Phase transport—control

Correlations of the kind that appear in Fig. 3.4 must be tempered, however, with the reminder that Eqs. 3.1 and 3.7 always represent hypotheses about dissolution and precipitation processes. If the rates of these processes are controlled by how quickly aqueous-solution species can approach the surface of the solid phase transport control), then a rate law based solely on an assumed chemical reaction at the surface reaction control) is quite irrelevant. This issue cannot be decided simply by fitting rate data to models like that in Eq. 3.7, but instead must be resolved through direct experimentation (e.g., by comparing the temperature dependence of the reaction with that for aqueous species transport,... 

Phase transport-controlled corrosion suggests that the wetting of the metal surface by a corrosive phase is flow-dependent. This may occur because one liquid phase separates from another or because a second phase forms from a liquid. The distribution and morphology of the corrosive attack will be related to the distribution of the corrosive phase the corroded sites will frequently display rough, irregular surfaces and be coated with or contain thick, porous corrosion deposits [29]. 

Both these diffusion controlled and the vapour phase transport processes may be described by tire general equation... 

Simple Diffusion Phase-Boundary Controlled Material Transport... 

GL 28] [R 2] [P 30] Ammonia absorption in dilute acidic solution containing Cresol Purple indicator was rapid, as expected [7]. By appropriate choice of processing parameters, neutralization was achieved close to the gas/liquid contacting zone or distributed over the full contact length. This is evidence for having controls by both solution and gas-phase transport. 

FIG. 19 Normalized concentration profiles (solid lines) of the reactants and products in the DCE (a) or aqueous (b) receptor phase for the reaction between Fc (DCE) and IrClg (aqueous) with 0.1 M CIO4 in both DCE and the aqueous phase. In each case, the reactant concentration in the receptor phase was 1 mM, with 10 mM reactant inside the droplet. Drop times and final sizes were (a) 5.54 s and 0.96 mm, and (b) 6.32 s and 1.00 mm. The theoretical profiles (dashed lines) are for a transport-controlled reaction, with no transfer of the product ions. (Reprinted from Ref. 80. Copyright 1999, Royal Society of Chemistry.)... 

The usual prescription for controlling triboelectrification in pneumatic transport is to limit the flow rate, but this solution conflicts with the tendency to increase plant production levels. One alternate proposal for the control of tribocharging is to exploit the so-called dense-phase transport mode (G. Butters, 1985) however, there seems to be some dispute about the efficacy ofthis scheme (Konrad, 1986). 

Figure 6.14. Scheme of the experimental apparatus for gravimetric measurements described by Zavrazhnov et al. (2003) in their investigation of the phase composition control in chemical transport reactions. (1) quartz ampoule, (2) thermocouples, (3) two-zone furnace, (4) quartz rods, (5) wire for suspending the ampoule, (6) support, (7) weighing beam of the analytical balance,... 

Chemical transport reactions as a new variant of the phase composition control... 

DMFC modeling thus aims to provide a useful tool for the basic understanding of transport and electrochemical phenomena in DMFC and for the optimization of cell design and operating conditions. This modeling is challenging in that it entails the two-phase treatment for both anode and cathode and that both the exact role of the surface treatment in backing layers and the physical processes which control liquid-phase transport are unknown. 

Understanding the kinetics of contaminant adsorption on the subsurface solid phase requires knowledge of both the differential rate law, explaining the reaction system, and the apparent rate law, which includes both chemical kinetics and transport-controlled processes. By studying the rates of chemical processes in the subsurface, we can predict the time necessary to reach equilibrium or quasi-state equilibrium and understand the reaction mechanism. The interested reader can find detailed explanations of subsurface kinetic processes in Sparks (1989) and Pignatello (1989). 

Mass transfer rates are increased in the presence of eruptions because the interfacial fluid is transported away from the interface by the jets. For mass transfer from drops with the controlling resistance in the continuous phase, the maximum increase in the transfer rate is of the order of three to four times (S8), not greatly different from the estimate of Eq. (10-4) for cellular convection. This may indicate that equilibrium is attained in thin layers adjacent to the interface during the spreading and contraction. When the dispersed-phase resistance controls, on the other hand, interfacial turbulence may increase the mass transfer rate by more than an order of magnitude above the expected value. This is almost certainly due to vigorous mixing caused by eruptions within the drop. 

Because the cellulose ether alkoxide is present entirely in the aqueous phase, the rate-limiting step may be the partitioning (phase transport) of the hydrophobic electrophile across the interface from the organic to aqueous phase. If the reaction rate is controlled by diffusion of the electrophile across the interface, then one would expect a correlation between water solubility of the hydrophobe and its alkylation efficiency. The fact that the actual alkylation reaction is probably occurring in the aqueous phase (or at the interface) yet the electrophile itself is principally soluble in the organic phase has important mechanistic ramifications. This type of synthetic problem, in which one reactant is water soluble and the other organic soluble, should be amenable to the techniques of phase transfer catalysis (PTC) to yield significant improvements in the alkylation efficiency. 

The Damkohler numbers are useful measures of the characteristic transport time relative to the reaction time. If the surface Damkohler number (sometimes referred to as the CVD number see reference 7) is large, mass transfer to the surface controls the growth. For small Damkohler numbers, surface kinetics governs the deposition. Similarly, if the gas-phase Damkohler number is large, the reactor residence time is an important factor, whereas if it is small, gas-phase reactions control the deposition. 

Any surface reaction that involves chemical species in aqueous solution must also involve a precursory step in which these species move toward a reactive site in the interfacial region. For example, the aqueous metal, ligand, proton, or hydroxide species that appear in the overall adsorption-desorption reaction in Eq. 4.3 cannot react with the surface moiety, SR, until they leave the bulk aqueous solution phase to come into contact with SR. The same can be said for the aqueous selenite and proton species in the surface redox reaction in Eq. 4.50, as another example. The kinetics of surface reactions such as these cannot be described wholly in terms of chemically based rate laws, like those in Eq. 4.17 or 4.52, unless the transport steps that precede them are innocuous by virtue of their rapidity. If, on the contrary, the time scale for the transport step is either comparable to or much longer than that for chemical reaction, the kinetics of adsorption will reflect transport control, not reaction control (cf. Section 3.1). Rate laws must then be formulated whose parameters represent physical, not chemical, processes. 

This point can be appreciated more quantitatively after consideration of an important (but simple) model of transport-controlled adsorption kinetics, the film diffusion process.34 35 This process involves the movement of an adsorptive species from a bulk aqueous-solution phase through a quiescent boundary layer ( Nemst film ) to an adsorbent surface. The thickness of the boundary layer, 5, will be largest for adsorbents that adsorb water strongly and smallest for aqueous solution phases that are well stirred. If j is the rate at which an... 

The film diffusion process assumes that reactive surface groups are exposed directly to the aqueous-solution phase and that the transport barrier to adsorption involves only the healing of a uniform concentration gradient across a quiescent adsorbent surface boundary layer. If instead the adsorbent exhibits significant microporosity at its periphery, such that aqueous solution can effectively enter and adsorptives must therefore traverse sinuous microgrottos in order to reach reactive adsorbent surface sites, then the transport control of adsorption involves intraparticle diffusion.3538 A simple mathematical description of this process based on the Fick rate law can be developed by generalizing Eq. 4.62 to the partial differential expression36... 

The classification of separations should reflect the patterns of component transport and equilibrium that develop in the physical space of the system. The transport equations show that we have two broad manipulative controls that can be structured variously in space to affect separative transport. First is the chemical potential which controls both relative transport and the state of equilibrium. Chemical potential, of course, can be varied as desired in space by placing different phases, membrane barriers, and applied fields in appropriate locations. A second means of transport control is flow, which can be variously oriented with respect to the phase boundaries, membranes, and applied fields—that is, with respect to the structure of the chemical potential profile. 

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