Introduction
The viscosity of a fluid is related to the quantitative index of the tendency of the fluid to resist flow. In the general case of passive particle motion, there is a mutual resistance realized through frictional forces directed tangentially to the surfaces of the moving layers. It estimates the distribution of stresses in the fluid caused by the applied shear stress. For example, a flat Couette flow is the primary demonstration of fluid flow.
Couette flow, as shown in Figure 1, depicts fluid flow through two plates, one of which moves tangentially to the other, which is static. The dynamics of the plates create the conditions for shear displacement, which ultimately causes the fluid to flow. Also, the speed of the upper plate depends on the viscosity of the fluid: thus, the greater the viscosity of the fluid, the slower it will move. The directional motion of particles can also be considered in terms of infinitesimal transverse rings: the flow of molecules or atoms passing through such hypothetical rings, the necessary force to overcome resistance through the ring area will be calculated as follows:
The above equation is formulated as Newton’s law for viscous flow. The coefficient η in [1] reflects the viscosity of a particular substance or mixture, the inverse of which is called fluidity: F = 1/η
It is noteworthy that if an ideal mixture of liquids is used as the substance under study, the resulting viscosity can be determined by the Kendall’s equation:
At the same time,
In addition, the temperature can have a significant effect on the amount of viscosity of a liquid. In liquids, viscosity decreases with increasing temperature due to the larger space between the molecules. This is clearly seen in [6], where A is a constant, and Eη is the activation energy, in which temperature demonstrates an inverse proportionality with the viscosity coefficient:
η = A exp (Eη/RT)
Reagents
- Toluene
- p-Xylene
- Methanol
- HPLC Grade Acetone
Procedure
- prepare all the for 10mL of Methanol/H2O solutions.
- Set up a water bath from a 2L beaker on a hot plate.
- Then, a viscometer must be underwater beneath its upper mark.
- Fill the beaker with water, then warm the water up to 25oC.
- Use the viscometer to do the measurements for the time it takes for a 3.00mL distilled water which is the reference liquid sample to travel from the top calibration mark until it reaches the bottom calibration mark.
- Repeat those steps three times and the measurements must be within +/- 0.2s.
- Follow the same steps for the rest of the solutions, then record all the data in a table as stated in the Table 1 bellow.
- Do the same thing for the 10mL of Toluene/p-Xylene solutions and then record the data in a separate table as stated in table 2 bellow.
- Follow the same procedure for pure p-xylene, but this time the temperature changes and the solution is the same for all trials, at 25oC, 35oC, 45oC, 55oC, and 65oC.
- Repeat those steps three times and the measurements must be within +/- 0.2s, record all data in a sperate table as well.
Note: In the case of switching between solutions, the viscometer should be fully rinse with acetone and let air dry.
Data measurements
Table one for 10mL of Methanol with H2O:
Table two for 10mL of Toluene with p-Xylene:
Table three trials for Water/Methanol Solutions
Table four trials for Toluene/ p-xylene Solutions
Table five trials for Temperature Dependence: 100% p-xylene Solution
Data Analysis
For a binary mixture consisting of toluene and p-xylene, time values were measured using a viscometer. Based on the calculations in MS Excel, the data shown in Table 6 were obtained. A significant result evident from this table shows the relative constancy of the viscosity for all six solutions. Consequently, it can be concluded that the Toluene/p-Xylene mixture is ideal because the components have equivalent viscosity both in their pure form and as a mixture. However, one can see a tendency that the fluidity time tended to fall slowly with increasing concentration, which is consistent with the previous conclusion but shows a smooth shift toward the ideal time for a particular pure component. It is also noteworthy that the theoretical and practical fluidity values turn out to be very close, which further confirms the ideality of this binary system. Consequently, the Toluene and p-Xylene molecules hardly interact with each other to form complexes.
Table 6. Experimental viscosity and fluidity data for Toluene/p-Xylene mixture.
Sample #1 calculations for η (cP) using equation #4:
Sample #2 calculation for fluidity using equation Ln(η) [3]
Sample #2 calculation for fluidity using equation #2:
Sample#3 calculation for fluidity 0% using equation #5:
Similar results can be obtained for a mixture of methyl alcohol and water. Analysis of Table 7 shows that the average viscosity for different alcohol concentrations differed significantly. The critical conclusion is predictable: when the substances are mixed, the viscosity increases, and the fluidity decreases compared to the exact data for the pure components of the binary mixture. The patterns found for the fluidity time relationship (reaches a maximum at equivalent concentration and then decreases) show that the intermolecular forces in a non-ideal binary mixture are significantly greater than in the individual components of this mixture. The non-idealness of the mixture is also confirmed by examining both forms of fluidity: they are neither equal nor similar. A probable reason for this phenomenon may be the morphology of the molecules: there are hydrogen bonds within methanol that can bind water, forming complexes.
Table 7. Experimental viscosity and fluidity data for the Methanol/H2O mixture.
Sample #4 calculations for η (cP) using equation #4:
Sample #2 calculation for fluidity using equation Ln(η) [3]
Sample#5 calculation for fluidity 0% using equation #2:
Sample#6 calculation for fluidity 0% using equation #5:
Table 8. Data on the relationship between yield time and temperature for p-Xylene.
Sample #7 calculation for viscosity at 298.15K (25C):
Regarding the relationship between viscosity and temperature stated in the introduction, conclusions can be drawn based on the data in Table 8 and Figure 2. It can be seen that as the temperature increases, the overall flow time decreases. In terms of Figure 2, this relationship is described by linear regression with high accuracy (R2=0.9916), which means that the relationship between the variables can indeed be considered as inverse linear.
Moreover, based on equation [7] and the linear regression equation in Figure 2, it becomes possible to find the activation energy. The activation energy required to initiate the p-Xylene reaction was calculated according to the following scheme:
Reference to Massoudi, (2016) shows that the reference value of the activation energy for the substance is 8.3920 kJmol-1. In this case, the error percentage is:
Therefore, this experiment is considered successful because those values are very similar to one another.
Conclusion
To summarize, the fluidity time calculation method used in this experiment is workable for measuring the viscosity of solutions and binary mixtures and determining their ideality. It was shown that the Toluene/p-Xylene mixture could be regarded as ideal, whereas in Methanol/H2O, the intermolecular bonds tend to form aggregates. In addition, one of the present work results was a test of the relationship between viscosity and temperature: it was found that an increase in temperature leads to a decrease in the flow time and thus to a decrease in viscosity. This relationship is perfectly described by linear regression with minimal error (R2=0.9977). Finally, it was confirmed that it was possible to calculate the activation energy using the above method, which was close to the reference value.
References
Massoudi, M., & Tran, P. X. (2016). The Couette–Poiseuille flow of a suspension modelled as a modified third-grade fluid. Archive of Applied Mechanics, 86(5), 921-932.
Viscosity of Liquids, CHEM 481 2021, provided by O. Stewart.