Reactant transport schematics

Fluid-fluid reactions are reactions that occur between two reactants where each of them is in a different phase. The two phases can be either gas and liquid or two immiscible liquids. In either case, one reactant is transferred to the interface between the phases and absorbed in the other phase, where the chemical reaction takes place. The reaction and the transport of the reactant are usually described by the two-film model, shown schematically in Figure 1.6. Consider reactant A is in phase I, reactant B is in phase II, and the reaction occurs in phase II. The overall rate of the reaction depends on the following factors (i) the rate at which reactant A is transferred to the interface, (ii) the solubihty of reactant A in phase II, (iii) the diffusion rate of the reactant A in phase II, (iv) the reaction rate, and (v) the diffusion rate of reactant B in phase II. Different situations may develop, depending on the relative magnitude of these factors, and on the form of the rate expression of the chemical reaction. To discern the effect of reactant transport and the reaction rate, a reaction modulus is usually used. Commonly, the transport flux of reactant A in phase II is described in two ways (i) by a diffusion equation (Pick s law) and/or (ii) a mass-transfer coefficient (transport through a film resistance) [7,9]. The dimensionless modulus is called the Hatta number (sometimes it is also referred to as the Damkohler number), and it is defined by... 

Here we are intending to give a sense as to how to treat the reactant transports within the electrode layer roughly as well as what is its effect on the electron-transfer kinetics. Figure 2.12(A) shows the schematic of such an electrochemical electrode system consisted of the current collector, matrix electrode layer, and the electrolyte. 

Figure 2. Schematic of reaction XY + Z X + YZ in condensed phase showing energy transfer into the system and reactant transport to the reaction zone. The compnted rate constant would be valid if neither the energy transfer nor the reactant transport is rate hmiting.

Figure 2. Schematic view of electrode reactions at the electrode/electrolyte interfaces and reactants transport through a polymer electrolyte membrane in a direct methanol fuel cell.

Fig. 20. Schematic representation of the solid + solid reaction A + B -> AB in which constituents of the relatively mobile reactant (A) are transported to the outer surfaces of the product phase (AB) and rate is controlled by diffusion of constituents of A and/ or B across the barrier layer AB.

To ensure that the detector electrode used in MEMED is a noninvasive probe of the concentration boundary layer that develops adjacent to the droplet, it is usually necessary to employ a small-sized UME (less than 2 /rm diameter). This is essential for amperometric detection protocols, although larger electrodes, up to 50/rm across, can be employed in potentiometric detection mode [73]. A key strength of the technique is that the electrode measures directly the concentration profile of a target species involved in the reaction at the interface, i.e., the spatial distribution of a product or reactant, on the receptor phase side. The shape of this concentration profile is sensitive to the mass transport characteristics for the growing drop, and to the interfacial reaction kinetics. A schematic of the apparatus for MEMED is shown in Fig. 14. 

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. 

Schematically, in its simplest version, the reactant X (to be transported) is placed at the end of a vacuum sealed tube together with a small quantity of the transporting agent Z. Inside the tube a temperature gradient must be maintained.

Figure 4.1 shows a schematic of a typical polymer electrolyte membrane fuel cell (PEMFC). A typical membrane electrode assembly (MEA) consists of a proton exchange membrane that is in contact with a cathode catalyst layer (CL) on one side and an anode CL on the other side they are sandwiched together between two diffusion layers (DLs). These layers are usually treated (coated) with a hydrophobic agent such as polytetrafluoroethylene (PTFE) in order to improve the water removal within the DL and the fuel cell. It is also common to have a catalyst-backing layer or microporous layer (MPL) between the CL and DL. Usually, bipolar plates with flow field (FF) channels are located on each side of the MFA in order to transport reactants to the... 

Generally speaking, PEVD is a modified form of chemical vapor deposition (CVD). A comparison between PEVD and conventional CVD is schematically shown in Figure 1 for a product (D) formed from reactants (A) and (B). In a CVD process, both reactants (A) and (B) are supplied through a vapor phase at the same side of a solid substrate (E). They react chemically at the surface of the solid substrate (E), aided by some type of catalytic effect, to form a desired product (D). In a PEVD process, one reactant (A) is transported from one side (source) of a solid substrate (E) to the other side (sink) under well-controlled thermodynamic and kinetic conditions. At the sink side, reaction with (B) occurs to form (D). Further growth of (D) into a continuous thin film with the desired thickness in a PEVD process also relies on (A) transported in the solid state now through (E) and (D) to react with (B). 

Under open circuit conditions, the PEVD system is in equilibrium after an initial charging process. The equilibrium potential profiles inside the solid electrolyte (E) and product (D) are schematically shown in Eigure 4. Because neither ionic nor electronic current flows in any part of the PEVD system, the electrochemical potential of the ionic species (A ) must be constant across both the solid electrolyte (E) and deposit (D). It is equal in both solid phases, according to Eqn. 11, at location (II). The chemical potential of solid-state transported species (A) is fixed at (I) by the equilibrium of the anodic half cell reaction Eqn. 6 and at (III) by the cathodic half cell reaction Eqn. 8. Since (D) is a mixed conductor with non-negligible electroific conductivity, the electrochemical potential of an electron (which is related to the Eermi level, Ep) should be constant in (D) at the equilibrium condition. The transport of reactant... 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

FIGURE 20.15 Schematic showing the principal elements in the complex diamond CVD process flow or reactants into the reactor, activation of the reactants hy the thermal and plasma processes, reaction and transport of the species to the growing snrface, and surface chemical processes depositing diamond and other forms of carhon. (From Pehrsson, P.E., Cehi, F.G., and Butler, J.E., in Chemical Mechanisms of Diamond CVD, Davis, R.E., Ed., Noyes Puhhcations, New Jersey, 1993.)... 

Figure 13.5. Transport vs surface controlled dissolution. Schematic representation of concentration in solution, C, as a function of distance from the surface of the dissolving mineral. In the lower part of the figure, the change in concentration (e.g., in a batch dissolution experiment) is given as a function of time, (a) Transport controlled dissolution. The concentration immediately adjacent to the mineral reflects the solubility equilibrium. Dissolution is then limited by the rate at which dissolved dissolution products are transported (diffusion, advection) to the bulk of the solution. Faster dissolution results from increased flow velocities or increased stirring. The supply of a reactant to the surface may also control the dissolution rate, (b) Pure surface controlled dissolution results when detachment from the mineral surface via surface reactions is so slow that concentrations adjacent to the surface build up to values essentially the same as in the surrounding bulk solution. Dissolution is not affected by increased flow velocities or stirring. A situation, intermediate between (a) and (b)—a mixed transport-surface reaction controlled kinetics—may develop.

In all the above mentioned cases conversion can only take place when the components are transferred to the catalytic phase or at least to the interface in which the reaction proceeds. Transport from one phase to the other(s) requires a driving force, i.e., the existence of concentration gradients. Figure 2 shows schematically the principal steps of a homogeneously catalyzed gas-liquid-liquid reaction (eq.(7)), where the reaction product P, is formed by the reaction between a gaseous reactant Ai and reactant A2 in the liquid phase 1 in presence of a second liquid phase which contains the catalyst. Both liquid phases are immiscible and Ai is only soluble in liquid phase 1. 

For disk-type electrodes, usually with a radius of O.l-l.O cm the thickness of the diffusion layer that is depleted of reactant is much smaller than the electrode size so that mass transport can be described in terms of planar diffusion of the electroactive species from the bulk solution to the electrode surface as schematized in Figure 1.2a, where semi-infinite diffusion conditions apply. The thickness of the diffusion layer can be estimated as for a time electrolysis t and usually ranges between 0.01 and 0.1 mm (Bard et al., 2008). For an electrochemically reversible -electron transfer process in the absence of parallel chemical reactions, the variation of the faradaic current with time is then given by the Cottrell equation ... 

Figure 14.4.6 Schematic concentration profiles for the general case of mediated (catalytic) reduction of the primary reactant. A, by electrogenerated Q. The electrode is held at a potential where all P at the electrode surface is reduced to Q, so that the concentration of Q at the electrode surface is C (= r /< ). Within the solution (x > (f>), the concentration profile for A is approximately linear. Xf and Xb are the rate constants for the transport of A into and out of the film, respectively. [Reprinted from J. Leddy, A. J. Bard, J. T. Maloy, and J.-M. Saveant, J. Electroanal. Chem., 187, 205 (1985), with permission from Elsevier Science.]...

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