Fluid stagnant, diffusion through

Equimolar Counter-Diffusion vs. Diffusion through Stagnant Fluid... 

Diffusion Through a Stagnant Fluid (Spherical Coordinates). 200... 

Another classification involves the number of phases in the reaction system. This classification influences the number and importance of mass and energy transfer processes in the design. Consider a stirred mixture of two liquid reactants A and B, and a catalyst consisting of small particles of a solid added to increase the reaction rate. A mass transfer resistance occurs between the bulk liquid and the surface of the catalyst particles. This is because the small particles tend to move with the liquid. Consequently, there is a layer of stagnant fluid that surrounds each particle. This results in reactants A and B transferring through this layer by diffusion in order to reach the catalyst surface. The diffusion resistance gives a difference in concentration between... 

Fig. 5. Case 3. Sherwood numbers far the transpart of finite size particles through a stagnant fluid to n spherical cellectnr under the action of diffusion and London forces...

The diffusion through the stagnant gas film surrounding the particles as well as the diffusion through the pores can play an important role in limiting the overall rate of reaction [1], In the case of heterogeneous reactions, in which a fluid contacts a solid... 

FIGURE 16 Schematic representation of the origins of zone-broadening behavior and mass transfer effects of a polypeptide or protein due to Brownian motion, eddy diffusion, mobile phase mass transfer, stagnant fluid mass transfer, and stationary-phase interaction transfer as the polypeptide or protein migrated through a column packed with porous particles of an interactive HPLC sorbent. 

For a solid-catalyzed reaction to take place, a reactant in the fluid phase must first diffuse through the stagnant boundary layer surrounding the catalyst particle. This mode of transport is described (in one spatial dimension) by the Stefan-Max well equations (see Appendix C for details) ... 

In catalytic reactions mass transfer from the fluid phase to the active phase inside the porous catalyst particle takes place via transport through a fictitious stagnant fluid film surrounding the particle and via diffusion inside the particle. Heat transport to or from the catalyst takes the same route. These phenomena are summarized in Fig. 8.15. 

For the same driving force (concentration gradient), J is the same for both cases, but different. Since i-y is always less than one, we see that equimolar counter-diffusion (126) is slower than diffusion through a stagnant fluid (127). This can be qualitatively understood as follows. Suppose that to get to class, you need to walk down a corridor that s crowded with other students. If everyone else was standing almost still (stagnant fluid), it would be easier to walk around them than if everyone is walking toward you (counter diffusion). 

Diffusion is not restricted to molecular transfer through stagnant layers of solid or fluid. It also takes place in fluid phases by physical mixing and by the eddies of turbulent flow, just as heat flow may occur by convection. This is called eddy diffusion. Sometimes the diffusion process is accompanied by bulk flow of the mixture in a direction parallel to the direction of diffusion, and it is often associated with heat flow. 

In considering the transport of a species from a fluid in turbulent flow toward a solid surface, for example, an electrochemically active species to an electrode, Nemst assumed that the transport was governed by molecular diffusion through a stagnant film of fluid of thickness 6. This model, although having questionable physical relevance, is quite useful for correlating effects such as the influence of chemical reaction on mass transfer. A few simple examples of the use of film theoiy to describe mass transfer in the presence of chemical reaction are considered here. 

I. Operating-line derivation. For the case of solute A diffusing through a stagnant gas and then into a stagnant fluid, an overall material balance on component A in Fig. 10.6-6 for a packed absorption tower is... 

In the practical applications of the mass-transfer operations, the fluids are always in motion, even in batch processes, so that we do not have stagnant fluids. While occasionally the moving fluids are entirely in laminar flow, more frequently the motion is turbulent. If the fluid is in contact with a solid surface, where the fluid velocity is zero, there will be a region in predominantly laminar flow adjacent to the surface. Mass transfer must then usually take place through the laminar region, and molecular diffusion predominates there. When two immiscible fluids in motion are in contact and mass transfer occurs between them, there may be no laminar region, even at the interface between the fluids. 

In the film theory description of the mass-transfer process occurring between two fluid phases or between a solid and a fluid phase, the complex mass-transfer phenomenon is substituted by the notion of simple molecular diffusion of the species through a stagnant fluid fUm of thickness <5. The actual concentration profiles of species A being transferred from phase 2 to phase 1 are shown in Figures 3.1.6 (a) and (b) in one phase only for a solid-liquid and a gas-iiquid system, respectively. The concentration of A in the liquid phase at the solid-liquid or the gas-Uquid interface is C. Far away from the interface it is reduced to a low value in the liquid phase. In turbulent flow, the curved profile of species A shown would correspond to the time-averaged value (Bird et al, 1960, 2002). According to the... 

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