Transport effects

The rate expressions obtained by chemical kinetics describe file dependency of the reaction rate on kinetic parameters related to the chemical reactions. These rate expressions are commonly referred to as the intrinsic rate expressions of the chemical reactions (or intrinsic kinetics). However, in many instances, file local species concentrations depend also on the rate that the species are transported in the reacting medium. Consequently, the actual reaction rate (also referred to as the global reaction rate) is affected by the transport rates of the reactants and products. 

The effects of transport phenomena on the global reaction rate are prevalent in 

Fluid-fluid (liquid-liquid, gas-liquid) reactions 

Incorporating the effects of species transport rates to obtain the global rates of the chemical reactions is a difficult task since it requires knowledge of the local temperature and flow patterns (hydrodynamics) and numerous physical and chemical properties (porosity, pore size and size distribution, viscosity, diffusion coefficients, thermal conductivity, etc.). 

The species transfer flux to/from an interface is often described by a product of a mass-transfer coefficient, Icm, and a concentration difference between the bulk and the interface. The mass-transfer coefficient is correlated to the local flow conditions [13,21, 26-29]. For example, in a packed bed the mass-transfer coefficient from the bulk of the fluid to the surface of a particle is obtained from a correlation of the form 

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Systematic experimental investigations of these transport effects on reaction rates can either be done by varying solvents in a homologous series to change viscosity without affecting other physicochemical or chemical properties... 

Compton R G, Ekiund J C, Page S D, Mason T J and Walton D J 1996 Voltammetry in the presence of ultrasound mass transport effects J. Appl. Electrochem. 26 775... 

The effect of physical processes on reactor performance is more complex than for two-phase systems because both gas-liquid and liquid-solid interphase transport effects may be coupled with the intrinsic rate. The most common types of three-phase reactors are the slurry and trickle-bed reactors. These have found wide applications in the petroleum industry. A slurry reactor is a multi-phase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles. The reactor may operate continuously as a steady flow system with respect to both gas and liquid phases. Alternatively, a fixed charge of liquid is initially added to the stirred vessel, and the gas is continuously added such that the reactor is batch with respect to the liquid phase. This method is used in some hydrogenation reactions such as hydrogenation of oils in a slurry of nickel catalyst particles. Figure 4-15 shows a slurry-type reactor used for polymerization of ethylene in a sluiTy of solid catalyst particles in a solvent of cyclohexane. 

These quantum effects, though they do not generally affect significantly the magnitude of the resistivity, introduce new features in the low temperature transport effects [8]. So, in addition to the semiclassical ideal and residual resistivities discussed above, we must take into account the contributions due to quantum localisation and interaction effects. These localisation effects were found to confirm the 2D character of conduction in MWCNT. In the same way, experiments performed at the mesoscopic scale revealed quantum oscillations of the electrical conductance as a function of magnetic field, the so-called universal conductance fluctuations (Sec. 5.2). 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

The term numerical diffusion describes the effect of artificial diffusive fluxes which are induced by discretization errors. This effect becomes visible when the transport of quantities with small diffusivities [with the exact meaning of small yet to be specified in Eq. (42)] is considered. In macroscopic systems such small diffusivities are rarely found, at least when being looked at from a phenomenological point of view. The reason for the reduced importance of numerical diffusion in many macroscopic systems lies in the turbulent nature of most macro flows. The turbulent velocity fluctuations induce an effective diffusivity of comparatively large magnitude which includes transport effects due to turbulent eddies [1]. The effective diffusivity often dominates the numerical diffusivity. In contrast, micro flows are often laminar, and especially for liquid flows numerical diffusion can become the major effect limiting the accuracy of the model predictions. 

A detailed study on velocity profiles, pressure drop and mass transport effects is given in [3]. This, in quantitative terms, precisely underlines the advantages (and limits) of the porous-polymer-rod micro reactor concept. 

Schneider A, Colmenaies L, Seidel YE, Jusys Z, Wickman B, Kasemo B, Behm RJ. 2008. Transport effects in the oxygen reduction reaction on nanostructuied, planar glassy carbon supported Pt/GC model electrodes. Phys Chem Chem Phys 10 1931-1943. 

In situ perfusion studies assess absorption as lumenal clearance or membrane permeability and provide for isolation of solute transport at the level of the intestinal tissue. Controlled input of drug concentration, perfusion pH, osmolality, composition, and flow rate combined with intestinal region selection allow for separation of aqueous resistance and water transport effects on solute tissue permeation. This system provides for solute sampling from GI lumenal and plasma (mesenteric and systemic) compartments. A sensitive assay can separate metabolic from transport contributions. 

Simpson, I. A., Appel, N. M., Hokari, M. etal. Blood-brain barrier glucose transporter effects of hypo- and hyperglycemia revisited. /. Neurochem. 72 238-247,1999. 

The starting points for the continuity and energy equations are again 21.5-1 and 21.5-6 (adiabatic operation), respectively, but the rate quantity7 (—rA) must be properly interpreted. In 21.5-1 and 21.5-6, the implication is that the rate is the intrinsic surface reaction rate, ( rA)int. For a heterogeneous model, we interpret it as an overall observed rate, (—rA)obs, incorporating the transport effects responsible for the gradients in concentration and temperature. As developed in Section 8.5, these effects are lumped into a particle effectiveness factor, 77, or an overall effectiveness factor, r]0. Thus, equations 21.5-1 and 21.5-6 are rewritten as... 

Kamdar, G., Penado, K. M., Rudnick, G., and Stephan, M. M. (2001) Functional role of critical stripe residues in transmembrane span 7 of the serotonin transporter. Effects of Na+, Li+, and methanethiosulfonate reagents. J. Biol. Chem. 276,4038 1045. 

Various works has pointed out the role of the nanostructure of the catalysts in their design.18-26 There is a general agreement that the nanostructure of the oxide particles is a key to control the reactivity and selectivity. Several papers have discussed the features and properties of nanostructured catalysts and oxides,27-41 but often the concept of nanostructure is not clearly defined. A heterogeneous catalyst should be optimized on a multiscale level, e.g. from the molecular level to the nano, micro- and meso-scale level.42 Therefore, not only the active site itself (molecular level) is relevant, but also the environment around the active site which orients or assist the coordination of the reactants, may induce sterical constrains on the transition state, and affect the short-range transport effects (nano-scale level).42 The catalytic surface process is in series with the transport of the reactants and the back-diffusion of the products which should be concerted with the catalytic transformation. Heat... 

Bilger, R. W. (1982). Molecular transport effects in turbulent diffusion flames at moderate Reynolds number. AIAA Journal 20, 962-970. 

With respect to the considerations above, research is split into three parts. The first is connected to the kinetic description of the release of ammonia from the biomass as function of temperature. This research employs infrared spectroscopy using a tunable diode laser. Here very small biomass particles are used that are heated up very rapidly in a small reactor, which ensures that transport effects are virtually excluded from the kinetic release effects. Since ammonia is released in very small quantities it is quite hard to detect. Therefore, we first measure CO release, which is easier. In the second part we investigate the propagation of a conversion front in biomass layers. Here we perform experiments and try to establish a modeling approach for the propagation by analytical and numerical approaches. In the third part the gas-phase conversion processes are described in terms of... 

Figure 5.17 Schematic diagram of the effect of mixing on the concentration of substrate in the liquid and solid phases of a triphasic reaction a represents a reaction that is limited only by the intrinsic reactivity b represents a reaction that is limited by a combination of intrinsic reactivity and mass transport effects c represents a reaction which is limited by mass transport only...

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

To calculate the electron-transport effect through GDL and flow plate, the charge conservation equation for the electronic phase must be solved additionally, namely... 

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