## Objectives

This course is a general introduction to fluid mechanics for physicists and chemists. It aims to provide the fundamental ideas for an understanding of flow dynamics and of mass and heat transfer. The focus is on appropriate orders of magnitude, and on the judicious use of dimensionless physical parameters and law of scale reasoning.The course is completed by 4 sessions of exercises (kinematics, lubrication flows, potential flows, boundary layers) and by 2 sessions of tutoring (experimental micro-project).

This course is also associated to experimental classes (typically 4 experiments selected among a list of 11 experiments).

## Syllabus

- What is a fluid?

- in the microscopic state

- link with macroscopic: ρ, η, E, γ

- the Maxwell model

- in the microscopic state
- How to describe its movement?

- conservation laws (general)

- phenomological laws (specific: Newtonian and other)

- Navier-Stokes equation and Reynolds number

- conservation laws (general)
- Under which conditions is it unable to flow?

- Archimedes and atmosphere

- The sea is flat, but not droplets

- Archimedes and atmosphere
- What happens if I shake it?

- speed of sound

- surface wave

- Rayleigh-Taylor instability

- speed of sound
- How does honey flow?

- Flow at low Reynolds number

- Low Reynolds number propulsion

- Flow at low Reynolds number
- How does a superfluid flow?

- perfect fluid flow

- propulsion in a perfect fluid

- perfect fluid flow
- What happens if I shake it?

- waves, ripples and furrows

- Kelvin-Helmholtz.instability

- welcome to the world of the vortex!

- waves, ripples and furrows
- How to planes fly?

- boundary layer

- boundary layer separation

- What lies behind Kutta and Joukowski

- boundary layer
- How does water flow? : POORLY!

- Instability cascade

- Vortex cascade: Homogeneous-isotropic turbulence

- Instability cascade
- Faster than the speed of sound?

- compressible flows

- Analogy with shallow waster flows

- compressible flows
- Fluid and Elasticity coupling

- Origami, water lilies and cobwebs

- flagella

- flags and wheat fields

- Origami, water lilies and cobwebs

## Preceptorship

- Law of scale analyses

- Animal propulsion

- Avalanches and gravity currents

- Fluid/elastic structure interaction

- Understanding and interpreting various flows using videos

## Laboratory sessions

We illustrate the following thematics

- Sedimentation / fluidisation :

- Fluidized bed: fluidization of of a bed of particles with an upward flow, then sedimentation (low Reynolds number).

- Beads and bubbles : sedimentation (high Reynolds number), bubble rise in a large bath or in confined environments, ring bubbles.

- Fluidized bed: fluidization of of a bed of particles with an upward flow, then sedimentation (low Reynolds number).
- Flow fields :

- Thermal wake: monitoring of a thermal wake through PIV in a convective flow.

- Waves : propagation of waves along a bath, dispersion relation, attenuation, visualization of the flow field.

- Leaves under wind: monitoring of the velocity field behind an obstacle through hot wire anenometry. Evolution of the drag coefficient of an object deformed by the flow.

- Wake behind a blunt obstacle (experiment): monitoring of the velocity field through laser Doppler anenometry. Measurment of the instabilty threshold and of the oscillating frequency of the flow beyond the threshold.

- Wake behind a blunt obstacle (numerics): numerical simulation with finite elements (FreeFem++ software) de l'instabilité du sillage d'un écoulement derrière un obstacle. Taux de croissance, amplitude et fréquence des oscillation.

- Thermal wake: monitoring of a thermal wake through PIV in a convective flow.
- Interfaces, wetting, tensiometry:

- Capillarity: wicking, viscous drainage, coating.

- Impacts : study of the impact of water droplets through high speed imaging.

- Diffusion and viscosity: dispersion of a dye in a microfluidic flow, measurement of an unknown viscosity with a microfluidic device.

- Capillarity: wicking, viscous drainage, coating.
- Granular matter :

- Avalanches : study of the flow of a dry granular medium on an inclined plane. Critical avalenche angles and relation between thickness and the velocity of the avalanche.

**Requirements :**basic notions in fluid mechanics: perfect fluids, viscous flows, notion of Reynolds number, scaling law approach

**Evaluation mechanism :**written exam (lectures) 2 reports randomly selected and lab notebook (lab teaching)

**Last Modification :**Friday 28 April 2017