Transfer Considerations

The basic mass transfer processes of interest are migration, diffusion, and convection. We will examine some simple relations in this section. Detailed treatment is beyond the scope of this book. Initially we consider stationary planar electrodes immersed in an unstirred electrolyte. A general treatment is given by Delahay (1954), and a practical approach by Adams (1969). 

Charge migration results from forces exerted by an electric field on charged particles in solution. If we have a parallel-planar electrode con- 

Equating mechanical (Newton s second law) and electrical (Coulomb s law) forces and neglecting charge interactions and body forces such as gravity, 

The trajectory solution is subject to various boundary conditions. 

In laboratory voltammetric determinations, background electrolytes are normally used, as indicated in Section 3.2, and migration effects are negligible (Adams, 1969). 

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Thermodynamic and Mass-Transfer Considerations Multi-component vapor mixture includes several different cases all the components may be hquids at the lowest temperature reached in the condensing side, or there may be components which dissolve substantially in the condensate even though their boiling points are below the exit temperature, or one or more components may be both noncondensable and nearly insoluble. 

This expression insures that the heat-transfer considerations of the second law of thermodynamics are satisfied. For a given pair of corresponding temperatures (T, t) it is thermodynamically and practically feasible to transfer heat from any hot stream whose temperature is greater than or equal to T to any cold stream whose temperature is less than or equal to t. It is worth noting the analogy between Eqs. (9.2) and (3.5). Thermal equilibrium is a special case of mass-exchange equilibrium with T,t and AT " corresponding to yi,Xj and ej, respectively, while the values of rrij and bj arc one and zero, respectively. 

As we noted earlier, there may be heat transfer considerations or other factors that dictate the use of a CSTR even when the yield considerations are unfavorable. In such cases the yield... 

This problem indicates the considerations that enter into the design of a tubular reactor for an endothermic reaction. The necessity of supplying thermal energy to the reactor contents at an elevated temperature implies that the heat transfer considerations will be particularly important in determining the longitudinal temperature profile of the reacting fluid. This problem is based on an article by Fair and Rase (1). 

Mass transfer considerations are critical in any bioprocess. In typical, aerobic, suspended cell fermentations, the major concern is the oxygen transfer rate, determined by the overall mass transfer coefficient, kft, and the driving force. In three-phase biofluidization, in which the cells are immobilized as a biofilm or within carrier particles, the situation is further complicated by possible intraparticle diffusion limitations. Numerous recent studies have addressed these issues. 

The distillation residue contains mainly glycerol however, condensation and polymerization reactions also took place indicated by coloration of the liquid. These reactions might increase viscosity and decrease heat transfer considerably. 

This involves solution of equation 18.4-6 together with equations 18.4-2 and -3. A stepwise algorithm is as follows, with indicated as the highest allowable value of T for whatever reason (heat transfer considerations, product stability, etc.) ... 

Equation (65), the working equation for mass transfer, contains two independent variables and R. A second equation can be obtained from momentum transfer considerations. In the absence of surface tension forces, the momentum equations for a Newtonian fluid reduce to... 

Thus the initial growth is largely controlled by inertial restraints and the radius increases linearly with time [Eq. (12)], whereas at long times heat transfer considerations become predominant and the growth is given by Eq. (16). The actual variation of r with t is less than either of these two asymptotic extremes (see Theofanous, 1969). 

U02)2 + Charge- transfer Considerably long decay time ( 0.1-1 ms)... 

Several factors need to be kept in mind concerning x-ray resist design. Firstly, source design has mainly utilized electron bombardment of the target material to generate x-rays. Power output is limited by heat transfer considerations, and when account is also taken of the separation between source and exposure plane (wafer) as necessitated by geometrical considerations, it... 

Statistical considerations necessitate a minimum dose for uniform exposure and, when coupled with energy transfer considerations, dictate the use... 

The change in concentration of the phase would depend on the flow-rate, even if the transfer coefficients and rate of transfer did not. This equation is not truly one for the additivity of resistances, for each resistance has a scale factor, LM or GM. The ratio of GM to Lm is usually dictated by the plant production the individual values GM and LM are normally controlled by the physical capacity of the equipment rather than by mass transfer considerations, which control the contacting length rather than the flow-area of the equipment. 

With the average elongational strain rate of the flow field between the eddies and the relaxation time of the polymer molecules, one can define a dimensionless characteristic number, the Deborah number, which represents the ratio of a characteristic time of flow and a characteristic time of the polymer molecule, and thus one can transfer considerations in porous media flow to the turbulent flow region. 

MASS TRANSFER CONSIDERATIONS FOR THE ENANTIOSELECTIVE HYDROGENATION OF a-KETO ESTERS CATALYZED BY CINCHONA MODIFIED Pt/Al203... 

At the present time it is difficult to find order or correlations in experimental data on any aspect of electronic energy transfer. Consideration of the factors which may influence the rates of such processes provides pointers which indicate where... 

Mass Transfer Considerations in Entrapped Culture Systems. 32... 

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