Driving force overall

Unfortunately, the overall design problem is even more complex in practice. Spare driving forces in the process could be exploited equally well to allow the use of moderate utilities or the integration of heat engines, heat pumps, etc. in preference to distillation integration. 

Mass transfer rates may also be expressed in terms of an overall gas-phase driving force by defining a hypothetical equiHbrium mole fractionjy as the concentration which would be in equiHbrium with the bulk Hquid concentration = rax ) ... 

Expressions similar to equations 6 and 7 may be derived in terms of an overall Hquid-phase driving force. Equation 7 represents an addition of the resistances to mass transfer in the gas and Hquid films. The analogy of this process to the flow of electrical current through two resistances in series has been analyzed (25). 

In situations where the gas film resistance is predominant (gas film-controlled situation), k Pis much smaller than and the tie line is very steep. approachesjy so that the overall gas-phase driving force and the gas-film driving force become approximately equal, whereas the Hquid-film driving force becomes negligible. From equation 7 it also follows that in such cases. The reverse is tme if the Hquid film resistance is controlling. Since the... 

Log arithmic-Mean Driving Force. As noted eadier, linear operating lines occur if all concentrations involved stay low. Where it is possible to assume that the equiUbrium line is linear, it can be shown that use of the logarithmic mean of the terminal driving forces is theoretically correct. When the overall gas-film coefficient is used to express the rate of absorption, the calculation reduces to solution of the equation... 

Fig. 9. Simple model of adiabatic gas absorption. A, nonisotherm a1 equihbrium line for overall gas-phase driving force y = B, nonisotherm a1...

Tray Efficiencies in Plate Absorbers and Strippers Compn-tations of the nnmber of theoretical plates N assnme that the hqnia on each plate is completely mixed and that the vapor leaving the plate is in eqnihbrinm with the liqnid. In actnal practice a condition of complete eqnihbrinm cannot exist since interphase mass transfer reqnires a finite driving-force difference. This leads to the definition of an overall plate efficiency... 

Overall Resistance With a linear isotherm (R = 1), the overall mass transfer resistance is the sum of intraparticle and extraparticle resistances. Thus, the overall LDF coefficient for use with a particle-side driving force (column 2 in Table 16-12) is ... 

In oiological systems, the most frequent mechanism of oxidation is the remov of hydrogen, and conversely, the addition of hydrogen is the common method of reduc tion. Nicotinamide-adenine dinucleotide (NAD) and nicotinamide-adenine dinucleotide phosphate (NADP) are two coenzymes that assist in oxidation and reduction. These cofactors can shuttle between biochemical reac tions so that one drives another, or their oxidation can be coupled to the formation of ATP. However, stepwise release or consumption of energy requires driving forces and losses at each step such that overall efficiency suffers. 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Boiling is to be inside /l -in. 16 BWG steel tubes, 8 ft long. Condensing steam at 25 psig is available for heating. An overall coefficient U = 300 Btu/ (hr) (fti) (°F) is expected. For the given duty and a total driving force of 20°F, the inside surfece required is 285 fti This is equivalent to 96 tubes. 

When the coating metal halide is formed in situ, the overall reaction represents the transfer of coating metal from a source where it is at high activity (e.g. the pure metal powder, = 1) to the surface of the substrate where is kept less than 1 by diffusion. The formation of carbides or intermetallic compounds such as aluminides or silicides as part of the coating reaction may provide an additional driving force for the process. 

Fig. 2.4. The resultant growth rate which is due to a barrier and a driving force term. The driving force increases with l, but at a slower rate than the decrease of the force due to the barrier term. Hence the overall growth rate is positive for l > lmi but decreases to zero at large I, with a maximum in between...

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

If it is assumed that each element resides for the same time interval te in the surface, equation 10.115 gives the overall mean rate of transfer. It may be noted that the rate is a linear- function of the driving force expressed as a concentration difference, as in the two-film theory, but that it is proportional to the diffusivity raised to the power of 0.5 instead of unity. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

The driving force in the overall reaction (the dienone-phenol rearrangement) is of... 

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