wall of the cell shows that the latter are representative of the flow in the case of reticulated media but not in the case of packed beds of particles for which the use of internal probes is necessary. Results are expressed thanks to a pore Reynolds number Rep, based on a capillary representation of the porous media. Rep≈180 characterises the end of the stable laminar regime in packed beds of particles presenting an isotropy in the plane perpendicular to the main direction of the fluid flow. A ‘laminarising effect’ is observed for synthetic foams. For each porous media tested, the percentage of viscous and inertial contributions in the pressure drop are given at the onset of fluctuations.

Liquid—solid mass transfer in packed beds of variously shaped particles at low Reynolds numbers: experiments and model

Abstract The cathodic reduction of ferricyanide ions is used to characterize liquid—solid mass transfer in porous electrodes in the creeping flow regime. Our study deals with packed beds of spheres, long cylinders and plates of low height-to-side ratio. Correlations are proposed and compared with predictive equations based on the association of the capillary representation of the porous medium with the analytical solution for mass transfer at a pipe wall, for fully developed laminar flow in short tubes. The model leads to satisfying values of the mass transfer coefficient in the case of beds packed with spheres and parallelepipedal particles.

Modelling of power law liquid-solid mass transfer in packed beds at Darcy regime

A model of liquid-to-particle mass transfer in packed beds with single phase non-Newtonian creeping flow is derived using a coherent approach which associates the Leveque solution with a capillary-type representation of the porous structure. The model is compared to experimental data obtained with spherical and anisotropic parallelepipedal particles, respectively, as well as to literature results. The model allows to predict mass transfer in fixed beds of spheres and anisotropic parallelepipedal particles with a mean relative error of 11%. It is also shown that a better prediction of mass transfer is obtained for parallelepipedal particles if the surface area really offered to fluid flow is considered. Dimensionless numbers based on the pore dimension are shown to be more suitable than those based on a particle diameter.

Numerical Study of the Flow and Mass Transfer in Micromixers

Computational fluid dynamic simulations are used to characterize the flow and the liquid mixing quality in a micromixer as a function of the Reynolds number. Two micromixers are studied in steady flow conditions; they are based on two geometries, respectively T-shaped and cross-type (⊤ and + shapes). Simulations allow, in the case of ⊤ micromixers, to chart the topology of the flow and to describe the evolution of species concentration downstream the intersection. The streamline layout and the mixing quality curves reveal the three characteristic types of flow, depending on Reynolds number: stratified, vortex and engulfment flows. Vortices appear after impingement, in the exit channel. They become asymmetrical and gain in length with an increase in Re making the flow unsteady, which induces an enhancement of the mass transfer by advection between the two liquids. In the case of cross-type micromixers, the structure of the flow is strongly three-dimensional. It is characterized by symmetrical vortices in both output channels. In the zone close to the impingement, a back flow is observed which induces strong shear stresses. The results show that the + shaped system can improve the mixing process in comparison with the micromixers having ⊤ geometry. The numerical study also allows to select the locations of the most relevant zones of study, from an experimental point of view. It will allow to choose the location of PIV planes and local non intrusive sensors, such as electrochemical microprobes, in order to experimentally investigate the flow.© 2008 ASME

Characterisation of Flow and Mass Transfer in Cross Shape and T-Shape Micromixers

The understanding of physical phenomena such as flow behaviour and mass transfer performance is needed in order to develop appropriate micromixers for industrial or biomedical applications. In this work, CFD is used to characterize the flow and the liquid mixing quality in a micromixer as a function of the Reynolds number. Two micromixers are studied in steady flow conditions; they are based on two geometries, respectively T-shaped (⊤) and cross-type (+). Simulations allow, in the case of ⊤ micromixers, to chart the topology of the flow and to describe the evolution of species concentration downstream the crossing. The streamlines layout and the mixing quality curves reveal three characteristic types of flow previously reported in the literature, depending on Reynolds number: stratified, vortex and engulfment flows. In the case of cross-type micromixers, the structure of the flow is strongly three-dimensional and is characterized by symmetrical vortices in both output channels. The results show that the + shaped system can improve the mixing process in comparison with the micromixers having ⊤ geometry. The second part of the study is experimental. Two cells are constructed, for both geometries (T-shaped and cross) using square channels with 400 μm hydraulic diameter. In order to use particle image velocimetry (PIV), a system has been adapted to measure velocity fields for various channel plans at different channel depths. This allows observing the evolution of the flow and the vortices development along the microchannels. A second experimental technique, the electrochemical one involving microelectrodes implemented at several positions on the channel wall located near the crossing, has been used. The electrochemical method can locally characterize the formation of swirling flows. These two complementary experimental results will be analysed and a comparison with the CFD results will be performed.Copyright