Assignment 5, Part 1: viscosity and diffusivity in glycerol-water mixtures

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20.309: Biological Instrumentation and Measurement

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This is Part 1 of Assignment 5.

Estimating the diffusion coefficient by tracking suspended microspheres

Imaging chamber for fluorescent microspheres diffusing in water:glycerol mixtures

1. Track some 0.86μm Pink 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: Ensure that the focal plane you choose to image is not near the coverslip or the slide. If some particles don't move or hardly move at all, it is likely that they are stuck to the coverslip. Adjust the focus so that you are viewing a plane near the middle of the sample. (A good way to do this is to focus on the top and bottom of the sample chamber and then split the difference.)
Tip 2: Each full frame of the full camera field of view takes up almost 2.5 MB of memory, so movies can get large very fast. Try to limit image data variables to a reasonable size by keeping the length of the movie short or limiting the Region of Interest (ROI) to a fraction of the full field of view.( A full-field, three minute move takes up about 4 GB, which is certain to push MATLAB over the edge.)

2. Record movies of beads diffusing in the two glycerol solutions and use your newly developed code to estimate the diffusion coefficient of each sample.

  • Consider how many particles you should track and for how long. What is the uncertainty in your estimate?
  • Calculate the viscosity of the solution and estimate the glycerin/water weight ratio of each solution. (Hint: what is the relationship between diffusion coefficient and viscosity? You may find that this chart is a useful reference.)


Turn in for the viscosity part:

  1. Include a snapshot of the 0.86 μm fluorescent beads monitored.
  2. Document the samples you prepared and how you captured images (camera settings including frame acquisition rate, number of frames, number of particles in the region of interest, choice of sample plane, etc)
  3. Plot two or more example bead trajectories for each of the glycerin samples. (Hint: If you subtract the initial position from each trajectory, then you can plot multiple trajectories on a single set of axes.)
  4. Plot the average MSD vs τ results for the two glycerin samples (A and B); use log-log axes. Use the minimum number of axes that can convey your results clearly.
  5. Include a table of the diffusion coefficient, viscosity and glycerin/water ratio for each of the samples (A and B)
  6. How do your viscosity calculations compare to your expectations? (This chart is a useful reference.)
  7. Include a thorough discussion of error sources and your approaches to minimize them. It may be helpful to list out the error sources in a table, including a category for the error source, type of error (random, systematic, fundamental, technical, etc.), the magnitude of the error, and a description and way to minimize each one.


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