Question

Newtonian) The following shear stress-shear rate data were obtained on a 6 wt% solution of sodium cellulose sulfate polymer in water at 24.5 °C. Shear rate (s) 0.23 Shear stress (Pa) Shear rate (s) Shear stress (Pa) 5.5 5.8 52 0.29 7 7.2 57 0.36 8.5 9.1 63 0.46 11.5 11 69 0.58 13 14.5 74 0.72 15 18 80 0.91 17.5 23 85 15 20.5 29 92 1.45 24 36 100 108 1.8 27.5 46 2.3 31.5 58 113 20 2.9 36 72 3.6 41 91 130 4.6 46 log-log scale Plot the viscosity-shear rate function on a a. b. Is there a shear rate range in which the fluid appears to be Newtonian? Is there a range in which the viscosity follows a power law relation? If so determine the power law constants and state what type of non-Newtonian fluid it is The polymer solution is to be used in a process at a shear rate of 5000 s. Estimate the viscosity under these conditions from the available data. Do you think that the estimated c. d. value is reliable?

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Answer 1

Part a.

The plot of Log(shear stress) vs Log(shear rate) can be drawn as follows.

Log(Shear stress) 1.5 2.0 0.5 1.0 Log(Shear rate)

The equation of the plot: Log(Shear stress) = 0.50697*Log(Shear rate) + 1.24333

Part d.

If shear rate = 5000 s^-1, Log(Shear rate) = Log(5000) = 3.69897

i.e. Log(Shear stress) = 0.50697*3.69897 + 1.24333

i.e. Log(Shear stress) = 3.1186

Hence, the shear stress or viscosity = 1314.0044 Pa