Rate controlling mechanism

Under natural conditions the rates of dissolution of most minerals are too slow to depend on mass transfer of the reactants or products in the aqueous phase. This restricts the case to one either of weathering reactions where the rate-controlling mechanism is the mass transfer of reactants and products in the soHd phase, or of reactions controlled by a surface process and the related detachment process of reactants. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Duncan and Frankenthal report on the effect of pH on the corrosion rate of gold in sulphate solutions in terms of the polarization curves. It was found that the rate of anodic dissolution is independent of pH in such solutions and that the rate controlling mechanism for anodic film formation and oxygen evolution are the same. For the open circuit behaviour of ferric oxide films on a gold substrate in sodium chloride solutions containing low iron concentration it is found that the film oxide is readily transformed to a lower oxidation state with a Fe /Fe ratio corresponding to that of magnetite . 

A CVD reaction is governed by thermodynamics, that is the driving force which indicates the direction the reaction is going to proceed (if at all), and hykinetics, which defines the transport process and determines the rate-control mechanism, in other words, how fast it is going. 

Identify the predominant rate-controlling mechanism kinetic, mass or heat transfer. Choose a suitable reactor type, based on experience with similar reactions, or from the laboratory and pilot plant work. 

The importance of "parabolic kinetics" in laboratory studies of mineral dissolution has varied as interpretations of the underlying rate-controlling mechanism have changed. Much of the research on silicate mineral weathering undertaken in the past decade or so served to test various hypotheses for the origin of parabolic kinetics. 

These rate-controlling mechanisms are characterized as follows ... 

When chemical reaction is the rate controlling mechanism, then the increase in molecular weight is linear with time. This was shown to be the case at 160 °C with a pellet size <2.1 mm [29], However, under normal industrial SSP conditions, where the standard pellet diameter is between 2 and 3 mm and temperatures are >200 °C, the reaction rate decays over time. Typically, the molecular weight increase is proportional to the square root of time, as shown in Figure 4.6. This has been confirmed in other studies [15, 36-38], Such behaviour is said to be typical for a reaction involving both chemical reaction and diffusion within the material [29],... 

The influence of pellet size has been generally used to identify the rate controlling mechanism of the overall reaction rate. If the rate controlling mechanism is chemical-reaction limited then the pellet size will have no effect on the reaction rate. If the diffusion of by-products to the pellet surface is the rate controlling mechanism, then the reaction rate will decrease as the pellet size increases, due to the increase in the length of the diffusion path. 

If we postulate that the rate-controlling mechanism involves the collision or interaction of a single molecule of A with a single molecule of B, then the number of collisions of molecules A with B is proportional to the rate of reaction. But at a given temperature the number of collisions is proportional to the concentration of reactants in the mixture hence, the rate of disappearance of A is given by... 

From the following conversion data (by chemical analysis) or core size data (by slicing and measuring) determine the rate controlling mechanism for the transformation of solid. 

It is obvious that for the whole flow-rate range, the rate-controlling mechanism is expected to be the solid diffusion control (Hi > 41). Furthermore, the flow can be characterized as ideal plug flow for flow rates above 2.15 BV/h, where PeL is higher than about 100. However, the liquid holdup is very low (56.83%) and this could be proved a serious problem, even with the use of a liquid distributor at the top of the bed. In order to have a satisfying liquid holdup, i.e about 80%, the relative flow rate should be about 5.62 BV/h. Then, by means of a liquid distributor at the top of the bed, it is possible to achieve a holdup near 100%. Thus, for downflow operation the limits of the relative flow rate are (BV/h)... 

In an attempt to provide further information relative to the validity of the diffusion mechanism, a typical set of results was selected from the isothermal release work, and the volume of volatile matter released was plotted against the square root of time. For a pure diffusion process such a plot should be almost linear initially (4) whereas for a true logarithmic time law, dVt/dt should tend to infinity for very small values of t. Figure 12 shows that by this criterion the rate controlling mechanism appears to be diffusion and not chemisorption. The fact that the curve does not pass through the origin is undoubtedly caused by the fact that it was not possible to heat the sample to... 

Figure 15.23. Hypersorber continuous moving bed gas phase adsorption system (See Mantell, Adsorption, McGraw-Hill, New York, 1951). (a) Schematic pattern of flows of gas and solid adsorbent (Hengstebeck, Petroleum Processing, McGraw-Hill, New York, 1959). (b) Solids flow rate control mechanism, (c) Typical separation performance.

Only then may one confidently apply absolute rate theory and establish the nature of the detailed rate-controlling mechanism. 

RATE CONTROLLING MECHANISM - MEMBRANE DOW CORNING" Silicone Tubing Elastomers... 

Dissolution occurring by a surface reaction is often slower than by transport-controlled kinetics because the latter results from more rapid surface detachment. There appears to be a good correlation between the solubility of a mineral and the rate-controlling mechanism for dissolution. Table 7.1 lists dissolution rate-controlling mechanisms for a number of substances. The less soluble minerals all dissolve by surface reaction-controlled kinetics. Silver chloride is an exception, but its dissolution... 

TABLE 7.1 Dissolution Rate-Controlling Mechanism for Various Substances Arranged in Order of Solubilities in Pure Water (Mass of Mineral That Will Dissolve to Equilibrium)0... 

In the case of YTZP, on which a large number of studies have been performed, the data could be fitted to a constitutive equation, which is identical to that found in metals when lattice diffusion is the rate-controlling mechanism 29... 

Chapter 5). AU these models have similar trends with respect to conversion, Xp versus dimensionless time. When the time scale is dimensional, it is easy to determine the rate controlling mechanism. 

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