Channel mass transport

Operation of a fuel cell depends on a number of transport processes such as flow of reactant gases through the gas flow channels, mass transport of reactant gas species from gas flow channels and through the porous electrodes, ion transport through the membranes, and electron transport through electrodes and interconnects. Figure 6.1 shows transport of gas flow in flow channels as well heat and mass transport through the channels and electrode-membrane tri-layers of the fuel cell. 

Fig. 2 shows a schematic diagram of a micro-channel of reformer section to be examined in this study. A multi-physics computer-aided numerical model framework integrating kinetics, mass transport, and flow dynamics in micro-channel reactors has been established. 

OS 43] [R 14] [P 32] Using a three-liquid layer (water/oil/water) flow instead of a two-liquid layer flow at constant channel dimensions decreases the liquid lamellae width and doubles the absolute value of the organic/aqueous interface. As a consequence, mass transport is facilitated compared with the two-flow configuration. Hence it was found that a much higher yield was obtained for the three-liquid layer flow when performing experiments of both flow configurations imder the same experimental conditions (210 s, 0.2 pi min room temperature, 300 W, > 300 nm... 

The major attempts so far were to demonstrate the benefits of enhancing mass transport in micro channels, especially by decreasing the hydraulic diameter [30]. 

Lla. Landau. U., LBL-2702 Ph.D. thesis. University of California, Berkeley, January 1976. Lib. Landau, U., and Tobias, C. W., Mass Transport and Current Distribution in Channel Type Electrolyzers in the Laminar and Turbulent Flow Regimes, Ext. Abstr., No. 266, Electrochemical Society Meeting, Washington D.C., May 1976, 663. 

As seen above (equation (5)), the basis of the simple bioaccumulation models is that the metal forms a complex with a carrier or channel protein at the surface of the biological membrane prior to internalisation. In the case of trace metals, it is extremely difficult to determine thermodynamic stability or kinetic rate constants for the adsorption, since for living cells it is nearly impossible to experimentally isolate adsorption to the membrane internalisation sites (equation (3)) from the other processes occurring simultaneously (e.g. mass transport complexation adsorption to other nonspecific sites, Seen, (equation (31)) internalisation). 

In hydrodynamic techniques, convection is the principal mode of mass transport, and is brought about by the controlled movement of the electrode in the solution or by pumping the electrolyte through a pipe or channel. 

In Section 7.2, we looked at electroanalytical systems where the electrode rotates while the bulk of the solution remained still. In this present section, we will reverse this experimental concept by considering the case where it is the solution which flows - this time past a stationary electrode. Here, we shall be looking at flow ceils and channel electrodes. The principal mode of mass transport in both cases is convection, since the solution moves relative to the electrode. 

Convection That form of mass transport in which the solution containing electroanalyte is moved natural convection occurs predominantly by heating of solution, while forced convection occurs by careful and deliberate movement of the solution, e.g. at a rotated disc electrode or by the controlled flow of analyte solution over a channel electrode. 

In a follow-up study, Koptyug et al. 115) reported images of both liquid and gas flow and mass transport phenomena in two different cylindrical monolith catalysts (one with triangular channels, the other with square channels) at various axial locations within the monolith. Heibel et al. 116,117) addressed two-phase flow in the film flow regime and reported investigations of liquid distributions in the plane perpendicular to the direction of superficial flow, in particular, addressing the accumulation of liquid in the corners of the square channels of the monolith. 

In these electrode configurations, the solution moves past the electrodes embedded in the wall of a tube or channel. It turns out, as is to be expected, that for high Schmidt numbers (thin diffusion layer) the mass transport in the appropriate dimensionless variables is virtually identical for both electrodes. 

Fig. 3. The parabolic flow profile in a thin wall channel. In addition to flow, mass transport can occur by molecular diffusion and by thermal convention...

Mass transport within the electrodes is of particular importance in determining the reflection of the porous media structure on the fuel cell performance. In fact, the main results of mass transport limitation is that the reactant concentrations (H2 and CO for the anode, and O2 for the cathode) at the reaction zone are lower than in the gas channel. When applying Equations (3.40) and (3.42), the result is that the lower the concentration of the reactants, the lower the calculated cell performance. The loss of voltage due to the mass transport of the gas within the electrodes is also referred to as concentration overpotential. Simplified approaches for determining concentration overpotential include the calculation of a limiting current, i.e. the maximum current obtainable due to mass transport limitation (cf. Appendix A3.2). 

For sake of simplicity, we will refer only to the anode side. As described by Equations (3.47-3.59), the gas concentration of H2 and H2O in the gas channel is different from that in the reaction zone. Diffusion phenomena occurring in the porous media, in fact, are based on the existence of a concentration gradient, as expressed by Equations (3.47-3.49), i.e. gas concentration variation in the space domain enables the mass transport. 

Since both OCV and activation overpotential depend on some gas species concentration, and since in a PEN lumped structure the mass transport cannot be directly modeled within the domain thickness, the so-called concentration losses are introduced. They represent the voltage reduction due to the fact that the gas species concentration reacting in the reaction zone is different from that used in the calculation (i.e. the concentration relative to the gas channel, also referred to as the bulk ). 

As explained in Section 3.3, concentration loss represents the voltage reduction due to mass transport of the gas species through the electrodes. The main result of the mass transfer in a porous electrode, in fact, is that concentration of the gas species in the reaction zone is different from that in the gas channel. The mathematical expression for the concentration loss is given by Equation (3.77)... 

Convective and diffusive mass transport is considered in the gas channels, while in the porous media the convective term is neglected. Diffusion is modeled through Fick s law, as described in Chapter 3. 

Laminar flow reactors are equipped with microstructured reaction chambers that have the desired low Reynolds numbers due to their small dimensions. Mass transport perpendicular to the laminar channel flow is dominated by diffusion, a phenomenon known as dispersion. Without the influence of diffusion, laminar flow reactors could not be used in heterogeneous catalysis. There would be no mass transport from the bulk flow to the walls as laminar flow, in contrast to turbulent flow, cannot mix the flow macroscopically. 

Mass transport in laminar flow is dominated by diffusion and by the laminar velocity profile. This combined effect is known as dispersion and the underlying model for the theoretical derivation of a kinetic study had to be derived from the dispersion model, which Taylor [91] and Aris [92] developed. Taylor concluded that in laminar flow the speed of an inert tracer impulse initially given to a channel will have the same speed as the steady laminar carrier gas flow originally prevailing in this channel. 

Scale-up is in principle straightforward. Larger channel geometries (e.g., in the internally finned monolith channels) allow countercurrent operation of gas and liquid. Monolith reactors are intrinsically safer. The monolith channels have no radial communication in terms of mass transport, and the development of runaway by local hot spots in a trickle-bed reactor cannot occur. Moreover, when the feed of liquid or gas is stopped, the channels are quickly emptied. 

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