Interfacial Fluid Mechanics

Overview

This course will introduce the student to the wonderful and beautiful world of interfacial fluid dynamics. These are fluid systems dominated by surface or interfacial tension. First half of the course will deal with many examples of fluid systems dominated by surface tension followed by a detailed discussion of the relevant governing equations and boundary conditions. Static systems – shape of a meniscus, shape of a drop, etc will also be discussed. Second half of the course will focus on specific fluid systems, viz. thin films, shape of a falling jet, coating flows, well-known instabilities like the Rayleigh-Taylor and Rayleigh-Plateau instabilities, Marangoni effects, contact lines, etc. Throughout the course, theoretical concepts will be related to real-world examples.

Syllabus 12

Week 1
- Non-dimensional numbers in interfacial flows
- Integral form of governing equations
- Boundary (Jump) conditions at a fluid-fluid interface (no surface tension)
Week 2
- On surface tension and interfacial energy
- Introduction to surface tension effects
- Boundary (Jump) conditions at a fluid-fluid interface (with surface tension) part 1
- Boundary (Jump) conditions at a fluid-fluid interface (with surface tension) part 2
- Summary of equations
Week 3
- Capillary statics shape of meniscus part 1
- Capillary statics shape of meniscus part 2
- Shape of static meniscus-Energy minimisation part 1
- Calculus of variations (a primer): Euler-Lagrange equations
- Shape of static meniscus-Energy minimisation part 2
Week 4
- Method of Lagrange multipliers
- On wetting and shape of a drop
- The Young’s Equation: Partial wetting
- Variational approach to the Young-Laplace equation part 1
- Variational approach to the Young-Laplace equation part 2
- Shape of a puddle - large/heavy drops
Week 5
- Wetting on rough and textured surface part 1
- Wetting on rough and textured surface part 2
- Wetting on rough and textured surface part 3
- Law of capillary rise
Week 6
- Dynamics of capillary rise:
- Dynamics of capillary rise: Analysis of regimes
- Forced wetting and coating flows
- More on coating & Landau-Levich equation
Week 7
- Lubrication approximation and thin films
- Free surface flows and interface conditions
- Uniform flow down an incline
- Shape of a falling jet
Week 8
- A quick tour of stability analysis
- Rayleigh-Plateau instability: Part-1
- Rayleigh-Plateau instability: Part-2
- Rayleigh-Plateau instability: Part-3
Week 9
- Rupture of thin films - part 1
- Rupture of thin films - part 2
- Rupture of thin films - Effect of van der Waals force
- Rupture of thin films - part 3
- Rupture of thin films - part 4
Week 10
- Benard-Marangoni Instability part 1
- Benard-Marangoni Instability: part-2
- Benard-Marangoni Instability: part-3
- Benard-Marangoni Instability: part-4
Week 11
- Kelvin helmholtz instability part 1
- Kelvin helmholtz instability part 2
- Kelvin helmholtz instability part 3
- Kelvin helmholtz instability part 4
Week 12
- Contact angle hysterisis
- Thin film down an incline-a contact line problem part 1
- Thin film down an incline-a contact line problem part 2
- Local flow near a moving contact line
- Modelling of moving contact line

Advantages and disadvantages

Advantages

Taught by IIT and IISc professors, and it follows the Indian university syllabus closely.
All videos and assignments are free on NPTEL and SWAYAM.
The certificate is recognised by many Indian universities for credit transfer and by GATE aspirants.
Great for GATE and semester exam preparation.
From Indian Institute of Technology Hyderabad, a well-regarded name.
Completely free.
Self-paced: start any time.
A clear syllabus (12 parts) you can see before you start.

Disadvantages

The certificate needs a proctored exam at a centre, which has a fee.
Recorded classroom lectures: thorough, but slower than made-for-online courses.
New runs start on fixed dates (January and July).
Learning is free, but the certificate costs money.

Some points apply to every course of this kind; see how we rank.

Free to learn

Free: Every video and assignment is free on NPTEL and SWAYAM. Enrol when the next run opens.
Certificate: Optional. It needs a proctored exam at a centre, which has a fee.

Before you start

Students should have completed a basic course (UG or PG level) in fluid mechanics and should be comfortable with multivariable calculusINTENDED AUDIENCE: Students in Chemical Engineering, Mechanical Engineering and Engineering Physics; Industry personnel working in the broad area of multiphase flows.