Convection, mass-transfer-controlled reactions

The mass transfer coefficient, K, is defined as the ratio of the mass transport controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection depends on molecular diffusivity, while the turbulent component depends on eddy diffusivity (4). The mass transfer coefficient considers the combination of the two transport mechanisms, empirically. 

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 ... 

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 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. 

As our first approach to the model, we considered the controlling step to be the mass transfer from gas to liquid, the mass transfer from liquid to catalyst, or the catalytic surface reaction step. The other steps were eliminated since convective transport with small catalyst particles and high local mixing should offer virtually no resistance to the overall reaction scheme. Mathematical models were constructed for each of these three steps. 

Membrane diffusion illustrates the uses of Fick s first and second laws. We discussed steady diffusion across a film, a membrane with and without aqueous diffusion layers, and the skin. We also discussed the unsteady diffusion across a membrane with and without reaction. The solutions to these diffusion problems should be useful in practical situations encountered in pharmaceutical sciences, such as the development of membrane-based controlled-release dosage forms, selection of packaging materials, and experimental evaluation of absorption potential of new compounds. Diffusion in a cylinder and dissolution of a sphere show the solutions of the differential equations describing diffusion in cylindrical and spherical systems. Convection was discussed in the section on intrinsic dissolution. Thus, this chapter covered fundamental mass transfer equations and their applications in practical situations. 

The fact that transport limits the rate of the overall electrode reaction affects the fastest timescale accessible. Once transport controls the rate, faster reaction steps cannot be characterized. It is thus important to enhance mass transfer, for example, by increased convection with high flow rates [37, 38]. 

Component exchange between phases is controlled by mass transfer. Between solid phases, mass transfer is through diffusion where the exchange of components may be used as a geospeedometer (Lasaga, 1983). Convection rather than diffusion may play a dominant role if fluid phases are involved. In reactions between solid and fluid phases, diffusion in the solid phase is usually the slowest step. However, dissolution and reprecipitation may occur and may accomplish the exchange more rapidly than diffusion through the solid phase. 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is... 

The following discussion represents a detailed description of the mass balance for any species in a reactive mixture. In general, there are four mass transfer rate processes that must be considered accumulation, convection, diffusion, and sources or sinks due to chemical reactions. The units of each term in the integral form of the mass transfer equation are moles of component i per time. In differential form, the units of each term are moles of component i per volnme per time. This is achieved when the mass balance is divided by the finite control volume, which shrinks to a point within the region of interest in the limit when aU dimensions of the control volume become infinitesimally small. In this development, the size of the control volume V (t) is time dependent because, at each point on the surface of this volume element, the control volnme moves with velocity surface, which could be different from the local fluid velocity of component i, V,. Since there are several choices for this control volume within the region of interest, it is appropriate to consider an arbitrary volume element with the characteristics described above. For specific problems, it is advantageous to use a control volume that matches the symmetry of the macroscopic boundaries. This is illustrated in subsequent chapters for catalysts with rectangular, cylindrical, and spherical symmetry. 

The objective of this section is to begin with the generalized form of the dimensionless mass transfer eqnation, given by (22-1), and discuss the simplifying assumptions required to reduce this partial differential equation to an ordinary differential design eqnation for packed catalytic tubular reactors. It should be mentioned that the design equation for tubular reactors, which includes convection and chemical reaction, is typically developed from a mass balance over a differential control volume given by... 

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