Water Transport Rate Equation

In a cation transfer fuel cell such as PAFC and PEMFC with positively charged ion, water is produced by the electrochemical reaction at the electrolyte-cathode interface. On the other hand, in an anion transferfuel cell such as AFC, MCFC, and SOFC with negatively charged ion, water is produced at the anode-electrolyte interface. 

Water produced at the electrode-electrolyte interfaces transports through the electrode-gas diffusion layers by diffusion and convection toward the gas flow channels where it may be transferred to the reactant gas flow streams by convection and diffusion if the gas streams are sufficiently dry. It is essential that water is removed from the electrolyte-electrode interface either by the flowing gas streams or by some external water collection system in order to prevent any accumulation or flooding of the electrode-electrolyte interface regions ftat blocks the pores of the electrode-gas diffusion layer and prevents reactant gas to reach reaction sites causing cell concentration polarization or mass tranter loss. Water flooding issue and mass transfer loss are 

Water generation at cathode-electrolyte interface for SOFC 

Water transport by diffusion and convection between gas stream and anode 

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It is probable that capillary flow of water contributes to transport in the soil. For example, a rate of 7 cm/year would yield an equivalent water velocity of 8 x 10-6 m/h, which exceeds the water diffusion rate by a factor of four. For illustrative purposes we thus select a water transport velocity or coefficient U6 in the soil of 10 x 10 6 m/h, recognizing that this will vary with rainfall characteristics and soil type. These soil processes are in parallel with boundary layer diffusion in series, so the final equations are... 

A major problem in the quantification of air-water transport phenomena in terms of the rate expression [Equation (4.18)] is to find appropriate values for Kl. As far as sewer systems are concerned, the most well-established knowledge concerning air-water mass transfer is on reaeration (Section 4.4). 

Quantitative estimation of ventilation by indirect methods in mussels requires four assumptions (16) a) reduction of concentration results from uptake, b) constant ventilation (pumping) rate, c) uptake of a constant percentage of concentration (first order process), d) homogeneity of the test solution at all times. Our transport studies have utilized antipy-rine (22, 23) a water soluble, stable chemical of low acute toxicity to mussels. It is readily dissolved in ocean water or Instant Ocean and is neither adsorbed nor volatilized from the 300 ml test system. Mussels pump throughout the 4 hour test period and this action is apparently sufficient to insure homogeneity of the solution. Inspection of early uptake and elimination curves (antipyrine concentration as a function of time) prompted use of Coughlan s equation (16) for water transport. 

Speleothem precipitation rates from thin water films open to the cave atmosphere are controlled by three processes (Baker and Smart, 1995 Baker et al., 1998) 1) chemical reactions at the calcite-solution interface as described by the rate equations of Plummer et al. (1978) through which precipitation rates can be calculated when the concentrations of reactants are known 2) mass transport of reactants through the solution towards or away from the speleothem surface and 3) the rate-limiting reaction H" + HCO = H2O + CO2, through which CO2 is released into the cave atmosphere. Buhmann and Dreybrodt (1985a,b) have solved the transport equations taking into consideration these three mechanisms in order to obtain precipitation rates. For speleothems, Eq.3 can approximate these processes within 10% ... 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

Mineral-water reactions that are controlled by transport in the dissolved phase are characterized by a rate equation that describes the flux of reactants through a laminar layer of thickness 8 adjacent to the mineral. Transport in this very thin layer is by molecular diffusion therefore Eq. (9.20) becomes... 

The membrane area based on water transport is calculated by equating the water flow rate in the permeate product to the rate of water permeation from Equation 18.49 ... 

Nonequilibrium treatment " of EOD under these conditions yields the following rate equations for the simultaneous transport of matter (i.e., water) and electricity (i.e., current), assuming that the diaphragm is uniform ... 

There are many equations which allow calculation of sediment transport rate within a water body, or sediment flux (see for example Task Committee of Computational Modeling of Sediment Transport Processes, 2004 for a review). However, these equations tend to be for a uniform sediment distribution, which is far from the variable source supply of material seen in events when the majority of sediment is moving. It is also generally considered that a particular flow has a maximum capacity to transport sediment, although the concentration this relates to depends again on sediment characteristics. Hence tliere are examples in China where sediment concentrations can reach several tens of thousands of parts per million for very fine particles, whereas a flow may become saturated with sand-sized particles at far lower concentrations. Rivers are often considered to be either capacity- or supply-limited in terms of their sediment transporting dynamics. However, in practice for most rivers, most of the time, sediment transport is limited by a complex and dynamic pattern of sediment supply. 

Hence, there are two criteria to properly design a container for water transport. The first is to insure the polymer is rate limiting (Equation 7), and the second is to insure a minimum weight loss over the shelf life. To properly apply these equations, the wall thickness required for a given polymer is found from Equation 8. This wall thickness then is the minimum value to use in Equation 7. That is, apply Equation 7 with the P/l from Equation 8. If the L from Equation 8 is less than 4, then increase the wall thickness with the criteria that Equation 7 must be greater than or equal to 4. If these conditions cannot be met practically or economically, the designer will need to iterate on polymer choice to insure these requirements can be met. 

The use of the one-dimensional model allows estimates of reaction rates to within a factor of —1.5 of those predicted by the more complex two-dimensional model. This close agreement is due largely to the rapid attenuation of Mn " production rates with depth and suggests that in such cases the distribution of a nonconservative pore-water constituent can be modeled reasonably accurately by use of the transport-reaction equation in one dimension. 

Cohen and Monod (C2) have summarized experimental evidence which shows indeed that special mechanisms of transport of organic nutrients occur in bacteria. They call such transport systems permeases. This term ending in -use implies that the system involves enzymes—an implication not yet proved by available data. At any rate, it is found that permease systems can lead to transport against an apparent rise in concentration, as well as other effects not possible with Fickian diffusion. Various hypothetical mechanisms for operation of permease systems yield rates of permeation which exhibit the Michaelis-Menten type of dependence on substrate (including water) concentration. Perhaps it is in the occurrence of one of these mechanisms that the rate equation [Eq. (38)] assumed by Monod and almost all subsequent workers finds its justification. [For further information on biological transport, see, e.g., Christensen (Cl).]... 

The nature of the dissolution medium can profoundly affect the shape of a dissolution profile. The relative rates of dissolution and the solubilities of the two polymorphs of 3-(3-hydroxy-3-methylbutylamino)-5-methyl-a5-triazino[5,6-Z)7indole were determined in USP artificial gastric fluid, water, and 50% ethanol solution [69]. In the artificial gastric fluid, both polymorphic forms exhibited essentially identical dissolution rates. This behavior has been contrasted in Fig. 6 with that observed in 50% aqueous ethanol, in which Form II has a significantly more rapid dissolution rate than Form I. If the dissolution rate of a solid phase is determined by its solubility, as predicted by the Noyes-Whitney equation, the ratio of dissolution rates would equal the ratio of solubilities. Because this type of behavior was not observed for this triazinoindole drug, the different effects of the dissolution medium on the transport rate constant can be suspected. 

One of the early mechanistic models for a PEM fuel cell was the pioneering work of Bemardi and Verbrugge [45, 46]. They developed a one-dimensional, steady state, isothermal model which described water transport, reactant species transport, as well as ohmic and activation overpotentials. Their model assumed a fully hydrated membrane at all times, and thus calculated the water input and removal requirements to maintain full hydration of the membrane. The model was based on the Stefan Maxwell equations to describe gas phase diffusion in the electrode regions, the Nemst-Planck equation to describe dissolved species fluxes in the membrane and catalyst layers, the Butler Volmer equation to describe electrode rate kinetics and Schlogl s equation for liquid water transport. 

As it has been stressed already, oceans strongly influence the climate by storing heat. Moreover, there are also currents that transport warm water from the equator to higher latitudes and cold water from the poles to the equator. The Gulf Stream flows from the coast of North America toward northern Europe, at a flow rate of 10-12 km/hour. This current carries 100 times more water than all rivers on earth put together. In tropical seas the water is warmed by the sun, diluted by rainwater and aerated by waves. In higher latitudes surface waters are cold and more dense. Those dense waters sink to the bottom to the ocean floors flowing toward the equator, warm water however is less dense and floats on top of this cold water. Also different salinity plays an important role in these processes. 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

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