Sink term defined

Considering the two source terms (emission and in-scattering) and the two sink terms (absorption and out-scattering) defined on the right-hand side of the previous expression, one can transform the preceding fimdamental law in a more formal mathematical definition ... 

As for the integral source terms considered hitherto, the integral in physical space is not appropriate as it is based on the assumption that two particles that coalesce at a particular location in space can produce a larger particle elsewhere. Following the same procedure as described above, the sink term due to coalescence can be re-defined as ... 

For the time being, low viscous systems shall be considered only. With this restriction the power input by the agitator may be neglected as a first approximation. In addition, the absence of any further heat sources or sinks, such as evaporation cooling, is assumed. In a next step the special theoretical case that all components fed into the reactor do not react with each other shall be discussed. If the two terms defined in Equ. (4-48) and (4-49) are inserted into the general integral heat balance and if the steady state is evaluated, a mixing temperature Tij will be observed ... 

All symbols have their usual meaning and only more important ones are defined here. Cj is the concentration of component j in the aqueous phase (e.g. polymer, tracer, etc.). The viscosity of the aqueous phase, rj, may depend on polymer or ionic concentrations, temperature, etc. Dj is the dispersion of component j in the aqueous phase Rj and qj are the source/sink terms for component j through chemical reaction and injection/production respectively. Polymer adsorption, as described by the Vj term in Equation 8.34, may feed back onto the mobility term in Equation 8.37 through permeability reduction as discussed above. In addition to the polymer/tracer transport equation above, a pressure equation must be solved (Bondor etai, 1972 Vela etai, 1974 Naiki, 1979 Scott etal, 1987), in order to find the velocity fields for each of the phases present, i.e. aqueous, oleic and micellar (if there is a surfactant present). This pressure equation will be rather more complex than that described earlier in this chapter (Equation 8.12). However, the overall idea is very similar except that when compressibility is included the pressure equation becomes parabolic rather than elliptic (as it is in Equation 8.12). This is discussed in detail elsewhere (Aziz and Settari, 1979 Peaceman, 1977). Various forms of the pressure equation for polymer and more general chemical flood simulators are presented in a number of references (Zeito, 1968 Bondor etal, 1972 Vela etal, 1974 Todd and Chase, 1979 Scott etal, 1987). 

Electrode reactions are inner-sphere reactions because they involve adsorption on electrode surfaces. The electrode can act as an electron source (cathode) or an electron sink (anode). A complete electrochemical cell consists of two electrode reactions. Reactants are oxidized at the anode and reduced at the cathode. Each individual reaction is called a half cell reaction. The driving force for electron transfer across an electrochemical cell is the Gibbs free energy difference between the two half cell reactions. The Gibbs free energy difference is defined below in terms of electrode potential,... 

Fig. 4. Cross section of a rotary kiln. I is the wall area that is in contact with the solids (see eq. 10) A is the wall area that is in contact with the gases A is the radiation sink area r and r are the inner and outer radii, respectively. Other terms are defined in text.

Specially dc.signcd finned surfaces called heat sinks, which are commonly used in the cooling of electronic equipment, involve one-of-a-kind complex geometries, as shown in Tabic 3-6. The heat transfer performance of heat sinks is usually expressed in terms of their thermal resistances R in CAV, wliich is defined as... 

Historically, water hardness was defined in terms of the capacity of cations in the water to replace the sodium or potassium ions in soaps and to form sparingly soluble products that cause scum in the sink or bathtub. Most multiply charged cations share this undesirable property. In natural waters, however, the concentrations of calcium and magnesium ions generally far exceed those of any other metal ion. Consequently, hardness is now expressed in terms of the concentration of calcium carbonate that is equivalent to the total concentration of all the multivalent cations in the sample. 

Electrolyte stratification has been responsible for the failure of many flooded battery banks. In simple terms, this phenomenon can be defined as a build-up of higher strength acid at the bottom of the battery. Stratification occurs because sulfuric acid has a higher density than water and, when formed during the charging process, will sink to the bottom of the battery container. Such behaviour results in a decrease in battery capacity due to uneven utilization of the active material [12]. Moreover, if the resulting concentration gradient is allowed to remain for extended periods, premature failure of the battery can occur. 

In practical terms, an indoor air quality model should provide a reasonable description of the mass balance of the test chamber experiments, trying to address factors such as material emissions, airflows into and out of the chamber and chemical/physical decay or other removal and/or transformation processes of the VOCs. VOC concentrations are increased by emissions within the defined volume of the chamber and by infiltration from external air to the chamber. Similarly, concentrations are decreased by transport via exiting chamber air, by removal to chemical and physical sinks within the chamber air, or by transformation of a VOC to other chemical forms. A general mass balance equation concerning the concentration of a VOC in a test chamber can be written in the form of one or more differential equations representing the rate of accumulation and the VOC gain and loss. This concept for a VOC concentration C (mass units/ m ) in a chamber of volume V (m ) is translated into the following differential equation ... 

Through this step and based on experimental evidence we try to develop the appropriate model to describe the test chamber kinetics. As was anticipated in the introduction of this Chapter, from a conceptual point of view, two broad categories of models can be developed empirical-statistical and physical-based mass transfer models. It should be emphasized that, in several cases, even the fundamentally based mass transfer models are indistinguishable from the empirical ones. This happens because the mass transfer models are generally very complex in both the physical concept involved and the mathematical treatment required. This often leads the modelers to introduce approximations, making the mass transfer models not completely distinguishable from some empirical models in terms of both functional formulations and descriptive capabilities. Considering the current status of models which have been developed to describe VOC emissions (and/or sink processes), we could define the mass transfer models as hybrid-empirical models. 

Consequently, it would be expected that the predictive capability of the two models will also be equivalent, and any limitations in terms of prediction of one model will reflect analogous limitations of the other model. Indeed, if the vapor pressure model fails to describe the tailing of the concentration versus time curve - which is an indication of sink effects - the mass transfer model is also unable to describe the same part of the experimental data (Tichenor et al., 1993). It should be noted, however, that the parameters of the mass transfer model have well-defined physical meanings [e.g., vapor pressure (C ), molecular diffusivity (Dy), boundary layer thickness ( )], and the parameter estimation does not rely heavily on curve fitting. The parameter estimation is the first step in the model performance and validation process, as we will see later in this Chapter. 

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