Mass transport coefficient, overall

The resulting values are shown in Table 4. As expected, the diffusion coefficients of prenal and citral are smaller in water than in n-hexane. Since the mass transport coefficients in each boundary layer directly correlate with the diffusion coefficient (Eq. 3), this result confirms the assumption that the overall mass transport resistance can be predominantly referred to the aqueous catalyst phase ... 

The overall mass transport coefficient for mass transport from the dispersed organic phase into the continuous aqueous phase was then calculated according to the Calderbank equation (Eq. 4) ... 

Table 5 Overall mass transport coefficients kn and kna values for the mass transport of prenal and citral in the Diphasic system n-hexane/water...

As expected, the overall reaction rate increases with increasing catalyst volume rate. The effect can be explained in terms of the dependency of the mass transport coefficient ll on the Re munber (Eq. 12). Due to the increase of the volume hold-up of the aqueous phase, the residence time of the organic phase decreases, so that the observed conversion degrees do not change within the limits of the investigated regime. 

Average body weight of the treated rats in the critical study (Paulet and Desbrousses 1972) was 0.225 kg. Since the overall mass transport coefficient (Kg) is not available, the value has been assumed to equal 1. 

Figure 9 Comparison of previously reported values of kSA for reduction by Fe° with external mass transport coefficients estimated for batch, column, and rotating disk electrode reactors. References for the overall rate coefficients are given in Fig. 1 of Ref. 101. Mass transport coefficients were estimated for the batch and column reactors based on empirical correlations discussed in Refs. 125 and 101. Mass transport coefficients for the RDE were calculated using the Levich equation [178].

The resistances to the mass transport that a species encounters when is transferred from the gas to the hquid phase are reported in Figure 38.3. Gas and liquid phases contribute to the overall resistance because of the formation of boundary layers close to the membrane surface. This imphes that the concentration of a generic species i in the bulk of the two phases is different from its concentration at the membrane surfaces. The resistance offered by the membrane with gas-filled pores will be different (generally lower) than that with liquid-filled pores, due to the different effective diffusion coefficients. The overall mass-transport coefficient is given by... 

Here, Nq2 designates the oxygen flux at the surface and Co2,b the oxygen concentration in the bulk. The overall mass transport coefficient, contains two terms the coefficient km which characterizes the convective transport and the coefficient kf. 

Erosion is one of several wear modes involved in tribocorrosion. Solid particle erosion is a process by which discrete small solid particles, with inertia, strike the surface of a material, causing damage or material loss to its surface. This is often accompanied by corrosion due to the environment. A major environmental factor with significant influence on erosion-corrosion rates is that of flow velocity, but this should be set in the context of the overall flow field as other parameters such as wall shear stress, wall surface roughness, turbulent flow intensity and mass transport coefficient (this determines the rate of movement of reactant species to reaction sites and thus can relate to corrosion wall wastage rates). For example, a single value of flow velocity, referred to as the critical velocity, is often quoted to represent a transition from flow-induced corrosion to enhanced mechanical-corrosion interactive erosion-corrosion processes. It is also used to indicate the resistance of the passive and protective films to mechanical breakdown [5]. 

Rate constant for first order chemical process Rate constant for the forward (cathodic) process Rate constant for the reverse (anodic) process Rate constant for an electron transfer process at 0 V vs. the reference electrode Standard rate constant for an electrode process Mass transport coefficient Averaged, overall heat transfer coefficient Kohlrausch constant Selectivity constant for species i Characteristic length Length of a plate electrode Molality of cation Molality of anion... 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

The first row describes the condition if 1000 kg/h is emitted into the air. The result is similar to the Level II calculation with 19700 kg in air, 57 kg in water, 24 kg in soil and only 0.2 kg in sediment. It can be concluded that benzene discharged to the atmosphere has very little potential to enter other media. The rates of transfer from air to water and air to soil are both only about 0.4 kg/h. Even if the transfer coefficients were increased by a factor of 10, the rates would remain negligible. The reason for this is the value of the mass transfer coefficients which control this transport process. The overall residence time is 19.8 hours, similar to Level II. 

Rafler et al. showed in an early work [102] that the diffusion coefficient of EG varies with the overall effective polycondensation rate and they proposed a dependency of the diffusion coefficient on the degree of polycondensation. This dependency is obvious, because the diffusion coefficient is proportional to the reciprocal of the viscosity which increases by four orders of magnitude during polycondensation from approximately 0.001 Pas (for Pn = 3) to 67Pas (for Pn = 100) at 280 °C. In later work, Rafler et al. [103, 104, 106] abandoned the varying diffusion coefficient and instead added a convective mass-transport term to the material balance of EG and water. The additional model parameter for convection in the polymer melt and the constant diffusion coefficient were evaluated by data fitting. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

The large S02 mass accommodation coefficient (7 - 0.11) indicates that interfacial mass transport will not limit the rate of S02 uptake into clean aqueous cloud and fog droplets. Either gas phase diffusion, Henry s law solubility, or aqueous reactivity will control the overall rate of aqueous S(IV) chemistry. This conclusion is demonstrated by modeling studies of S02 oxidation in clouds by Chamedies (3) showing that the conversion time of S(FV) to S(IV) is independent of the mass accommodation coefficient for 1 7 > 10 2 Schwartz (1 ) has also shown that, with 7 as large as our measured value, the interfacial mass transport is unlikely to inhibit the oxidation of SC by or Ho02 in cloud droplets for gas concentrations typical of non-urban industrialized regions. 

The overall mass-transfer rates on both sides of the membrane can only be calculated when we know the convective velocity through the membrane layer. For this, Equation 14.2 should be solved. Its solution for constant parameters and for first-order and zero-order reaction have been given by Nagy [68]. The differential equation 14.26 with the boundary conditions (14.28a) to (14.28c) can only be solved numerically. The boundary condition (14.28c) can cause strong nonlinearity because of the space coordinate and/or concentration-dependent diffusion coefficient [40, 57, 58] and transverse convective velocity [11]. In the case of an enzyme membrane reactor, the radial convective velocity can often be neglected. Qin and Cabral [58] and Nagy and Hadik [57] discussed the concentration distribution in the lumen at different mass-transport parameters and at different Dm(c) functions in the case of nL = 0, that is, without transverse convective velocity (not discussed here in detail). 

When a species is transferred from a phase to another phase by means of a membrane contactor, the mass-transport resistances involved are those offered by the two phases and that of the membrane (see Figure 20.5). The overall mass-transfer coefficient will, therefore, depend on the mass-transfer coefficient of the two phases and of the membrane. 

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