3) Results

Figure 2: (Original figure) Sample of intensity data taken.

This intensity data collected, shown in figure 2, resembles noise but in fact contains information about the motion of the particles within the suspension. This information is extracted by comparing the data to itself after a short time delay, using the equation:

The results from this equation were plotted, which showed that the ACF decays exponentially.

Figure 3: (Original figure) ACF results that correspond to the sample of collected intensity data in figure 1.

This exponential decay was then modeled using the equation:

where is a corrective coefficient that is determined by the size of the area being observed by the photodiode, is the scattering vector and is time. The ACF calculated is plotted on a semi-log plot of base e for ease of analysis since in the semi-log plot the analysis involves a linear fit, not an exponential. This transforms the previous equation into the following form:

Thus the slope of the fit line gives the value of 𝐷 and the intercept gives 𝑙𝑛𝛽, which in turn

gives the number of coherence areas analyzed.

Table 1 shown below depicts the results from the four different glycerol-water samples. The uncertainty in the expected viscosity was because the concentration of the glycerol-water solutions was only known within 1%.

Table 1

It is clear that the measured viscosities do not match up with the expected viscosities, even after considering the uncertainties. The chi plot lends some insight into why this was so. The chi plot from one of the trials is displayed below in figure 4.

Figure 4: The chi plot

The approximate shape of this plot was common to all data sets and this provides information that explains the discrepancy between the measured viscosities and the expected viscosities. The shape of this plot suggests that there is more than the expected linear dependence involved. This is a result of the background noise that was present during each trial. Figure 5 below shows the ACF calculated for a glycerol-water sample with no spheres in it.

Figure 5: Calculated ACF of glycerol-water sample with no spheres in it.

This plot shows clearly that there was noise present during collection of data. There were two kinds of noise present. One was a fast-decaying noise and the other was a sine wave with a frequency of about 60Hz. Attempts were made to electronically shield the photodiode from this background noise and while we were able to decrease the amplitude of the noise, we were not able to eradicate it completely.