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Module 3: Brownian motion with colloids
Introduction and motivation: measuring viscosity with colloids
One of the most significant scientific advances in the 20th century was the complete description of Brownian motion. When Einstein's theory for Brownian motion, and Stokes's solution for drag on a sphere in a viscous liquid were merged to form the StokesEinstein relation, a whole new world for scientific development opened up. Indeed, this simple equation:
$latex D = \frac{k_B T}{6 \pi \eta r} $,
where $latex D$ represents the diffusion coefficient, $latex k_B$ is Boltzmann's constant, $latex T$ is the temperature, $latex \eta$ the liquid viscosity and $latex r$ the particle radius, has been implicated in no fewer than three Nobel prizes!
In this module, we will derive this expression, and use it to measure the viscosity of a waterglycerol mixture. This will be achieved by embedding a low numerical concentration of 1.1 microndiameter colloids. To do this, we will track the motion of these particles, and measure their meansquared displacement, which grows linearly with the lagtime. The constant of proportionality is related to $latex D$.
Readings
Week 2
Helpful alternative references for this week's lecture:
Review these notes on Einstein's analysis (link here)
Review these notes on Stokes drag (link here)
Review the particlehandling information sheet (link here), and review our particle's properties (link here)
Carefully read the 1st chapter from Howard Berg's book on random walks (from last week). You should be able to relate the diffusion coefficient to the meansquare displacment to D for a given diffusive trajectory in 2D. Read chapter 1 from Howard Berg's book on random walks (link here)
Week 3
I suggest you look at the scientific literature to help develop your discussion and conclusion. Be sure to cite any references you use. Can you identify an open question? How about a question that was recently addressed using colloids that diffuse? For a point of reference, there are some cool questions related to farfrom equilibrium thermodynamics that can be approached with colloids: Spatial Crossover Between FarFromEquilibrium and NearEquilibrium Dynamics in Locally Driven Suspensions (aps.org)
Exercises
Week 1

Calculate the volume proportions of glycerol and water for the viscosity you will prepare for your assigned viscosity. The assigned viscosity is the number of your group x 10 cSt. The total target volume of water + glycerol + particles is 1 ml. Here is a link for an online calculator

calculate a `reasonable' concentration of particles for your measurement: approximately 50 particles per 1 mm x 1mm x 10 microns (!)
 write a protocol for steps 1 & 2 to carry out next week to include as an appendix to your lab reports

Download the mfiles from http://site.physics.georgetown.edu/matlab/ or, if you prefer python, download the trackpy package, located here.
Week 2
Groups for module 3
G1  Colleen Algisi  Joseph Bernaert  Andrea Leon De la Torre  Karim Azzouzi 
G2  Cassandre Pitz  Cameron Bush  Syrielle Wicki  Alexandre Mehdi Clement 
G3  Joao Barini Ramos  Dogukan Ustun  Filippo Brignolo  Abhijeet Singh 
G4  Benjamin Colety  Nathan SouryLavergne  Julien Jeandroz 
Axel Guede 
G5  Aymeric Roy  Nicolas Avellan Marin  Pierre Garrabos  Victor Solelhac 
G6  Joseph Bejjani  MiLane Bouchez  Leo Assier de Pompignan  James Ziadeh 
G7  Xinyue Wei  Lebo Molefe  Renata Osypova  Tian Yang 
Lecture notes 2021
Group Submissions
Group 4 (2022): Concentration of glycerol in the glycerol bottle.
Group 6 (2022): How to Use a Micropipette.pdf
Group 5  Matlab code to get the required volumes for a given viscosity and temperature.
Make sure to write the good path in the Matlab code 'visosity2volume.m'.
https://wiki.epfl.ch/emem2022/documents/Matlab_viscosity2volume.zip