- 1.1 What Is Mass Transfer?
- 1.2 Preliminaries: Continuum and Concentration
- 1.3 Flux Vector
- 1.4 Concentration Jump at Interface
- 1.5 Application Examples
- 1.6 Basic Methodology of Model Development
- 1.7 Conservation Principle
- 1.8 Differential Models
- 1.9 Macroscopic Scale
- 1.10 Mesoscopic or Cross-Section Averaged Models
- 1.11 Compartmental Models
- Review Questions
1.7 Conservation Principle
The conservation principle is the consequence of the law of mass conservation, which states that a species A cannot appear from nowhere and must be conserved. The species mass balance is therefore the starting point:
Species A can cross into the control volume from a part of the control surface (the in term) and leave out of the rest of control surface.
Species may also be consumed (depletion) or produced (generation) within the control volume by chemical reaction.
Finally, the species concentration in the control volume may change with time due to the accumulation of the species within the control volume. The various processes involved are shown schematically in Figure 1.8.
Figure 1.8 Schematic of the conservation principle applied to a control volume.
The depletion is normally taken as a negative generation term and is often not included separately. In such cases, the generation is to be understood as net generation, which is equal to generation – depletion.
Similarly the out – in term is often written as a net efflux term. Hence another form of the conservation statement is
(Net) Generation = Net efflux + Accumulation
We now illustrate the use of this principle for the three levels of models discussed earlier and indicate which additional relations are needed to complete the model.