Product layer diffusion control

A linear relationship between t and the term in brackets is indicative of product layer diffusion control. However, the product layer diffusion resistance must be zero initially when no product layer exists. Product layer diffusion resistance may increase rapidly as the product layer thickness increases, and, particularly at high temperature, can become rate-controlling during a large portion of the reaction. 

This characterizes the diffusional resistance to the flow of gas (zero for kinetic control and infinity for product layer diffusion control). Expressions for S and 5 depend on the reaction model used. Thus, for the grain model. 

For pure product layer diffusion control, 4) is large and... 

For the chemical reaction and product layer diffusion controlling regimes conversion-time relations for the unreacted core model simplifies Kinetics controlling ... 

Accumulatory pressure measurements have been used to study the kinetics of more complicated reactions. In the low temperature decomposition of ammonium perchlorate, the rate measurements depend on the constancy of composition of the non-condensable components of the product mixture [120], The kinetics of the high temperature decomposition [ 59] of this compound have been studied by accumulatory pressure measurements in the presence of an inert gas to suppress sublimation of the solid reactant. Reversible dissociations are not, however, appropriately studied in a closed system, where product readsorption and diffusion effects within the product layer may control, or exert perceptible influence on, the rate of gas release [121]. 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

Costa and Smith " studied the hydrofiuorination of nonporous uranium dioxide pellets under conditions where external mass transfer resistance was negligible. The global rate was initially controlled by the surface chemical reaction resistance, but switched to product layer diffusion as the reaction progressed and the product layer thickness increased. 

Borgwardt and Bruce (1986) used the unreacted core model with product layer diftusion control and showed good aggrement with the experimental data obtained with 1 /im particles. Combining Eq.2.11 with Eq.2.10, and expressing the diffusion coefficient (DJ in the product layer in Arrhenius form (see Section 2.3) and writing the grain radius in terms of surface area as... 

C. They found that below 750°C the reaction was chemically controlled but above this value the overall rate was controlled by product layer diffusion. An interesting recent investigation was reported by Mendoza et al. [44], who investigated this reaction within the range 1030-1334°K and interpreted their results in terms of a sophisticated distributed model. 

Kodama and Brydon [631] identify the dehydroxylation of microcrystalline mica as a diffusion-controlled reaction. It is suggested that the large difference between the value of E (222 kJ mole-1) and the enthalpy of reaction (43 kJ mole-1) could arise from the production of an amorphous transition layer during reaction (though none was detected) or an energy barrier to the interaction of hydroxyl groups. Water vapour reduced the rate of water release from montmorillonite and from illite and... 

While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps. 

The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the... 

These results take into account three possible processes in series mass transfer of fluid reactant A from bulk fluid to particle surface, diffusion of A through a reacted product layer to the unreacted (outer) core surface, and reaction with B at the core surface any one or two of these three processes may be rate-controlling. The SPM applies to particles of diminishing size, and is summarized similarly in equation 9.1-40 for a spherical particle. Because of the disappearance of the product into the fluid phase, the diffusion process present in the SCM does not occur in the SPM. 

If the transport process is rate-determining, the rate is controlled by the diffusion coefficient of the migrating species. There are several models that describe diffusion-controlled processes. A useful model has been proposed for a reaction occurring at the interface between two solid phases A and B [290]. This model can work for both solids and compressed liquids because it doesn t take into account the crystalline environment but only the diffusion coefficient. This model was initially developed for planar interface reactions, and then it was applied by lander [291] to powdered compacts. The starting point is the so-called parabolic law, describing the bulk-diffusion-controlled growth of a product layer in a unidirectional process, occurring on a planar interface where the reaction surface remains constant ... 

Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... 

The diffusion-controlled, hydroperoxide-initiated, oxidation regime (oxidation is restricted to a superficial layer). The shape of the distribution of oxidation products depends on the 02 solubility in the polymer (Fig. 14.15). 

In the grain model, it is assumed that the CaO consists of spherical grains of uniform size distributed in a porous matrix. The rate of reaction is controlled by the diffusion of SO2 through the porous matrix and the product CaSO layer formed on each grain (11). Allowance can be made for a finite rate of the CaO/SC reaction (12). The models have been found to describe experimental data for many limestones (13) by adjusting the constants in the model, most notably the diffusivity through the product layer. 

The selection of diffusion equation solutions included here are diffusion from films or sheets (hollow bodies) into liquids and solids as well as diffusion in the reverse direction, diffusion controlled evaporation from a surface, influence of barrier layers and diffusion through laminates, influence of swelling and heterogeneity of packaging materials, coupling of diffusion and chemical reactions in filled products as well as permeation through packaging. 

For the weathering of rock-forming minerals, the solution kinetics is determined by the solubility product and transport in the vicinity of the solid-water-interface. If the dissolution rate of a mineral is higher than the diffusive transport from the solid-water interface, saturation of the boundary layer and an exponential decrease with increasing distance from the boundary layer results. In the following text this kind of solution is referred to as solubility-product controlled. If the dissolution rate of the mineral is lower than diffusive transport, no saturation is attained. This process is called diffusion-controlled solution (Fig. 23 right). 

A bioelectrode functioning optimally has a short response time, which is often controlled by the thickness of the immmobilized enzyme layer rather than by the sensor as well as many other factors (see Table 7). The biosensor response time depends on (1) how rapidly the substrate diffuses through the solution to the membrane surface, (2) how rapidly the substrate diffuses through the membrane cmd reacts with the biocatalyst at the active site, and (3) how rapidly the products formed diffuse to the electrode surface where they are measured. Mathematical models describing this effea are thoroughly presented in the biosensor literature (5, 68). 

The equations used to describe the combustion wave propagation for microstructural models are similar to those in Section IV,A [see Eq. (6)]. However, the kinetics of heat release, 4>h may be controlled by phenomena other than reaction kinetics, such as diffusion through a product layer or melting and spreading of reactants. Since these phenomena often have Arrhenius-type dependences [e.g., for diffusion, 2)=9)o exp(— d// T)], microstructural models have similar temperature dependences as those obtained in Section IV,A. Let us consider, for example, the dependence of velocity, U, on the reactant particle size, d, a parameter of medium heterogeneity ... 

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