This course deals with solid-state diffusion, homogeneous and heterogeneous chemical reactions, and spinodal decomposition. Topics covered include: heat conduction in solids, convective and radiative heat transfer boundary conditions; fluid dynamics, 1-D solutions to the Navier-Stokes equations, boundary layer theory, turbulent flow, and coupling with heat conduction and diffusion in fluids to calculate heat and mass transfer coefficients.

Course outline

The following aspects will be treated:
1. Mathematical Review
Differential operators (gradient, divergence, curl, laplacian) and tensors in cartesian and curvilinear (spherical, cylindrical) coordinates. Eulerian and Lagrangian derivatives.
2. Momentum and Heat Transport in Materials
Mass conservation: the continuity equation. Momentum flux and stress tensor. Newtonian and non-newtonian fluids. Momentum conservation: the motion equation and related boundary conditions. Bernoulli’s theorem. Flow fields in ducts and past solid bodies. Creeping and potential flow. Laminar and turbulent regimes. Heat flux: Fourier’s law. Energy conservation: the internal-energy equation. Velocity and temperature pertubations in bounded and unbounded systems. Adimensional transport equations and adimensional numbers.
3. Diffusion in Multi-Component Materials
Average mass and molar velocity. Absolute and relative fluxes. Mass flux: diffusion mechanisms and generalized Fick’s law. Continuity, motion and internal-energy equations for multi-component systems in dimensional and adimensional forms. Concentration perturbations.
4. Numerical Methods for Transport Equations
Finite-difference methods: consistency, convergence, stability. Overview of finite-element methods.
5. Illustrative Applications in Materials Science
Flow problems in polymer technology. Anisotropic flows and orientation dynamics in liquid crystals. Heterogeneous catalysts: diffusion with chemical reaction, kinetic control.