Modeling Tools for Environmental Engineers and Scientists

ChemicalinjectionAirMassinjectedm1AqueousphasecontentX1GasphasecontentY1Ym2X2Y2Waterm3X3Y3m4X4Y4Magneticstirrerm5X5Y500XFigure 4.1 Linear partitioning in air-water binary system.where, K a–w is the nondimensional air-water partition coefficient (–). Similarpartitioning phenomena can be observed between other phases as well. Someof the more common two-phase environmental systems and the appropriatepartition coefficients for those systems are summarized in Appendix 4.1. It isimperative that these definitions be used consistently to avoid confusionabout units and inverse ratios, i.e., K 1–2 vs. K 2–1 .Experimentally measured data for many of these partition coefficients canbe found in handbooks and the literature. Alternatively, structure activity relationship(SAR) or property activity relationship (PAR) methods have alsobeen proposed to estimate them from molecular structures or other physicochemicalproperties. A comprehensive compilation of such estimation methodscan be found in Lyman et al. (1982).4.3.1 STEADY STATE AND EQUILIBRIUMThe concept of steady state has been referred to previously, implying nochanges with passage of time. The equilibrium conditions discussed abovealso imply no change of state with passage of time. The following illustrationadapted from Mackay (1991) provides a clear understanding of the similaritiesand differences between the two concepts.Consider the oxygen concentrations in the water and air, first, in a closedair-water binary system as shown in Figure 4.2(a). After a sufficiently longtime, the system will reach equilibrium conditions with an oxygen contentof 8.6 × 10 –3 mole/L and 2.9 × 10 –4 mole/L in the gas and aqueous phase,respectively. The system will remain under these conditions, seen as steadystate. Consider now the flow system in Figure 4.2(b). The flow rates remainconstant with time, keeping the oxygen contents the same as before. The systemnot only is at steady state, but also is at equilibrium, because the ratio of© 2002 by CRC Press LLC