Reaction rate limited transport

The overall mass-transfer rate can be limited by any of the diffusion resistances in the three liquid phases (diffusion-limited transport) and/or chemical reaction (complexation/decomplexation) rate resistances on the membrane-solution interfaces (reaction rate-limited transport). 

Reaction-Rate Limited Transport of Monovalent Ions. From H NMR studies it is known that decomplexation rates can be very slow and, as a consequence, complexes can be kinetically stable (35,36). Until recently the role of slow rates of cation release in SLM transport was unclear. Lehn et al (24) and Fyles (37) theoretically raised the question of the influence of slow rates of alkali metal cation release on transport through a BLM. Experimentally, this phenomenon has only been observed by Yoshida et al (38). They showed that cation transport through a BLM mediated by polynactin was limited by the rate of cation release from the membrane. In 1994, Echegoyen stated that in SLM transport the rate of cation release from the membrane could never... 

At k/kGa 1, the chemical reaction is much slower than the mass transfer rate. In this case, concentration difference in the gas boundary layer does not exists. Therefore, k/kGa can be interpreted as the ratio of the reaction rate without transport limitation (cs = cG) to the reaction rate at transport limitation (cs —> 0). 

It is now recognized that anomalously low Tafel slopes can be observed for the chlorine evolution reaction due to rate-limiting transport of gas away from the electrode surface [471, 474], e.g. in concentrated chloride solutions at high temperatures. 

Along the X direction, i.e., the surface of the ionic conducting material, the reaction rate-limiting step is electron transport in the product phase (D). The growth distance, x, can be expressed as ... 

Figure 9.24 The effect of membrane thickness on the coupled transport flux of nickel through reaction rate limited membrane.73 (Membrane Laminated Celgard 2400/30% Kelex 100 dissolved in Kermac 470B. Feed 0.2% nickel, pH 6.0. Product 100 g/fi HjSO. ...

These predictions were made for 200 um membranes. Industrial application of this technology will require the use of membranes which are two orders of magnitude thinner. In order to use the model to predict facilitation factors for thinner membranes, it is necessary to determine whether the reaction equilibrium assumption still applies. The parameter (tanh )/ has a value of 0 if the system is diffusion limited and 1 if the facilitated transport system is reaction rate limited. At a thickness of Ipm, the value of (tanh X)/X is of the order 10 , which implies that the system is diffusion limited and that the simplified analytical model can be used to predict facilitation factors. If the solubility of HjS, the pressure and temperature dependence of the equilibrium constant and the diffusion coefficients are known, then F could be estimated at industrial conditions. 

Loading Frequency—Slow frequency CF experiments may be necessary because of mass transport and electrochemical reaction rate limitations on damage, but are challenging... 

In region II the mechanism of fracture changes from the reaction-rate-limited process of region I to a transport-rate-limited process. The reason is that the stress-activated process at the crack tip has become faster than the rate at which water vapor can diffuse to the crack tip. 

In general, a technical reactor will be designed for conditions that are different from the laboratory conditions. There are obvious economic reasons that a technical reactor will be designed for a maximum capacity per unit volume, and this will require conditions of very high reaction rates, where transport limitations cannot be avoided. Therefore one may have to study the chemical kinetics in the laboratory under similar conditions. For this reason chemical reaction engineering science may also be required for designing the right laboratory experiments. 

For exothermic reactions the diffusivity of the unreacted material will limit the rate of reaction. This is shown schematically in Fig. 1. If the surface temperature T, is always higher than the reaction temperature and the reaction is exothermic, the reaction front will accelerate until the diffusivity of the reactant becomes limiting. At such time the reaction rate should remain constant and should be unaffected by surface temperature. The effect of increased surface temperatures should be to decrease the time necessary to achieve a constant reaction rate. (Note that it is assumed that an AB reaction occurs between very fine particles and that mass transport processes are not reaction rate-limiting however, if such is the case the rate is less than the limiting diffusivity value.)... 

This assumes no reverse reaction, which is the case if the reaction products are rapidly removed from the surface and swept away in the gas phase. Surface coverage dependent terms may also enter into this equation if the reaction rate is limited by available adsorption sites. If a reverse reaction can occur one must also consider the law of mass action behavior as in Equation 4.14, while if there are multiple critical steps one may need to account for this in the reaction rate, as in Equation 4.16. When kf hg the rate is surface reaction rate limited, while hg kf implies a gas phase transport limitation. 

The net result of the competition between reaction rate and gas transport rate in Equation 12.2 as a function of temperature is shown schematically in Figure 12.3. At low temperatures the exponential dependence of reaction rate on temperature reduces the reaction rate below the gas transport rate sufficiently that the process is surface reaction rate limited. At higher temperatures diffusion is the dominant rate-limiting step. 

The reaction may be surface reaction rate limited or gas phase transport limited. Gas phase transport limitations are controlled by reactant concentration in the gas and the viscosity, turbulence, flow rate, and other properties of the gas, while surface reaction rate limitations are controlled by surface temperature and the other processes typical of physical vapor deposition growth. 

The industrial economy depends heavily on electrochemical processes. Electrochemical systems have inherent advantages such as ambient temperature operation, easily controlled reaction rates, and minimal environmental impact (qv). Electrosynthesis is used in a number of commercial processes. Batteries and fuel cells, used for the interconversion and storage of energy, are not limited by the Carnot efficiency of thermal devices. Corrosion, another electrochemical process, is estimated to cost hundreds of millions of dollars aimuaUy in the United States alone (see Corrosion and CORROSION control). Electrochemical systems can be described using the fundamental principles of thermodynamics, kinetics, and transport phenomena. 

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