Resistance term

Aside from the lack of an explicitly defined liquid-phase-resistance term, the limitations on the use of Eq. (14-66) are related to the fact that its derivation implicitly assumes that the system is dilute iysM = 1) and that the operating and equilibrium curves are straight lines over the range of tower operation. Also, Eq. (14-66) is strictly vahd only for the temperature and pressure at which the original test was run even though the total pressure pf appears in the denominator. 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

It is anticipated that the equilibrium filter cake mass would depend strongly on the axial velocity through the cross-flow filter assembly. The shear rate at the filter surface will increase the entrainment of the catalyst solids for a given permeate flow rate. Therefore, for each differential pressure condition, the axial velocity will be varied in order to quantify the effect of the wall shear on the filter cake resistance term. 

The model for inviscid liquids is equally well applicable to viscous liquids also, provided that the resistance due to viscous drag is included in the analysis. As a first approximation, the viscous drag may be evaluated by a Stokes resistance term, since the bubble is not followed by a wake. Thus we proceed as before, first evaluating the force-balance bubble volume Kr and then the total bubble volume by reference to the detachment stage. 

In the viscous resistance term in Eq. (163), the radius r can be taken as 1.25 rfb without causing a great loss in accuracy. Equations (162) and (163) reduce to constant flow or constant pressure conditions, respectively, when Q is constant or when it is expressed in terms of orifice equation. 

For the purposes of answering DQ 2.1, we will take the resistance term R as representing the resistance of the circuit constructed to measure, say, a cell emf. The resistance comes from the leads connecting the voltmeter and all components within the cell the resistance of the cell itself (I ceii) will comprise resistance contributions from both the electrodes and the solution. We will take / to be the current passed during the measurement. The potential V is therefore the voltage induced by current flow through the voltmeter. 

Finally, it must be noted that tensides that are adsorbed at the interface cause a stiffening of the interface. They hinder or even stop the inner circulation and oscillation of drops, and reduce the mass transfer intensity. Moreover, they form a barrier against the mass transfer, so that a further resistance term should be considered in the overall mass transfer process [28] in Eq. (9.33). Since the nature and concentration of tensides in industrial processes cannot be predicted, such phenomena cannot be taken into consideration during equipment calculations. 

The reactance describes the part of the system that behaves as a capacitor or inductor while the resistance term describes the part of the system that behaves as a resistor. The magnitude of the impedance is determined by the square root of the stun of the squares for the resistance and reactance [19] ... 

Since the last resistance term in the general rate equation, Eq. 5, is negligible (large k), the rate form for this case is... 

Now for slightly soluble gases Hp is large hence, with all other factors unchanged the above rate equation shows that the liquid film resistance term is large. The reverse holds for highly soluble gases. Thus, we see that ... 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

The denominator the "resistance" term, reflects the real complexity of the detailed mechanism. We can present it as... 

As discussed by Fuchs and Sutugin (1970, 1971) and Motz and Wise (1960), in this continuous regime, distortion of the Boltzmann velocity distribution in the region close to the surface occurs if there is rapid uptake. In effect, the normal thermal velocity distribution is distorted so that the effective speed toward the surface is higher. In the case of a surface where the uptake occurs on every collision, the net speed toward the surface is effectively doubled. This adds an additional term to the rate of transfer of the gas to the surface, which when normalized using Eq. (PP), gives an additional resistance term of -1 /2. The overall normalized conductance is therefore given by... 

Hu et al. (1995) interpret this as evidence for an additional reaction channel corresponding to a rapid reaction at the interface itself. Several different approaches have been taken to introduce this additional reaction dimension into the resistance model. For example, Hu et al. (1995) add another resistance term to Fig. 5.16, l/rinturra(.u, shown by the dashed lines in that figure. Their data suggest that l/rintcrraa, is of the form [1 + k"ax /(k"axps), where k" is a measure of the... 

Keulegan and Patterson (K16), 1940 Determination of criterion for wave formation in turbulent flow in steep channels N . > f or Ner > 2, depending on use of Manning or Chdzy coefficients for resistance term. 

As in Example 4.6 the aim is again to evaluate the individual resistance terms in equation 4.35 and to examine them in tum. Also the overall rate of hydrogenation at the same hydrogen pressure of 30 bar will be calculated. 

When the fluid layer mass-transfer coefficient (kM) is large, the resistance Vkbe of this layer is small, and the overall resistance is determined only by the membrane. When the fluid layer mass-transfer coefficient is small, the resistance term 1 /kbb is large, and becomes a significant fraction of the total resistance to permeation. The overall mass transfer coefficient (kov) then becomes smaller, and the flux decreases. The boundary layer mass transfer coefficient is thus an arithmetical fix used to correct the membrane permeation rate for the effect of concentration polarization. Nothing is revealed about the causes of concentration polarization. 

The resistance term in Eq. (1), 2A, usually increases directly with the membrane thickness, so reducing thickness by some percentage generally increases flux by the same percentage. This generalization has some exceptions. For instance, reaction or complexation kinetics within the membrane or nonhomogeneous morphologies within the membrane can cause such exceptions in some cases (Crank, 1975). 

Particular cases of dynamic equation (3.11) were investigated by Ronca (1983) and by Hess (1986, 1988) who apparently did not know about previously published results. They made unsuccessful attempts to describe dynamics of macromolecule in an entangled system without the second dissipative term which is connected with the internal resistance forces. One can see in subsequent chapters that the properties of polymer melts cannot be understood correctly without this term. The importance of the internal resistance term was recognised by Pokrovskii and Volkov (1978b) after the first attempt to tackle the problem (Pokrovskii and Volkov 1978a). 

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