- 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
Mass transport phenomena are ubiquitous in nature and in industrial applications. In essence, the study of mass transfer is the main feature that distinguishes chemical engineering from other engineering disciplines. Mass transfer is caused by diffusion and convection.
Development of a mathematical model to describe a process is central to the analysis and design of a mass transport process. The model is expected to provide information on the concentration in the system and the rate at which a species is transported across the system or equipment.
Analysis of mass transport phenomena is based on the continuum approximation. This assumption permits us to assign a value for concentration at each and every Euclidean point in space.
Concentration can be defined in various ways (mole basis, mass basis, partial pressure, mole fraction, mass fraction), and the relation and conversion from one unit to other should be noted.
An important application of mass transfer is interfacial mass transfer, which refers to the transfer of a solute from one phase to another. For such problems, at a phase boundary (e.g., gas–liquid interface) the values of concentration are different on each side of the interface. This discontinuity is known as the concentration jump at the interface, and thermodynamic phase equilibrium relations are used to close the gaps between the two sides. Hence thermodynamic relations are always needed in the context of interfacial mass transfer.
Models for mass transfer can be developed at many levels. At the topmost level are differential models, which contain the maximum information in the context of the continuum assumption. A differential equation for the field variable, the species concentration, is then developed using the species conservation laws coupled with some constitutive models for transport of mass by diffusion, usually Fick’s law.
Differential models are rather complex to solve for many problems, so models with less details are also used. In general, in transport phenomena analysis, one usually develops model at three levels:
– Differential models provide the most detailed or pointwise information.
– Macroscopic models provide overall information of the system. They typically require some closure parameters on the level of mixing in the system and use of mass transfer coefficients.
– Mesoscopic models provide information on the variation of an averaged property as a function of the main flow direction. The main closure parameters are the transport coefficients and the dispersion coefficient to account for velocity profiles.
The macro- and meso-levels are the volume averaged and cross-sectional averaged description of the differential models, respectively. The definitions of various averages are an important part of the chemical engineer’s vocabulary. The concept of averaging is useful to inter-relate models at various levels of detail.
Compartmental models offer a simplified platform through which to represent complex systems, such as calculation of a drug metabolic process in the human body. These models usually comprise a set of macroscopic control volumes connected in some specified manner.