External through boundary layer

External Mass Transfer Through Boundary Layer... 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

There are several resistances which may hinder the movement of a molecule of adsorbate from the bulk fluid outside a pellet to an adsorption site on its internal surface, as shown in Figure 17.15. Some of these are sequential and have to be traversed in series, whilst others derive from possible parallel paths. In broad terms, a molecule, under the influence of concentration gradients, diffuses from the turbulent bulk fluid through a laminar boundary layer around a solid pellet to its external surface. It then diffuses, by various possible mechanisms, through the pores or the lattice vacancies in the pellet until it is held by an adsorption site. During desorption the process is reversed. 

The various layers of the fuel-cell sandwich described above are linked to each other through boundary conditions, which apply at the mesh point between two regions. There are two main types of boundary conditions, those that are internal and those that are external. The internal boundary conditions occur between layers inside the modeling domain, and the external ones are the conditions at the boundary of the entire modeling domain. 

The steps that must be involved in a catalytic reaction on a surface are shown in Figure 7-8. Reactant Ab in the bulk of the flowing fluid must migrate through a boundary layer over the pellet at the external surface of the peUet. It must then migrate down pores within the pellet to find surface sites where it adsorbs and reacts to form B, which then reverses the process to wind up in the flowing fluid, where it is carried out of the reactor. 

Diffusion of the reactants through a boundary layer or film adjacent to the external surface of the catalyst (film diffusion or interphase diffusion)... 

Diffusion of the products through the external boundary layer into the bulk fluid phase (interphasc diffusion)... 

The Prandtl number via has been found to be the parameter which relates the relative thicknesses of the hydrodynamic and thermal boundary layers. The kinematic viscosity of a fluid conveys information about the rate at which momentum may diffuse through the fluid because of molecular motion. The thermal diffusivity tells us the same thing in regard to the diffusion of heat in the fluid. Thus the ratio of these two quantities should express the relative magnitudes of diffusion of momentum and heat in the fluid. But these diffusion rates are precisely the quantities that determine how thick the boundary layers will be for a given external flow field large diffusivities mean that the viscous or temperature influence is felt farther out in the flow field. The Prandtl number is thus the connecting link between the velocity field and the temperature field. 

To analyze the heat-transfer problem, we must first obtain the differential equation of motion for the boundary layer. For this purpose we choose the jc coordinate along the plate and the y coordinate perpendicular to the plate as in the analyses of Chap. 5. The only new force which must be considered in the derivation is the weight of the element of fluid. As before, we equate the sum of the external forces in the x direction to the change in momentum flux through the control volume dx dy. There results... 

The present models describe the extraction of porous particles completely filled with a liquid solute. The dissolution of liquid is followed by intraparticle diffusion up to the particle surface and then by external diffusion through a solvent boundary layer into the flowing solvent bulk. Three different particle geometries were modeled spheres, cylinders with ends mechanically sealed and cylinders with open ends available for extraction. 

In stud dng stability of flows, it is convenient to pose the problem either as a temporal or as a spatial instability problem. While it is numerically expedient to take a temporal approach, many practical flows are known to follow spatial route. For example in lab experiments for external wall-bounded flows, it is noted that the disturbances grow in space as they travel downstream. This was established unambiguously through the experiments of Schubauer Skramstad (1947) for flat plate boundary layer and is an excellent example of spatial instability problems. However, there are many flows where the instability grows both in space and time. These type of problems to identify whether the flow suffers temporal and/ or spatial instability arise in linear stability analysis. Flow instability studied following descriptions of two independent routes, is an artificial way of treating general instability problems. 

Figure 6.1.1 depicts the concentration profile of a reactant in the vicinity of a catalyst particle. In region 1, the reactant diffuses through the stagnant boundary layer surrounding the particle. Since the transport phenomena in this region occur outside the catalyst particle, they are commonly referred to as external, or... 

Diffusion through the boundary layer to the external carbon surface... 

For the moment let s assume the transport of A from the bulk fluid to the external surface of the catalyst is the slowest step in the sequence. We lump all the resistance to transfer from the bulk fluid to the surface in the boundary layer surrounding the pellet. In this step the reactant A at a bulk concentration C most travel through the boundary layer of thickness 8 to the external surface of the pellet where the concentration is Cm as shown in Figure 10-8. The rate of transfer (and hence rate of reaction, -r ) for this slowest step is... 

Figure 10-8 Diffusion through the external boundary layer. [Also. see Figure El 1-1.1.]...

For a low-viscosity drop falling through a viscous liquid with no surface-active material present, the velocity boundary layer in the external fluid almost disappears. Fluid elements are exposed to the drop for short times and the mass transfer is governed by the penetration theory. It can be shown that the efiective contact time is the time for the drop to fall a distance equal to its own diameter, and application of the penetration theory leads to the equation... 

Physical transport processes can play an especially important role in heterogeneous catalysis. Besides film diffusion on the gas/liquid boundary there can also be diffison of the reactants (products) through a boundary layer to (from) the external surface of the solid material and additionally diffusion of them through the porous interior to from the active catalyst sites. Heat and mass transfer processes influence the observed catalytic rates. For instance, as discussed previously the intrinsic rates of catalytic processes follow the Arrhenius... 

External diffusion limitation by mass transfer through layers in front of the enzyme membrane, eg, a semipermeable membrane or the boundary layer at the solution/biosensor membrane interface. 

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