News
- The final recorded lecture is online. All the lectures will stay online for the forseeable future.
- The password for the videos, the Murals, and Zoom can be found on Ilias
Course Description
Granular matter is an example for a physical system far from equilibrium: Dissipative collisions among the constituent particles break time reversal symmetry and a constant energy input is necessary to establish a non-equilibrium steady state. The course shall give an overview of the current understanding of the physics of granular materials comprising theory, computer simulation as well as laboratory and microgravity experiments. Beyond the current state of the art, open research questions shall be reviewed as well as implications for applications.
Topics include
- Granular Phenomena in Nature
- Sand Piles; Avalanches; Formation and Migration of Dunes, etc.
- Granular Packings
- Mechanical Properties; Critical Behavior; Non-Destructive Techniques
- Granular Fluids
- Kinetic Theory; Rheology; Computer Simulation; Experiments in Microgravity
Lecture (online only)
- Tuesday
10:00 – 11:30
New video lectures may appear around this time
- Thursday
9:15 – 10:00
We will be live on Zoom for questions and comments and later in the semester for the seminar presentations
- Lecture November 3
Welcome & Organization (pdf)
Teaser & Outline
Some numbers & Terms
Some (more) numbers & Terms
Lecture November 5
Dissipation & Friction
- Lecture November 10
Forces in Granular Packings & Stress Birefringence
Force Chains & Heterogeneities
Lecture November 12
Sound Propagation in Granular Matter
- Lecture November 17
Granular Plasticity & Mohr's Circle (featuring a beautiful & exclusive experiment)
Mohr's Circle & The Coulomb Yield Criterion
Lecture November 19
The Mohr-Coulomb Failure Analysis
- Lecture November 24
Consequences of the Failure Analysis
Angle of Repose (featuring two(!) beautiful & exclusive experiments)
Lecture November 26
The Angle of Repose in Nature
- Lecture December 1
The Janssen Effect
Hour Glass Theory
Lecture December 3
Subtleties of the Granular Constant
- Lecture December 8
The Hunt for a State Variable
The Jamming Transition
Lecture December 10
Examples of Granular Flow
- Lecture December 15
Conservation of Mass & Diffusion
The Navier-Stokes Equation
Lecture December 17
The Temperature Field
- Lecture December 22
Inelastic Collisions
The whiteboard is frozen for part of this video. Apologies for that
Solving for the postcollisional Velocities
The Inelastic Collapse
Bonus: Calculate π by colliding blocks
- Lecture Januar 12
Excursion: The Isothermal Fluid
Hydrodynamic Modes
Lecture January 14
Estimating the Viscosity & Kinetic Theory
- Lecture January 19
The Liouville Operator
The BBGKY hierarchy & the Boltzmann Equation
- Lecture January 26
Haff's Law & The Collision Frequency
The Velocity Distribution & The Homogeneous Cooling State
- Lecture February 2
Stability of the Homogeneous Cooling State
From the Boltzmann Equation to the macroscopic Balance Equations
Sheared Granular Fluids & Bagnold Scaling
- Lecture February 9
The μ(I)-rheology
(Audio only, due to a technical glitch. Please refer to the Mural for written notes)
Integration Through Transients
Lecture February 11
Deriving the the μ(I)-Law
(Apologies for the simultaneous teaching by Philip & Till towards the end)
Recommended Reading
- Research Papers (see below for possible starting points)
- N. V. Brilliantov and T. Pöschel, Kinetic Theory of Granular Gases, Oxford University Press (2004)
Lecture Notes
Seminar
The seminar takes place on Thursdays 9:15 – 10:00. The dates are according to individual agreement. Questions should be addressed to Matthias Sperl
- Januar 7
- The Brazilnut Effect
- January 21
- A Minimal Model for Dunes
- January 28
- Wet Granular Matter
- February 4
- Stress Dip under a Sand Pile
Suggested Topics
Phenomena
- Radial segregation in rotating drum http://iopscience.iop.org/article/10.1209/0295-5075/30/1/002/meta
- Axial segregation in rotating drum https://link.springer.com/article/10.1007/s10035-003-0141-y; More axial segregation https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.118001
- Granular convection https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.078002
- Dune size distribution https://link.springer.com/article/10.1007/s10035-008-0120-4 ; Dunes on Mars https://journals.aps.org/pre/abstract/10.1103/PhysRevE.76.041307
- Stress dip under sandpile https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.028001
- Frustrated Bearings https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.125.104301
Experiments
- Brazil nut effect https://journals.aps.org/pre/abstract/10.1103/PhysRevE.74.011307
- Wet granular matter https://www.nature.com/articles/nmat2117
- Granular Glass Transition https://journals.aps.org/pre/abstract/10.1103/PhysRevE.74.031308
- Measuring coefficient of restitution https://aip.scitation.org/doi/abs/10.1063/1.868282
- Force chains https://www.nature.com/articles/nature03805
- Cratering https://www.nature.com/articles/nphys583
Experimental Techniques
A variety of imaging and tracking techniques could be discussedSimulation
Theory
- Tails of the velocity distribution https://journals.aps.org/pre/abstract/10.1103/PhysRevE.65.040301
- Instability of homogeneous granular gas https://aip.scitation.org/doi/abs/10.1063/1.858716
- Coefficient of restitution for viscoelastic particles https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.051304
- Modified Fouriers law https://pubs.acs.org/doi/abs/10.1021/jp0736490
- Inelastic collapse https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.1142