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

##### Lecture Details :

Multiphase flows:Analytical solutions and Stability Analysis by Prof. S.Pushpavanam,Department of Chemical Engineering,IIT Madras.For more details on NPTEL visit http://nptel.ac.in

##### Course Description :

Introduction and overview of the course: Multiphase flows - Stratified flow in a micro channel: Velocity profiles - Stratified flow in a micro channel: Effects of physical parameters - Flow regimes in microchannels: Modeling and Experiments - Scaling Analysis: Introduction - Scaling Analysis: Worked Examples - Interfacial tension and its role in Multiphase flows - Eulerian and Lagrangian approaches - Reynolds Transport Theorem and the Equation of Continuity - Derivation of Navier-Stokes equation - Vector operations in general orthogonal coordinates: Grad., Div., Lapacian - Normal and shear stresses on arbitrary surfaces: Force balance - Normal and shear stresses on arbitrary surfaces: Stress Tensor formulation - Stresses on deforming surfaces: Introduction to Perturbation Theory - Pulsatile flow: Analytical solution - Pulsatile flow: Analytical solution and perturbation solution for Rw 1 - Pulsatile flow: Perturbation solution for Rw 1 - Viscous heating: Apparent viscosity in a viscometer - Domain perturbation methods: Flow between wavy walls - Flow between wavy walls: Velocity profile

Introduction to stability of dynamical systems: ODEs - Stability of distributed systems (PDEs): reaction diffusion example - Stability of a reaction-diffusion system - Rayleigh-Benard convection: Physics and governing equations - Rayleigh-Benard convection: Linear stability analysis - Rayleigh Benard convection: Discussion of results - Rayleigh-Taylor heavy over light instability - Rayleigh-Taylor instability contd - Capillary jet instability: Problem formulation - Capillary jet instability: Linear stability analysis - Capillary jet instability: Rayleighs Work Principle - Tutorial Session: Solution of Assignment 4 on linear stability - Turing patterns: Instability in reaction-diffusion systems - Turing patterns: Results - Marangoni convection: Generalised tangential and normal stress boundary conditions - Marangoni convection: Stability analysis - Flow in a circular curved channel: Governing equations and scaling - Flow in a circular curved channel: Solution by regular perturbation - Stability of flow through curved channels: Problem formulation - Stability of flow through curved channels: Numerical calculation - Viscous Fingering: Darcys law - Viscous Fingering: Stability analysis - Shallow Cavity flows

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