Viscosity Measurements of Transparent Mixtures

 

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Determination of the Viscosity

 

We now have all parameters needed to extract the viscosity η from the measured correlation functions of the samples S1 to S5. This analysis can be done using the DWS RheoLab software, where the cor­relation functions are loaded and the parameters nsolv, l* and tracer particle size are edited. In the "Analysis" tab in the user interface the frequency dependent storage and loss moduli can be calculated and extracted. The viscosity η is related to the loss modulus G’' via:

 
 

\( \eta =G^{''}(\omega )/\omega , \)

 

(2)

 
 

where ω is the frequency. Figure 2 shows the obtained viscosity η using Equation 2 and G" given by the DWS RheoLab software. The results show basically no frequency dependency as expected for a Newtonian system. Moreover, the results de­mon­strate that the accessible fre­quen­cy range depends on the viscosity.  This range is shifted to high­er frequencies for lower viscosities, and can be tuned to some extent by modifying L and/or l*.

 

The measured viscosity η of the samples S1 to S5. The values are independent of the frequency as expected for a Newtonian system.

 

 Figure 2. The measured viscosity η of the samples S1 to S5. The values are independent of the frequency as expected for a Newtonian system.

 

From these results we calculate the mean values for η over the fre­quency range (see Table 1). Figure 3 shows the obtained viscosities of S1 to S5 (circles) and com­pares with tabulated values (line) for the viscosity of glycerol-water mixtures. Error bars represent the stan­dard deviation of 6 independent measurements and an estimated error in glycerol concentration of 1 wt%. The measured values are on the order of 10 % larger than the tabulated values (except S1 and S5, which are 20 % larger).

 

The constant shift towards higher values suggests a deviation of the glycerol concentration of the samples (e.g. due to erroneous glycerol concentration of the stock solution or evaporation). The experimental data is consistent with an error of about 3 wt% in the glycerol concentration.

 

Viscosity versus the glycerol concentration. The ex­peri­men­tal values (circles) correspond to S1 to S5 and the line re­pre­sents tabulated values [5].

 

Figure 3. Viscosity versus the glycerol concentration. The ex­peri­men­tal values (circles)

correspond to S1 to S5 and the line re­pre­sents tabulated values [5].

 
 

Conclusion

 

We applied DWS to initially transparent glycerol-water-mixtures. Tracer particles were added to ensure sufficient turbidity. This allowed us to access viscosities over a wide range (1:200) depending on the glycerol content of the sample. The mea­sured values are highly reproducible and independent of the frequency as expected for a Newtonian system and agree well with the literature. This de­monstrates that DWS microrheology is well suited for the quantitative cha­racte-r­ization of non-turbid systems if tracer particles are added.

 

References

[1]   D.A. Weitz, and D.J. Pine, Diffusing-Wave Spectroscopy. In Dynamic Light Scattering; Brown, W., Ed.; Oxford

       University Press: New York, 652-720 (1993).

[2]   D. Lopez-Diaz, and R. Castillo, Microrheology of solutions embedded with thread-like supramolecular structures,

       Soft Matter 7, 5926–5937 (2011).

[3]   W. M. Haynes, Handbook of Chemistry and Physics, 81st Edition, CRC press (2004).

[4]   Mie-theory based scattering calculator for suspension of spherical particles,

       http://www.lsinstruments.ch/mie_calculator/

[5]   N.E. Dorsey, The Properties of Ordinary Water Substance, New York (1940).