Diffusion reactant

Diffuse-thermal instabilities involve the relative diffusion reactants and heat within a laminar flame. These are the smaHest-scale instabilities (11). 

For a flat-plate porous particle of diffusion-path length L (and infinite extent in other directions), and with only one face permeable to diffusing reactant gas A, obtain an expression for tj, the particle effectiveness factor defined by equation 8.5-5, based on the following... 

Catalysis by sol gel doped silica-based materials has become in the last 20 years a prominent tool to synthesize a vast number of useful molecules both in the laboratory and in industrial plants.12 The underlying basic concept of all sol-gel applications is unique one or more host molecules are entrapped by a sol-gel process within the cages of an amorphous metal oxide where they are accessible to diffusible reactants through the inner pore network, which leads to chemical interactions and reactions (Figure 5.3). 

The convolution treatment of the linear and semi-infinite diffusion reactant transport (Section 1.3.2) leads to the following relationship between the concentrations at the electrode surface and the current ... 

If, however, both reactions were influenced by intraparticle diffusion effects, the rate of reaction of a particular component would be given by the product of the intrinsic reaction rate, fecg, and the effectiveness factor, Tj. Substituting eqn. (6) for the effectiveness factor gives (for a first-order isothermal reaction) the overall rate as 0tanh< >. As is often the case, the molecular weights of the diffusing reactants are similar and can be... 

It is of interest to examine quantitatively such potential-dependent redox equilibria as determined by SERS in comparison with that obtained by conventional electrochemistry. Figure 1 shows such data determined for Ru(NH3 )6 3" 2+at chloride-coated silver. The solid curves denote the surface concentrations of the Ru(III) and Ru(II) forms as a function of electrode potential, normalized to values at -100 and -500 mV vs SCE. These are determined by integrating cyclic voltammograms for this system obtained under conditions [very dilute (50 yM) Ru(NH3)63 +, rapid (50 V sec-1) sweep rate] so that the faradaic current arises entirely from initially adsorbed, rather than from diffusing, reactant (cf. ref. 6b). The dashed curves denote the corresponding potential-dependent normalized Ru(III) and Ru(II) surface concentrations, obtained from the integrated intensities of the 500 cm 1 and 460 cm-1 SERS bands associated with the symmetric Ru(III)-NH3 and Ru(II)-NH3 vibrational modes.(5a)... 

External mass transfer reduces the concentration of reactant gas close to the particle surface and thus reduces the overall process rate. Thus, consider gasification to be a first-order reaction. Then at steady state, the rate of gasification equals the rate of mass transfer. For a nonporous solid, the surface reaction (whose rate constant is k ) consumes the diffusing reactant ... 

D Effective Diffusivity of Porous Preform Effective Ordinary Binary Diffusivity Reactant Knudsen Diffusivity D = v dl3) Deposition Reaction Activation Energy / Reactive Species Mole Eraction Kn Knudsen Number (Kn = m Reactive Species Molecular Weight N Avogadro Number p Total Gas Pressure... 

The so-called primary titration technique is attempted only with electrodes of silver metal, silver-silver halide, or mercury amalgams, which are the source of the electrogenerated species. The substance to be determined reacts directly at the electrode or with a reactant electrogenerated from the working electrode. This class of titrations is limited generally to non-diffusible reactants such as mercury amalgams, silver ions generated by anodization of silver metal, and halides liberated by reduction of the appropriate silver-silver halide electrode. 

There are many instances in electrochemistry when we find it very difficult to obtain an explicit relationship between current, potential, and time. Either the system itself is intrinsically complex (e.g., a quasireversible charge transfer involving adsorbed and diffusing reactant species) or the experimental conditions are less than ideal (e.g., step experiments carried out on a time domain so short that the rise time of the potentiostat is not negligible). It is usually true in these and other cases that much simpler relationships exist in the Laplace domain between the perturbations and the observables. Thus it can be useful to transform the data and carry out the analysis in transform space (39-42). 

Figure 4.8. Scheme of the two steps in the reversible formation of the inhibited digitalis complex, in which D is digitalis, E the enzyme in the receptive state, D-P the uninhibited diffusive complex, IhP the inhibited isomerized complex, Ic ami Ic diffusion rate constants, and k% isomerization rate constants, and k and k the observed composite forward or reverse rate constants. Compared with the diffusional rate constant of slowly diffusing reactants, lying near 10 M s, the values were foumi by 4 to 6 orders of ten smaller, and the k values by 5 to 7 orders... 

TO carry out its complex function, a living cell requires a steady supply of reactants, such as nutrients and oxygen. A cell also requires a reliable system for removing the resulting waste products—carbon dioxide and water, for example. Both of these conditions are met by the simple process of diffusion. Reactants can diffuse into the cell through the thin cell membrane, and the products of cell function can diffuse out of the cell and be absorbed by the surrounding liquid. 

A mathematical model for DEFC was proposed by Pramanik and Basu describing different overpotentials [191]. The assumptions of their model are (i) the anode compartment considered as a well-mixed reactor, (ii) 1 bar pressure maintained both at the anode and cathode compartments, (iii) the transport processes are modelled in one dimension. The model accounts for Butler-Volmer-based descriptions of the ethanol electrooxidation mechanisms, diffusive reactants transport and ohmic losses at the electrode, current collector and electrode-current collector interfaces. The experiment data on current-voltage characteristics is predicted by the model with reasonable agreement and the influence of ethanol concentration and temperature on the performance of DEFC is studied by the authors (Fig. 8.19). 

The temperature difference is directly proportional to (i) the heat of reaction per mol of diffusing reactant and (ii) the fractional drop in concentration between the bulk fluid and the solid surface. The terms appearing on the right-hand side of the equation are... 

As an example, let us now calculate the Detr and Co values with ethanol (EtOH) as the solvent. First, H2 will be considered as the diffusing reactant, and the diffusivity of H2 in citral and the solvent can be estimated using equation 4.97, which is based on the method of Wilke and Chang [34], because the mole fraction of H2 in either liquid is very low, i.e.,... 

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