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: Rayleigh’s 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: Darcy’s law – Viscous Fingering: Stability analysis – Shallow Cavity flows

Other Resources

Course Curriculum

Introduction and overview of the course: Multiphase flows Details 52:7
Stratified flow in a micro channel: Velocity profiles Details 49:32
Stratified flow in a micro channel: Effects of physical parameters Details 47:34
Flow regimes in microchannels: Modeling and Experiments Details 12:53
Scaling Analysis: Introduction Details 0:45
Scaling Analysis: Worked Examples Details 40:47
Interfacial tension and its role in Multiphase flows Details 48:38
Eulerian and Lagrangian approaches Details 44:20
Reynolds Transport Theorem and the Equation of Continuity Details 48:27
Derivation of Navier-Stokes equation Details 47:42
Vector operations in general orthogonal coordinates: Grad., Div., Lapacian Details 51:49
Normal and shear stresses on arbitrary surfaces: Force balance Details 50:11
Normal and shear stresses on arbitrary surfaces: Stress Tensor formulation Details 54:55
Stresses on deforming surfaces: Introduction to Perturbation Theory Details 50:8
Pulsatile flow: Analytical solution Details 54:59
Pulsatile flow: Analytical solution and perturbation solution for Rw 1 Details 48:57
Pulsatile flow: Perturbation solution for Rw 1 Details 48:49
Viscous heating: Apparent viscosity in a viscometer Details 55:29
Domain perturbation methods: Flow between wavy walls Details 47:54
Flow between wavy walls: Velocity profile Details 46:13
Introduction to stability of dynamical systems: ODEs Details 58:18
Stability of distributed systems (PDEs): reaction diffusion example Details 49:55
Stability of a reaction-diffusion system contd Details 43:31
Rayleigh-Benard convection: Physics and governing equations Details 48:55
Rayleigh-Benard convection: Linear stability analysis part 1 Details 49:23
Rayleigh-Benard convection: Linear stability analysis part 2 Details 48:57
Rayleigh-Benard convection: Linear stability analysis part 3 Details 50:6
Rayleigh Benard convection: Discussion of results Details 49:55
Rayleigh-Taylor ‘heavy over light’ instability Details 50:54
Rayleigh-Taylor instability contd Details 48:24
Capillary jet instability: Problem formulation Details 51:48
Capillary jet instability: Linear stability analysis Details 48:11
Capillary jet instability: Rayleigh’s Work Principle Details 44:35
Tutorial Session: Solution of Assignment 4 on linear stability Details 55:3
Turing patterns: Instability in reaction-diffusion systems Details 50:18
Turing patterns: Results Details 42:52
Marangoni convection: Generalised tangential and normal stress boundary conditions Details 51:26
Marangoni convection: Stability analysis Details 41:4
Flow in a circular curved channel: Governing equations and scaling Details 49:21
Flow in a circular curved channel: Solution by regular perturbation Details 40:46
Stability of flow through curved channels: Problem formulation Details 51:10
Stability of flow through curved channels: Numerical calculation Details 37:27
Viscous Fingering: Darcy’s law Details 48:14
Viscous Fingering: Stability analysis Details 52:57
Shallow Cavity flows Details 47:28

This course is delivered by NPTEL, is part of IIT Madras online courses.

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