Short time solution, transport properties

The generalized transport equation, equation 17, can be dissected into terms describing bulk flow (term 2), turbulent diffusion (term 3) and other processes, eg, sources or chemical reactions (term 4), each having an impact on the time evolution of the transported property. In many systems, such as urban smog, the processes have very different time scales and can be viewed as being relatively independent over a short time period, allowing the equation to be "spht" into separate operators. This greatly shortens solution times (74). The solution sequence is... 

The equilibration process in oxide systems can be monitored by changes in a bulk crystal property that is nonstoichiometiy sensitive, such as weight, Aw, electrical conductivity, Ao, or thermopower, AS. The kinetics of the re-equilibration process, provoked by isothermal changes of p(02), are schematically illustrated in Figure 4.25. The rate of the equilibration is determined by chemical diffusion involving the transport of defects under a gradient of chemical potential (ambipolar diffusion). Chemical diffusion coefficients may be determined from the relevant solutions of Pick s second law for long and short times, respectively... 

Experiments were monitored by measuring the conductivity of the feed and strip streams. The transport of ions (cobalt and iron) from an acidic feed (HCl) to a basic strip solution (NH4OH) was accomplished. Their results suggest that there are three distinct transport regimes operable in the membrane. The first occurs at short times and exhibits very little ion transport. This initial time is termed the ion penetration time and is simply the transport time across the membrane. At long times, a rapid increase in indiscriminate transport is observed. At this critical time and beyond, there are stability problems that is, loss of solvent from the pores leading to the degradation of the membrane and the formation of channels that compromise the ion selective nature of the system and its barrier properties. 

Solution speciation exerts important controls on chemical behavior. Speciation is known to influence solubility, membrane transport and bioavailability, adsorptive phenomena and oceanic residence times, volatility, oxidation/reduction behavior, and even physical properties of solutions such as sound attenuation. In recogni-tion of such influences, substantial efforts have been made to characterize the chemical speciation of elements in seawater. While assessments of organic speciation have dominantly been obtained using modern voltammetric procedures and, as such, have a relatively short history, assessments of inorganic speciation typically involve a wide variety of analytical procedures that have been employed over many decades. 

Contaminants with very low water solubilities (e.g. polycyclic aromatic hydrocarbons) play an important role in risk assessment of dangerous wastes and development of soil remediation. The mobility of such hydrophobic substances can be strongly affected by the existence of carriers (e.g. dissolved organic carbon), which can adsorb the contaminant and thereby enhance or reduce its velocity. The numerical simulation of the spreading of these contaminants, requires the solution of reactive transport equations for all involved components, coupled by the contaminant s sorption to the carrier. Our development is based on a model [2], in which all the carrier s influence on the contaminant transport is contained in an effective adsorption isotherm, depending on the carrier concentration and thereby also on space and time. First we shortly summarize the modelling of reactive transport of a single component (carrier, contaminant, carrier bound contaminant) in a porous medium, then in section 3 we combine the two equations for the contaminant components. The properties of the contaminant s effective isotherm and its influence on the transport equation are discussed in section 4. 

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