Lecture 1 - Introduction and overview of the course: Multiphase flows

Lecture 2 - Stratified flow in a micro channel: Velocity profiles

Lecture 3 - Stratified flow in a micro channel: Effects of physical parameters

Lecture 4 - Flow regimes in microchannels: Modeling and Experiments

Lecture 5 - Scaling Analysis: Introduction

Lecture 6 - Scaling Analysis: Worked Examples

Lecture 7 - Interfacial tension and its role in Multiphase flows

Lecture 8 - Eulerian and Lagrangian approaches

Lecture 9 - Reynolds Transport Theorem and the Equation of Continuity

Lecture 10 - Derivation of Navier-Stokes equation

Lecture 11 - Vector operations in general orthogonal coordinates: Grad., Div., Lapacian

Lecture 12 - Normal and shear stresses on arbitrary surfaces: Force balance

Lecture 13 - Normal and shear stresses on arbitrary surfaces: Stress Tensor formulation

Lecture 14 - Stresses on deforming surfaces: Introduction to Perturbation Theory

Lecture 15 - Pulsatile flow: Analytical solution

Lecture 16 - Pulsatile flow: Analytical solution and perturbation solution for Rw 1

Lecture 17 - Pulsatile flow: Perturbation solution for Rw 1

Lecture 18 - Viscous heating: Apparent viscosity in a viscometer

Lecture 19 - Domain perturbation methods: Flow between wavy walls

Lecture 20 - Flow between wavy walls: Velocity profile

Lecture 21 - Introduction to stability of dynamical systems: ODEs

Lecture 22 - Stability of distributed systems (PDEs): reaction diffusion example

Lecture 23 - Stability of a reaction-diffusion system (Continued...)

Lecture 24 - Rayleigh-Benard convection: Physics and governing equations

Lecture 25 - Rayleigh-Benard convection: Linear stability analysis - Part 1

Lecture 26 - Rayleigh-Benard convection: Linear stability analysis - Part 2

Lecture 27 - Rayleigh-Benard convection: Linear stability analysis - Part 3

Lecture 28 - Rayleigh Benard convection: Discussion of results

Lecture 29 - Rayleigh-Taylor ‘heavy over light’ instability

Lecture 30 - Rayleigh-Taylor instability (Continued...)

Lecture 31 - Capillary jet instability: Problem formulation

Lecture 32 - Capillary jet instability: Linear stability analysis

Lecture 33 - Capillary jet instability: Rayleigh’s Work Principle

Lecture 34 - Tutorial Session: Solution of Assignment 4 on linear stability

Lecture 35 - Turing patterns: Instability in reaction-diffusion systems

Lecture 36 - Turing patterns: Results

Lecture 37 - Marangoni convection: Generalised tangential and normal stress boundary conditions

Lecture 38 - Marangoni convection: Stability analysis

Lecture 39 - Flow in a circular curved channel: Governing equations and scaling

Lecture 40 - Flow in a circular curved channel: Solution by regular perturbation

Lecture 41 - Stability of flow through curved channels: Problem formulation

Lecture 42 - Stability of flow through curved channels: Numerical calculation

Lecture 43 - Viscous Fingering: Darcy’s law

Lecture 44 - Viscous Fingering: Stability analysis

Lecture 45 - Shallow Cavity flows