Diffusional Operations
Module Notes
Module Details
1. Diffusion and Brownian Motion
-- Brownian motion, Langevin Equation, overdamped Langevin Equation
-- Brownian motion in a harmonic potential
-- Smoluchowski equation
-- Time correlation functions
-- Fluctuation - Dissipation Theorem
2. Molecular Origin of Diffusion: Theories
-- Kinetic Theory of Gases
-- Hydrodynamic Theories
-- Free volume theories
-- Transition-state / activated-state theories
3. Multicomponent Systems
-- Conservation Equations for Multicomponent systems and Multicomponent fluxes
-- Matrix approximation for Multicomponent Mass Transport
-- Dimensional analysis and scaling (Prandtl, Schmidt, Grashof and Damköhler numbers)
4. Transport equations and Irreversible Thermodynamics
-- Affinities, fluxes, coupled fluxes, Casimir-Onsager reciprocity principles
-- Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density
5. Other Mechanisms for Mass Transfer
-- The equation of change for entropy
-- Generalized Stefan-Maxwell equations
-- First applications of the Generalized Stefan-Maxwell equations
6. Other applications of the Generalized Stefan-Maxwell equations
-- Mass transfer across selectively permeable membranes (facilitated and active transport)
-- Mass Transfer in Biology and Medicine
-- Drug release from Delivery Systems
-- Mass transfer through a Biofilm
-- Diffusion in porous media
7. Transport in Electrolyte Solutions
-- Ion fluxes, Poisson-Boltzmann equation, Double-Layer Potential
-- Electro-osmotic Flow
8. Combined Transport and Reaction (homogeneous or heterogeneous)
-- Instantaneous Reactions, First Order Reactions
-- Vapor Deposition and Sublimation
-- Condensation and Evaporation
9. Dispersion & Turbulence
-- Convection-Dispersion (Taylor Dispersion)
-- Averaging--temporal and spatial
-- Dispersion and Chromatography
-- Turbulence (eddy diffusivities)
10. Overview of anomalous diffusion
-- Levi walks and their macroscopic interpretation
-- Subdiffusion and superdiffusion
Course textbooks
- Cussler, E.L. Diffusion: Mass Transfer in Fluid Systems (1984).
- R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Ed. , John Wiley & Sons (2002).
- Deen, W.M. Analysis of Transport Phenomena, 2nd Ed., Oxford Univ. Press (2012).
Additional Reading
- J. Crank, The Mathematics of Diffusion (1975).
- S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (1962).
- J.O. Hirschfelder, C.F. Curtis, and R.B. Bird, Molecular Theory of Gases and Liquids (1954).