Mass transfer rate constant

The binding of a small molecule ligand to a protein receptor follows a bimolecu-lar association reaction with second-order kinetics. For the reversible reaction of a ligand L and a protein P to form a non-covalendy bound complex C at equilibrium, Eq. (1) applies where kon and kgS represent the forward and reverse mass transfer rate constants. 

Equilibrium partitioning and mass transfer relationships that control the fate of HOPs in CRM and in different phases in the environment were presented in this chapter. Partitioning relationships were derived from thermodynamic principles for air, liquid, and solid phases, and they were used to determine the driving force for mass transfer. Diffusion coefficients were examined and those in water were much greater than those in air. Mass transfer relationships were developed for both transport within phases, and transport between phases. Several analytical solutions for mass transfer were examined and applied to relevant problems using calculated diffusion coefficients or mass transfer rate constants obtained from the literature. The equations and approaches used in this chapter can be used to evaluate partitioning and transport of HOP in CRM and the environment. 

So, if the mass-transfer rate constant is large in comparison to k, the rate reduces to — rc = k CB that is, the true kinetic rate is based directly on the bulk concentration. 

Membrane-enclosed packed-bed reactor. Plug-flow regime at both membrane sides. Isothermal system. No axial or radial diffusion. Mass transfer rate constant all over the membrane. Negligible pressure drop at the catalyst side. 

Comparison of equations 3 and 10 shows the essential difference between the stationary states of closed and continuous, open systems. For the closed system, equilibrium is the time-invariant condition. The total of each independently variable constituent and the equilibrium constant (a function of temperature, pressure, and composition) for each independent reaction (ATab in the example) are required to define the equilibrium composition Ca- For the continuous, open system, the steady state is the time-invariant condition. The mass transfer rate constant, the inflow mole number of each independently variable constituent, and the rate constants (functions of temperature, pressure, and composition) for each independent reaction are requir to define the steady-state composition Ca- It is clear that open-system models of natural waters require more information than closed-system models to define time-invariant compositions. An equilibrium model can be expected to describe a natural water system well when fluxes are small, that is, when flow time scales are long and chemical reaction time scales are short. 

Using the hodograph transform, Rhee and Amundson [3] have also shown that a plot of Q versus Q+i is a straight line (solid line in Figure 16.3), provided that these two components have the same axial dispersion coefficient (D ) and mass transfer rate constant (fcy), in addition to the competitive Langmuir isotherm behavior. The equation of this straight line is... 

Using the above type of experimental setup for propylene polymerization with TiCls-AlEts in n-heptane, the rate of polymerization was measured [5] at different speeds of stirring and constant propylene pressure. The results obtained indicated that there were two different steady-state rate curves for the stirring speeds of 400 and 600 rpm. In each case, a steady bulk monomer concentration was reached in about 3-4 hours. Show how the overall process at steady state can be modelled to show dependence of the polymerization rate on stirring speed and to enable determination of both the mass transfer rate constant and polymerization rate constant from rate measurements at different stirring speeds. 

We now recognize k as the ratio of kf to the steady-state mass-transfer coefficient niQ = DoIrQ. When k 1, the interfacial rate constant for reduction is very small compared to the effective mass-transfer rate constant, so that diffusion imposes no limitation on the current. At the opposite limit, where k >> 1, the rate constant for interfacial electron transfer greatly exceeds the effective rate constant for mass transfer, but the interpretation of this fact depends on whether k is also large. ... 

Interfacial areas per unit volume in falling-film microreactors have been reported to be as high as 25,000 m m, as compared with the values of 1-200 m m typical in bubble columns. This effect is particularly important in gas-liquid reactions because the rate of mass transfer from the gas to the liquid limits the reaction rate. For the hydrogenation of cyclohexene to cyclohexane in this type of reactor, the mass transfer rate constant Kid) was found to be in the range 3-7 s which is two orders of magnitude higher than that for conventional reactors. 

Roes and van Swaaij [35] (Pall rings) and Verver and van Swaaij [6,37] (double-channel baffle column) experimentally obtained values of the mass transfer rate constant, which were much lower than values calculated from experimental solids holdup data and the well-know Ranz-Marshall correlation [38,39]. The low experimental values are to be attributed to particle-shielding phenomena due to the formation of less diluted suspensions or trickles. 

The significance of the results presented in Figs. 43 5 is that they allow one to estimate the area over the surface where the flux (transfer rate) become uniform. The mass-transfer-rate constant (reduced flux) measured in this uniformly accessible area and referred to as A is of a particular significance because it can be analyzed theoretically in a much more efficient way than the local flux. Moreover, A can be directly used for determining the significance of various transport mechanisms like diffusion, interception, specific or external force, and so forth. 

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