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 0.84μm Pink Spherotech polystyrene beads in water-glycerin mixtures (Samples A and B contain 80% and 85% 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 factors determine the uncertainty and accuracy of your estimate?

  1. Include a snapshot of the 0.84 μm fluorescent beads monitored.
  2. Discuss any important considerations you made when preparing your samples and capturing your images. For example, how did you choose your exposure time, frame rate, number of particles in the region of interest, choice of sample plane, etc?
  3. Make an x-y plot of two or more example bead trajectories for each of the glycerin samples. (Hint: Subtract the initial position from each trajectory to 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 measured glycerin/water ratio for each of the samples (A and B)
  6. Is the viscosity you measured close to the theoretical value predicted by this website?
  7. List several error sources present in your measurement of the MSD of diffusing particles. Classify each error as random or systematic, and technical or fundamental. Which sources do you think most significantly affect your measured diffusion coefficient? Note that we will quantify the magnitude of these errors in the next assignment.


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