Multiphase flows:Analytical solutions and Stability Analysis


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