Convection, mass-transfer-controlled

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. 

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. 

For convective crystal dissolution, the dissolution rate is u = (p/p )bD/8. For diffusive crystal dissolution, the dissolution rate is u = diffusive boundary layer thickness as 5 = (Df), the diffusive crystal dissolution rate can be written as u = aD/5, where a is positively related to b through Equation 4-100. Therefore, mass-transfer-controlled crystal dissolution rates (and crystal growth rates, discussed below) are controlled by three parameters the diffusion coefficient D, the boundary layer thickness 5, and the compositional parameter b. The variation and magnitude of these parameters are summarized below. 

His treatment includes natural convection but is limited to mass transfer controlled deposition and equilibrium distributions in the gas phase. Pollard and Newman (20) detail Si deposition on a rotating disk treating the multicomponent mass and heat transfer... 

A more direct evaluation of the role of mass transfer is obtained by plotting the scaled impedance values as a function of dimensionless frequency p = co/Cl, which is scaled by the rotation speed. The real and imaginary parts of the scaled impedance, shown in Figures 18.2(a) and (b), respectively, are superposed at low frequencies. Thus, the impedance values are, at low frequencies, controlled by convective mass transfer to the rotating disk. Differences are seen at higher frequencies that can be attributed to electrode kinetics. 

Mixing has no impact on the intrinsic reaction kinetics, but it has a controlling effect on the temporal variation in species concentration and the mass transfer rate. This can be shown by examining the typical convective mass transfer rate equation ... 

In most respects, the SMDE presents a much simpler situation than the classical DME, because the drop is not growing during most of its life. In parallel with our discussion of diffusion-controlled currents at the DME, we confine our view now to the situation where the SMDE is held constantly at a potential in the mass-transfer controlled region. In the earliest stages of a drop s life (on the order of 50 ms), when the valve controlling mercury flow is open and the drop is growing, the system is convective. Mass transfer and current flow are not described simply. After the valve closes, and the drop stops growing, the current becomes controlled by the spherical diffusion of electroactive species. 

This is a surface-related phenomenon based on the mass flux vector of component i and the surface area across which this flux acts. Relative to a stationary reference frame, p, v, is the mass flux vector of component i with units of mass of species i per area per time. It is extremely important to emphasize that p, v, contains contributions from convective mass transfer and molecular mass transfer. The latter process is due to diffusion. When one considers the mass of component i that crosses the surface of the control volume due to mass flux, the species velocity and the surface velocity must be considered. For example. Pi (Vr — Vsurface) is the mass flux vector of component i with respect to the surface... 

A gas-phase mass balance can be written for each component because all four components are volatile and exist in both phases. In each case, the control volnme contains all gas bubbles in the CSTR. The units of each term in all of the gas-phase mass balances are moles per time. At steady state, the inlet molar flow rate of component j is balanced by the outlet molar flow rate and the rate at which component j leaves the gas phase via interphase mass transfer. The inlet and outlet molar flow rates represent convective mass transfer. Interphase transport is typically dominated by diffusion, but convection can also contribute to the molar flux of component j perpendicular to the gas-liquid interface. All of the gas-phase mass balances can be written generically as... 

The overall mass balance is helpful to develop an expression for the total outlet gas-phase flow rate. It is important to realize that there are no restrictions which require that the total outlet gas-phase flow rate be the same as the inlet flow rate of gaseous chlorine. If one adds all four of the hquid-phase mass balances and all four of the gas-phase mass balances, then the result is the overall mass balance, which does not represent another independent equation. It is interesting to note that the sum of the stoichiometric coefficients is zero, which implies that the total number of moles is conserved during the chemical reaction. Furthermore, all interphase transport terms cancel because they represent a redistribution of all four components between the two phases, but there are no input or output contributions from these terms when the control volume corresponds to the total contents of the CSTR. Hence, the overall mass balance is analyzed on a molar basis because the total number of moles is conserved. Each term in the equation has units of moles per time and represents convective mass transfer in either the feed streams or the exit streams. The input terms correspond to the flow rates of liquid benzene and chlorine gas in the two feed streams, (A b) + (A ci). The output terms in the liquid exit stream are J2j and Afgas represents convective mass transfer in the outlet gas stream. At steady state. 

The simplest way to contact food with osmotic solution is to immerse a basket with food into solution. The movement of solution is slight due to natural convection. Mass transfer is slow and most of processing parameters are not controlled. The method can be used to soft fruits. 

One of the simplest and widely used theories for modeling flux in pressure-independent mass transfer controlled systems is the film theory. As solution is ultrafiltered, solute is brought onto the membrane surface by convective transport at a rate, J defined as follows ... 

Heat and mass transfer are analogous processes. Molecular diffusion in homogeneous materials or phases is similar to heat transfer. Convective diffusion or convection in homogeneous materials or phases corresponds to heat transfer by convection. Mass transfer at the phase boundary corresponds to heat conduction. Mass transfer between phases occurs like heat transfer in several chronological steps. The slowest step controls the rate of the entire process. Thus the mathematical descriptions of heat and mass transfer operations are analogous. Calculation methods and approaches to calculate the heat transfer coefficients may similarly be used to calculate mass transfer coefficients. (See Table 1-18 in Chapter 1.7.2 for the analogy of heat and mass transfer.)... 

The experimental cell is controlled by a potentiostat/galvanostat, which is also coupled with a frequency response analyzer for EIS measurements. The potentiostat (connected to a computer) measures the WE potential ( ) with respect to the RE, and the current (/) through the CE. The resistor (> 1 Gf2) is internal to the potentiostat and prevents current flow in the RE. The electrochemical cell shown in Figure 3.4(a) can also be used with rotating disc electrodes (RDEs), with the addition of an RDE rotor/controUer. RDE-based experiments do not necessarily mimic the hydrodynamic conditions of CMP, because the fluid velocity prohle at the surface of an RDE (Bard, 2001) is different from that expected for a CMP pad (Thakurta et al., 2002). Nevertheless, certain details of the CMP-related reaction kinetics and the effects of convective mass transfer on such reactions can be examined using RDEs. 

Thus from this recall of heat transfer, with the similarity between the two processes of heat transfer and mass transfer controlled by diffusion, the necessity of admitting without ambiguity that the course for the mass transfer should emerge as follows diffusion through the thickness of the sheet associated with the convection into the liquid. Finally, the parameters of main importance for a polymer package in contact with a liquid food are the diffusivity and the coefficient of convection. The diffusivity is concentration-dependent, as for example the case of highly plasticised polyvinylchloride where the plasticiser concentration may reach up to 50% of the polymer, but in the present case of the low concentration of the additives distributed in the polymer of the packaging -which are necessary to provide its qualities - the diffusivity can be considered as constant. 

The theoretical treatment of the process of mass transfer controlled by diffusion-convection with liquid food or even by diffusion-diffnsion when the food is solid is described precisely. Emphasis is placed on the fact that an infinite rate of convection cannot exist at the package-liquid interface in our finite world, and conseqnently we have to deal with more complex equations. The question of the volume of the package as a fraction of the volume of the liquid is also considered. In fact, the problems of diffnsion are not simple to resolve, either by considering the experiments or by making calcnlations. 

Mass transport-controlled corrosion impHes that the rate of corrosion is dependent on the convective mass transfer processes at the metal/fluid interface. Mass transfer can have a significant effect on corrosion rates of metals and alloys depending on factors such as bulk solution chemistry, temperature, flow conditions, surface roughness, and geometry. 

The mass transfer flux, j, in the first extraction period, is controlled by the convection mass transfer and depends on solute concentration in the solid phase. It is expressed in Equation 5.6, whereas the flux inside the particles, which depends on the solute diffusion from the interior of the solid to the surface, is expressed by Equation 5.7 ... 

M. Cabodi, V.L. Cross, Z. Qu, K.L. Havenstrite, S. Schwartz, A.D. Stroock, An active wound dressing for controlled convective mass transfer with the wound bed, /. Biomed. Mat. Res. Part B Appl. Biomat., 82,210-222,2007. 

Furthermore, when the total pressure in the drying chamber is increased, the gradient of the total pressure dP/dx in the dried layer could be reduced, and this could decrease the convective velocity Vp and the total mass flux A (Equation 11.14 through Equation 11.16). As the freeze drying process will become internal, mass transfer controlled above a certain pressure (Dwin, e and Nt decrease with increasing pressure, and kis increases with pressure), the highest rate... 

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