Mass transfer convection

Concentration fully developed region The region where the dimensionless concentration profile remains invariable along the longitudinal length of the channel. 

Concentration boundary layer for flow over a solid surface. 

Concentration entry length and fully developed region for internal flow in a charmel. 

Concentration entry length (L J The length required for the dimensionless concentration profile to become fully developed. 

Since the fluid is stationary at the solid surface, the mass of species i is transferred by molecular diffusion normal to the surface and is expressed by the diffusion rate equation (Equation 1.78) as 

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Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

Note Equation (4.241) characterizes diffusion when the mixture element is in steady state with no turbulence. Diffusion in a pipe can be represented by Eq. (4.241) in convective mass transfer the flow and turbulence are important. 

Figures 4.34 and 4.35 represent two extreme cases. Drying processes represent the case shown in Fig. 4.34 and distillation processes represent Fig. 4.35. Neither case represents a convective mass transfer case while the gas flow is in the boundary layer, other flows are Stefan flow and turbulence. Thus Eqs. (4.243) and (4.244) can seldom be used in practice, but their forms are used in determining the mass transfer factor for different cases.

Fig. 10. Numerical solutions of the forced-convection mass-transfer equation for the case of irreversible first-order chemical reaction [after Johnson et al. (J4)] (Solid lines— rigid spheres dashed lines—circulating gas bubbles).

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

In the second example, let the case of forced convective mass transfer in pipe flow be considered. Let it be assumed that the turbulent flow of the fluid, B, through the pipe is accompanied by a gradual dissolution of the material, A, of the pipe wall. Experimental... 

Thus, the case of forced convective mass transfer in pipe flow, one has Sh — f (Re, Sc)... 

To consider the convective mass transfer problem of a rotating hemisphere electrode, we assume that sufficient inert salts are present in the electrolyte that the migrational... 

Convection is mass transfer that is driven by a spatial gradient in pressure. This section presents two simple models for convective mass transfer the stirred tank model (Section II.A) and the plug flow model (Section n.B). In these models, the pressure gradient appears implicitly as a spatially invariant fluid velocity or volumetric flow rate. However, in more complex problems, it is sometimes necessary to develop an explicit relationship between fluid velocity and pressure gradients. Section II.C describes the methods that are used to develop these relationships. 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Figure 2 The stirred tank, a simple model for convective mass transfer. The liquid in the tank is characterized by its volume (V), density (p), and the concentrations of the components (CA). Liquid enters through the inlet stream at a flow rate Qm and concentration CA0. Liquid exits through the outlet stream at volumetric flow rate Qml and concentration identical to that in the tank (CA). The concentration profile below the tank shows the step change in concentration encountered as the inlet stream is mixed with tank contents of lower concentration.

Figure 3 The plug flow model for convective mass transfer. The drawing shows a tube of diameter D and length L. Discrete fluid plugs (shaded rectangles) move down the tube fluid within each plug is completely mixed, while there is no mixing between adjacent plugs. The system is a cylindrical section of the tube between z + z and Az and is fixed in space. Fluid enters the system at z with density p(z) and volumetric flow rate q(z) fluid exits the system at z + Az with density p(z + Az) and volumetric flow rate q(z, + Az).

Convection Mass transfer driven by a gradient in pressure. 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

Of course, in free-convection mass transfer the transition time is dependent on the density difference generated at the electrode. The dimensionless time variable of the transient process is... 

Experimental results obtained at a rotating-disk electrode by Selman and Tobias (S10) indicate that this order-of-magnitude difference in the time of approach to the limiting current, between linear current increases, on the one hand, and the concentration-step method, on the other, is a general feature of forced-convection mass transfer. In these experiments the limiting current of ferricyanide reduction was generated by current ramps, as well as by potential scans. The apparent limiting current was taken to be the current value at the inflection point in the current-potential curve. 

Analysis of nonstationary convective mass transfer, under well-defined hydrodynamic conditions, may be helpful to understand the way in which the limiting current is established at electrodes of appreciable dimensions. As referred to in the previous section, the transition time to steady-state... 

In free-convection mass transfer at electrodes, as well as in forced convection, the concentration (diffusion) boundary layer (5d extends only over a very small part of the hydrodynamic boundary layer <5h. In laminar free convection, the ratio of the thicknesses is... 

The convective mass transfer coefficient hm can be obtained from correlations similar to those of heat transfer, i.e. Equation (1.12). The Nusselt number has the counterpart Sherwood number, Sh = hml/Di, and the counterpart of the Prandtl number is the Schmidt number, Sc = p/pD. Since Pr k Sc k 0.7 for combustion gases, the Lewis number, Le = Pr/Sc = k/pDcp is approximately 1, and it can be shown that hm = hc/cp. This is a convenient way to compute the mass transfer coefficient from heat transfer results. It comes from the Reynolds analogy, which shows the equivalence of heat transfer with its corresponding mass transfer configuration for Le = 1. Fire involves both simultaneous heat and mass transfer, and therefore these relationships are important to have a complete understanding of the subject. 

Convective mass transfer rate, 25 279 Conventional petroleum, 13 640 Conventional polymers, 13 541 Conventional reactive silicones, in fiber finishing, 22 593... 

Here we review some of the correlations of convective mass transfer. We will find that many reactors are controlled by mass transfer processes so this topic is essential in describing many chemical reactors. This discussion will necessarily be very brief and qualitative, and we win summarize material that most students have encountered in previous courses in mass transfer. Our goal is to write down some of the simple correlations so we can work examples. The assumptions in and validity of particular expressions should of course be checked if one is interested in serious estimations for particular reactor problems. We will only consider here the mass transfer correlations for gases because for liquids the correlations are more comphcated and cannot be easily generalized. 

Dne to the macroporons strnctnre of monolithic stationary phases (flow channels), the solvent is forced to pass the entire polymer, leading to faster convective mass transfer (compared to diffnsion), which provides for analyte transport into and out of the stagnant pore liqnid, present in the case of microparticulate columns. 

Even if the diminishment of interparticnlate voids as well as the convective mass transfer are generally assnmed to be the main reasons for the enhanced chromatographic properties of monolithic colnmns, the characteristics of organic and inorganic monolithic snpports have to be separately discnssed and evalnated, since they have been shown to complement one another regarding their applicability [29,100]. 

If the rate is controlled by convective mass transfer but steady state is not reached, then there may not be a simple relation between the growth distance and time. 

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