Boundary layers mass transfer

Liquid veloeity around a partiele affeets its mass transfer boundary layer (Figure 5.3) and lienee the mass flux. In foreed eonveetion, the dependenee of the mass transfer eoeffieient on hydrodynamies is given by the Frdssling equation... 

Perfect sink conditions externally with finite mass transfer boundary layers. 

Early investigators assumed that this so-called diffusion layer was stagnant (Nernst-Whitman model), and that the concentration profile of the reacting ion was linear, with the film thickness <5N chosen to give the actual concentration gradient at the electrode. In reality, however, the thin diffusion layer is not stagnant, and the fictitious t5N is always smaller than the real mass-transfer boundary-layer thickness (Fig. 2). However, since the actual concentration profile tapers off gradually to the bulk value of the concentration, the well-defined Nernst diffusion layer thickness has retained a certain convenience in practical calculations. 

Unsteady-state effects and transition times are also significant in forced convection. Whenever the mass-transfer boundary layer is large anywhere on the working electrode surface, the commonly employed experimental time range of a few minutes may not be adequate to reach the steady-state limiting current. 

Unsuitable position of the reference electrode resulting in inclusion of a high ohmic potential drop between reference and working electrode. Moreover, when extended surfaces are used over which the mass transfer boundary layer thickness depends on position, a suitable number of independent reference electrodes should be used to measure local overpotentials on electrically isolated segments of the working electrode. 

For flow parallel to an electrode, a maximum in the value of the mass-transfer rate occurs at the leading edge of the electrode. This is not only the case in flow over a flat plate, but also in pipes, annuli, and channels. In all these cases, the parallel velocity component in the mass-transfer boundary layer is practically a linear function of the distance to the electrode. Even though the parallel velocity profile over the hydrodynamic boundary layer (of thickness h) or over the duct diameter (with equivalent diameter de) is parabolic or more complicated, a linear profile within the diffusion layer (of thickness 8d) may be assumed. This is justified by the extreme thinness of the diffusion layer in liquids of high Schmidt number ... 

After initial start-up, it was found that the magnitude of transmembrane flux decreased dramatically, indicating that a mass transfer boundary layer may form on the filter media. This boundary layer appears to remain somewhat constant after about 6 h on-line, whereas the slope of the flux versus time plot (Figure 15.13) becomes fairly linear. This linear decrease in flux was found to continue over the next 43 h. This could be attributed to fouling of the membrane by the small iron/... 

The mass transfer boundary layer thickness, d, on a rotating disk electrode can be estimated by d = 1.6/J V a) where D is the substrate diffusion coefficient, v is the solution viscosity, and CO is the disk rotation speed. 

In an ideal stagnation flow, a certain amount of the flow that enters through the inlet manifold can leave without entering the thermal or mass-transfer boundary layers above the surface. For an axisymmetric, finite-gap, flow, determine how the bypass fraction depends on the separation distance and the inlet velocity. 

At the RDE, various approximate analytical treatments have been presented by dropping the highest order convective term [237], neglecting convection completely [238], and by assuming a linear concentration profile within a time-dependent mass transfer boundary layer [239]. The last of these gives... 

Mass transfer from a surface to the gas-solid suspension is significantly higher than that for particle-free conditions. This increase is due to a possible reduction of the mass transfer boundary layer and an increase in the interstitial gas velocity when particles are present. The effect on heat transfer is even more significant as solid particles also act as heat carriers. 

Mass-transfer boundary layer (Nernst diffusion layer)... 

FIGURE 3 Illustration of the concept of an external mass transfer boundary layer resistance and associated concentrations of the rejected species, B. 

The rate of reaction at atmospheric pressure can be estimated by equating the rate of the surface reaction given by 2 to the rate of diffusion through the mass transfer boundary layer at the catalyst surface. 

Boundary layer mass transfer Boundary layer heat transfer... 

Boundary layei—mass transfer Boundary layer—heat transfer... 

Fig. 19. Isoconcentration contours for a mass transfer boundary layer thickness equivalent to the notch depth d. (Figure and caption reprinted from Jordan and Tobias [57] by permission of the publisher, The Electrochemical Society, Inc.).

Fig. 20. Increase in flux as a function of distance along the perimeter for a mass transfer boundary layer thickness equivalent to the notch depth d. Note that the perimeter is longer than the distance in the X direction, hence the locations on the perimeter of the left corner, central trench, and right corner are also shown. (Figure and caption reprinted from Jordan and Tobias [57] by permission of the pubUsher, The Electrochemical Society, Inc.).

To begin our discussion on the diffusion of reactants from the bulk fluid to the external smface of a catalyst, we shall focus attention on the flow past a single catalyst pellet. Reaction takes place only on the catalyst and not in the fluid surroimding it. The fluid velocity in the vicinity of the spherical pellet will vaiy with position aroimd the sphere. The hydrodynamic boundary layer is usually defined as the distance from a solid object to where the fluid velocity is 99% of the bulk velocity U. Similarly, the mass transfer boundary layer thickness, 8, is defined as the distance from a solid object to where the concentration of the diffusing species reaches 99% of the bulk concentration. 

The influence of a wall on the turbulent transport of scalar (species or enthalpy) at the wall can also be modeled using the wall function approach, similar to that described earlier for modeling momentum transport at the wall. It must be noted that the thermal or mass transfer boundary layer will, in general, be of different thickness than the momentum boundary layer and may change from fluid to fluid. For example, the thermal boundary layer of a high Prandtl number fluid (e.g. oil) is much less than its momentum boundary layer. The wall functions for the enthalpy equations in the form of temperature T can be written as ... 

The Schmidt number for the mass transfer is analogous to the Prandtl number for heat transfer. Its physical implication means the relative thickness of the hydrodynamic layer and mass-transfer boundary layer. The ratio of the velocity boundary layer (S) to concentration boundary layer (Sc) is governed by the Schmidt number. The relationship is given by... 

But before the virtues of the results and the approach are extolled, the method must be described in detail. Let us therefore return to a systematic development of the ideas necessary to solve transport (heat or mass transfer) problems (and ultimately also fluid flow problems) in the strong-convection limit. To do this, we begin again with the already-familiar problem of heat transfer from a solid sphere in a uniform streaming flow at sufficiently low Reynolds number that the velocity field in the domain of interest can be approximated adequately by Stokes solution of the creeping-flow problem. In the present case we consider the limit Pe I. The resulting analysis will introduce us to the main ideas of thermal (or mass transfer) boundary-layer theory. 

Although the effects of blowing/suction that are due to mass transfer at the body surface thus play an important role in determining the rate of mass transfer, it is worthwhile to emphasize once again that the transport rate in this limit Sc -> oc was still assumed to be small enough that the flow is not modified at the leading order of approximation. We have seen that the normal velocity relevant to the mass transfer boundary layer is... 

Problem 11-7. Mass Transfer with Finite Interfacial Velocities. In Section G, we considered the problem of mass transfer at large Reynolds and Schmidt numbers from an arbitrary 2D body with a no-slip boundary condition imposed at the particle surface. We noted that the form of the solution would be different if the tangential velocity at the body surface were nonzero, i.e., us(x) / 0. Determine the form of the mass transfer boundary-layer equation for this case, and solve it by using a similarity transformation. What conditions, if any, are required of us(x) for a similarity solution to exist ... 

Transport of Electro-Active Species in the Mass Transfer Boundary Layer... 

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