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Multiphase Flows: Analytical Solutions and Stability Analysis

Multiphase Flows: Analytical Solutions and Stability Analysis. Instructor: Prof. S. Pushpavanam, Department of Chemical Engineering, IIT Madras. This course concentrates on obtaining analytical and semi-analytical solutions to multiphase flow problems. The emphasis is on using a very fundamental approach: equations of conservation of mass, momentum and energy without any empiricism. The focus is on getting approximate solutions using perturbation theory, and analysing stability of systems using linear stability analysis. This will help prepare students for doing research in these areas. (from nptel.ac.in)

Lecture 32 - Turing Patterns: Instability in Reaction-Diffusion Systems


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Lecture 01 - Introduction and Overview of the Course: Multiphase Flows
Lecture 02 - Stratified Flow in a Microchannel: Velocity Profile
Lecture 03A - Stratified Flow in a Microchannel: Effects of Physical Parameters
Lecture 03B - Flow Regimes in Microchannels: Modeling and Experiments
Lecture 04 - Scaling Analysis: Introduction
Lecture 05 - Scaling Analysis: Worked Examples
Lecture 06 - Interfacial Tension and its Role in Multiphase Flows
Lecture 07 - Eulerian and Lagrangian Approaches
Lecture 08 - Reynolds Transport Theorem and the Equation of Continuity
Lecture 09 - Derivation of Navier-Stokes Equation
Lecture 10 - Vector Operations in General Orthogonal Coordinates: Gradient, Divergence, Laplacian
Lecture 11 - Normal and Shear Stresses on Arbitrary Surfaces: Force Balance
Lecture 12 - Normal and Shear Stresses on Arbitrary Surfaces: Stress Tensor Formulation
Lecture 13 - Stresses on Deforming Surfaces: Introduction to Perturbation Theory
Lecture 14 - Pulsatile Flow: Analytical Solution
Lecture 15 - Pulsatile Flow: Analytical Solution and Perturbation Solution for Rw≪1
Lecture 16 - Pulsatile Flow: Perturbation Solution for Rw≫1
Lecture 17 - Viscous Heating: Apparent Viscosity in a Viscometer
Lecture 18 - Domain Perturbation Methods: Flow between Wavy Walls
Lecture 19 - Flow between Wavy Walls: Velocity Profile
Lecture 20 - Introduction to Stability of Dynamical Systems: ODEs
Lecture 21 - Stability of Distributed Systems (PDEs): Reaction Diffusion Example
Lecture 22 - Stability of a Reaction-Diffusion System (cont.)
Lecture 23 - Rayleigh-Benard Convection: Physics and Governing Equations
Lecture 24A - Rayleigh-Benard Convection: Linear Stability Analysis 1
Lecture 24B - Rayleigh-Benard Convection: Linear Stability Analysis 2
Lecture 24C - Rayleigh-Benard Convection: Linear Stability Analysis 3
Lecture 25 - Rayleigh-Benard Convection: Discussion of Results
Lecture 26 - Rayleigh-Taylor Heavy over Light Instability
Lecture 27 - Rayleigh-Taylor Instability (cont.)
Lecture 28 - Capillary Jet Instability: Problem Formulation
Lecture 29 - Capillary Jet Instability: Linear Stability Analysis
Lecture 30 - Capillary Jet Instability: Rayleigh's Work Principle
Lecture 31 - Tutorial Session: Solution of Assignment 4 on Linear Stability
Lecture 32 - Turing Patterns: Instability in Reaction-Diffusion Systems
Lecture 33 - Turing Patterns: Results
Lecture 34 - Marangoni Convection: Generalised Tangential and Normal Stress Boundary Conditions
Lecture 35 - Marangoni Convection: Stability Analysis
Lecture 36 - Flow in a Circular Curved Channel: Governing Equations and Scaling
Lecture 37 - Flow in a Circular Curved Channel: Solution by Regular Perturbation
Lecture 38 - Stability of Flow through Curved Channels: Problem Formulation
Lecture 39 - Stability of Flow through Curved Channels: Numerical Calculation
Lecture 40 - Viscous Fingering: Darcy's Law
Lecture 41 - Viscous Fingering: Stability Analysis
Lecture 42 - Shallow Cavity Flows