Module Notes
Faculty Member (Members):
Postgraduate, Spring/Fall Semester
Module Type: Core Courses
Teaching Language: English/Greek
Course Code:
ECTS Credits: 12
Module Availability on Erasmus Students: No
Module Details

1. Molecular Origin of Diffusion: Theories

-- Kinetic Theory of Gases

-- Hydrodynamic Theories

-- Free volume theories

-- Transition-state / activated-state theories

2. Diffusion and Brownian Motion

-- Brownian motion, Langevin Equation, overdamped Langevin Equation

-- Brownian motion in a harmonic potential

-- Smoluchowski equation

-- Time correlation functions, response functions

-- Fluctuation - Dissipation Theorem

-- Diffusion in polymers

-- Levi walks and their macroscopic interpretation

3. Fick’s law and Diffusional Transport: Concentration distributions in Solids and in Laminar Flows

a) Steady-State

                --one-dimensional (2nd order ODE solution)

                --multidimensional (PDEs and separation of variables)

b) Unsteady-State

                --infinite domains (similarity variables, Laplace transforms, integral solutions)

                --finite domains (separation of variables, asymptotic solutions)

4. 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)

5. Transport equations and Irreversible Thermodynamics

-- Affinities, fluxes, coupled fluxes, Casimir-Onsager reciprocity principles

-- Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density

6. Other Mechanisms for Mass Transfer

-- The equation of change for entropy

-- Generalized Stefan-Maxwell equations

-- Applications of the Generalized Stefan-Maxwell equations

7. 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

8. Transport in Electrolyte Solutions

-- Ion fluxes, Poisson-Boltzmann equation, Double-Layer Potential

-- Electro-osmotic Flow

9. Combined Transport and Reaction (homogeneous or heterogeneous)

-- Instantaneous Reactions (moving boundaries), First Order Reactions

-- Vapor Deposition and Sublimation

-- Condensation and Evaporation

10. Dispersion & Turbulence

-- Convection-Dispersion (Taylor Dispersion)

-- Averaging--temporal and spatial

-- Dispersion and Chromatography

-- Turbulence (eddy diffusivities)

11. Overview of anomalous diffusion (time permitting)

-- Levi walks and their macroscopic interpretation

-- Subdiffusion and superdiffusion

Course textbooks

  1. E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems (1984).
  2. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Ed., John Wiley & Sons (2002).
  3. W.M. Deen, Analysis of Transport Phenomena, 2nd Ed., Oxford Univ. Press (2012).

Additional Reading

  1. J. Crank, The Mathematics of Diffusion (1975).
  2. S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (1962).
  3. J.O. Hirschfelder, C.F. Curtis, and R.B. Bird, Molecular Theory of Gases and Liquids (1954).