We are interested in comparing our computer-generated results with those
of an actual experiment. The experimental results are reported in an unpublished
paper entitled "Mirror Image Method: A simple technique for tracking 3D motion of
a colloidal particle using digital video microscopy" by C.H. Sow, T.S. Sullivan,
J. Aizenberg, J.E. Cerise, and C.A. Murray. Our purpose is to verify the method
used in the paper to determine the diffusion coefficient Do.
Initially, we altered bsumsci2.c so that its parameters matched those of
the experiments. The number of time steps taken was changed from 80,000 to
76,000, and the temperature was decreased to 264 K (The temperature was changed
so that the diffusivity of the system would equal to 6.18 x 10-13
m-13, to match the experiment). In the experiment, the cell was so
small that hydrodynamic corrections to the theory are expected to be significant.
Our simulation does not yet take into account these corrections, so we used the
artificial method of changing the temperature to match the simulated and experimental
diffusion coefficients. The radius of the colloid particle and the viscosity of
fluid remain unchanged from the 'Program Validation' page. bsumsci2.c was then
run eight times, each run creating a data set comparable to that obtained in the
experiment. Each output file contains particle displacements during a given time
interval, from one to eight video frames. The expectation is that these
displacements will be normally distributed (see the Theory
page). If we then fit these distributions to
we expect that if we plot w2 vs. τ we will get a
linear graph since w2=4Doτ. Thus we can get
Do from a fit to the slope of these plots.
The following table gives the data produced by bumsci2.c and analyzed by Origin
and a portion of the LabTalk script, slopes.ogs for eight displacement files.