Difference between revisions of "Assignment 5, Part 1: viscosity and diffusivity in glycerol-water mixtures"
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2. Estimate the diffusion coefficient of these samples: MSD = <math>\left \langle {\left | \vec r(t+\tau)-\vec r(t) \right \vert}^2 \right \rangle=2Dd\tau</math>, where <i>r</i>(<i>t</i>) = position, <i>d</i> = number of dimensions, <i>D</i> = diffusion coefficient, and <math>\tau</math>= time interval. <br> | 2. Estimate the diffusion coefficient of these samples: MSD = <math>\left \langle {\left | \vec r(t+\tau)-\vec r(t) \right \vert}^2 \right \rangle=2Dd\tau</math>, where <i>r</i>(<i>t</i>) = position, <i>d</i> = number of dimensions, <i>D</i> = diffusion coefficient, and <math>\tau</math>= time interval. <br> | ||
:* '''Consider how many particles you should track and for how long. What is the uncertainty in your estimate?''' | :* '''Consider how many particles you should track and for how long. What is the uncertainty in your estimate?''' | ||
− | :* | + | :* From the viscosity calculation, estimate the glycerin/water weight ratio. (This [https://dl.dropboxusercontent.com/u/12957607/Viscosity%20of%20Aqueous%20Glycerine%20Solutions.pdf chart] is a useful reference. If that link doesn't work try [http://profs.engineering.uottawa.ca/biofluid/files/2011/08/viscosity-of-aqueous-glycerine-solutions.pdf this one].) |
{{Template:Assignment Turn In|message=for the viscosity part: | {{Template:Assignment Turn In|message=for the viscosity part: |
Revision as of 22:10, 14 August 2017
This is Part 1 of Assignment 5.
Estimating the diffusion coefficient by tracking suspended microspheres
1. Track some 0.84μm Nile Red Spherotech polystyrene beads in water-glycerin mixtures (Samples A and B contain 30% and 50% glycerin, respectively).
- Notes: Fluorescent microspheres have been mixed for you by the instructors into water-glycerin solutions A and B. (a) Vortex the stock Falcon tube, and then (b) transfer the bead suspension into its imaging chamber (consisting of a microscope slide, double-sided tape delimiting a 2-mm channel, and a 22mm x 40mm No. 1.5 coverslip, and sealed at both ends nail polish).
- Tip 1: Do not choose to monitor particles that remain stably in focus: these are likely to be 'sitting on the coverslip' and their motion will not be representative of diffusion in the viscous water-glycerol fluid.
- Tip 2: Limit the ROI to a region with only 3 or 4 particles. Long movies with the whole field of view is a sure way to make MATLAB complain.
2. Estimate the diffusion coefficient of these samples: MSD = $ \left \langle {\left | \vec r(t+\tau)-\vec r(t) \right \vert}^2 \right \rangle=2Dd\tau $, where r(t) = position, d = number of dimensions, D = diffusion coefficient, and $ \tau $= time interval.
for the viscosity part:
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