Laminar flows mass-transfer rate

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. 

When the flow in the boundary layer is turbulent, streamline flow persists in a thin region close to the surface called the laminar sub-layer. This region is of particular importance because, in heat or mass transfer, it is where the greater part of the resistance to transfer lies. High heat and mass transfer rates therefore depend on the laminar sublayer being thin. Separating the laminar sub-layer from the turbulent part of the boundary... 

Fig. 5. Local mass transfer rate on the surface of a rotating hemisphere in laminar flow. Here the meridional angle, 9, is given in degrees.

The Chilton-Colburn analogy can be also used to estimate the local mass transfer rate in laminar flow where the wall shear stress is related to the azimuthal velocity gradient by... 

Free convection flow around horizontal cylinders and spheres is laminar for moderate values of GrSc (see Table VII, Part C) mass-transfer rates obey correlations of the same type as that for a vertical plate electrode, Eq. (29a) ... 

Apart from the nature of the bulk flow, the hydrodynamic scenario close to the surfaces of drug particles has to be considered. The nature of the hydrodynamic boundary layer generated at a particle s surface may be laminar or turbulent regardless of the bulk flow characteristics. The turbulent boundary layer is considered to be thicker than the laminar layer. Nevertheless, mass transfer rates are usually increased with turbulence due to the presence of the viscous turbulent sub-layer. This is the part of the (total) turbulent boundary layer that constitutes the main resistance to the overall mass transfer in the case of turbulence. The development of a viscous turbulent sub-layer reduces the overall resistance to mass transfer since this viscous sub-layer is much narrower than the (total) laminar boundary layer. Thus, mass transfer from turbulent boundary layers is greater than would be calculated according to the total boundary layer thickness. 

Study of the eflSciency of packed columns in liquid-liquid extraction has shown that spontaneous interfacial turbulence or emulsification can increase mass-transfer rates by as much as three times when, for example, acetone is extracted from water to an organic solvent (84, 85). Another factor which may be important for flow over packing has been studied by Ratcliff and Reid (86). In the transfer of benzene into water, studied with a laminar spherical film of water flowing over a single sphere immersed in benzene, they found that in experiments where the interface was clean... 

The thickness of the liquid film on the rotor packing helps determine mass transfer rates. Film thickness can be shown to be inversely proportional to rotor speed to the 0.8 power (17). Visual measurements using a video camera attached to the rotor show a water film thickness of 20-80 microns on foam metal packing and 10 microns on wire gauze packing (15). Theoretical models estimate similar film thickness values (13,18,19). Film flow is expected to be laminar. In addition to rotor speed, liquid flow rate and fluid properties affect the film thickness (14). 

Metal monoliths can be shaped rather freely. A good example is given in Figure 4 (9), where it can be seen that in these parallel-channel systems the structure of the channels is such that the turbulence increases. The reasoning behind that is the wish to counteract the low mass transfer rates associated with laminar flow in the thin channels of the monolith. 

The electrode is uniformly accessible to the diffusing ions within dimensionless electrode radius, 0.1 < R/d < 1.0, for turbulent nozzle flow and, 0.1 < R/d < 0.5, for laminar nozzle flow. Within the region of uniform accessibility, the mass transport rate is relatively independent of the electrode size in both laminar and turbulent flow for 0.2 < Hjd < 6, where H is the nozzle-to-plate distance. Beyond the region of uniform accessibility, the mass transfer rate decreases with the radial distance. In the intermediate range, 1 < R/d < 4, the turbulent impinging jet changes from the stagnation flow to the wall-jet flow and for R/d > 4 the wall-jet flow predominates (- wall-jet electrode). 

These equations are identical to the equations describing mass transfer in monolithic reactors. For monolithic reactors it was shown [14] that when the reaction rate is very fast compared to the mass transfer rate in the fluid domain, the boundary condition of Eq. (1 5) becomes identical to the standard heat transfer boundary condition of constant wall temperature when the reaction rate is very slow compared to the mass transfer rate in the fluid domain, the boundary condition of Eq. (IS) becomes identical to the standard heat transfer boundary condition of constant heat flux. The influence of the boundary conditions on the mass transfer coefficient in case of laminar flow is discussed in the following section. 

Proof that the low intensity of colorization downstream of the entry region in the parallel-channel structure is due to formation of a laminar boundary layer, rather than to the lack of further ammonia for transfer, is offered by a second experiment conducted by Gaiser and illustrated in Fig. 8. Here a cross-flow structure is placed immediately downstream of the parallel-channel structure, and the mass transfer rate rises dramatically, indicating that much ammonia remained in the gas at the parallel-channel structure outlet. 

The velocity at the wall increases more steeply in turbulent flow than in laminar. The shear stress and with that the resistances to flow are larger in turbulent flows than in laminar. Likewise the temperature and concentration gradients at the surface and therefore the heat and mass transfer rates are larger for turbulent flows than in laminar ones. Therefore turbulent flows are to be strived for in heat and mass transfer and for this reason they are present in most technical applications. However better heat and mass transfer has to be paid for by the increased power required for a pump or blower to overcome the resistances to flow. 

Each particle in a bed of porous particles is surroimded by a laminar sublayer (Figure 5.4), through which mass transfer takes place only by molecular diffusion. On one side, this layer is exposed to the flowing mobile phase and is entirely accessible. On the other side, it wraps the particle wall and is accessible from the particle inside only at the pore openings. The thickness of this layer, hence the mass transfer coefficient, is determined by hydrodynamic conditions and depends on the flow velocity. The mass transfer rates can be correlated in terms of the effective mass transfer coefficient, fcy, defined according to a linear driving force equation ... 

As outlined earlier, hemodialysis and hemofiltration require the removal of solutes smaller than albumin from blood. Solute mass transfer rates across hemodialysis membranes cannot exceed the diffusivity of the solute In water. Solute diffusivity decreases with Increasing molecular diameter (Stokes-Einstein relationship) consequently, solute mass transfer rates for hemodlalyzers intrinsically decrease with increasing molecular size. In addition to limitations Imposed by diffusion In solution, mass transfer is further limited by diffusion resistance in the membrane as well as boundary layer effects resulting from laminar flow both of these effects are also functions of molecular size. The quantitation of mass transfer In hemodlalyzers has been reviewed extensively (22). 

The second example is also concerned with estimation of mass-transfer rates in the presence of unsteady, laminar fluid flows. The present problem was investigated because an understanding of mass-transfer rates behind bluff bodies may enable the development of mixing methods for high-end metallization applications. This example is chosen here to highlight the complexity in flow fields that can appear in an ostensibly simple geometry. 

In laminar incompressible flow with low mass-transfer rates and constant physical properties past a flat plate, the equations to be solved for a binary mixture are the following (Welty et al., 1984) ... 

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