The viscometer of Problem 2.67 is used to measure the...

The viscometer of Problem 2.67 is used to measure the apparent viscosity of a fluid. The data below are obtained. What kind of non-Newtonian fluid is this? Find the values of $k$ and $n$ used in Eqs. 2.16 and 2.17 in defining the apparent viscosity of a fluid. (Assume $\theta$ is 0.5 degrees.) Predict the viscosity at 90 and 100 rpm. $$\begin{array}{ccccccccc}\text { Speed (rpm) } & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \\ \mu\left(\mathbf{N} \cdot \mathbf{s} / \mathbf{m}^{2}\right) & 0.121 & 0.139 & 0.153 & 0.159 & 0.172 & 0.172 & 0.183 & 0.185 \end{array}$$

The viscometer of Problem 2.67 is used to measure the apparent viscosity of a fluid. The data below are obtained. What kind of non-Newtonian fluid is this? Find the values of $k$ and $n$ used in Eqs. 2.16 and 2.17 in defining the apparent viscosity of a fluid. (Assume $\theta$ is 0.5 degrees.) Predict the viscosity at 90 and 100 rpm.
$$\begin{array}{ccccccccc}\text { Speed (rpm) } & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \\
\mu\left(\mathbf{N} \cdot \mathbf{s} / \mathbf{m}^{2}\right) & 0.121 & 0.139 & 0.153 & 0.159 & 0.172 & 0.172 & 0.183 & 0.185
\end{array}$$

Key Concepts

Viscometry

Viscometry is the experimental measurement of a fluid's viscosity using instruments known as viscometers. These devices apply controlled shear rates or stresses to a fluid and measure its resistance to flow. Viscometry is a vital experimental technique in rheology to characterize both Newtonian and non-Newtonian fluids, providing key insights into their flow properties.

Non-Newtonian Fluids

These fluids do not have a constant viscosity; their viscosity changes with the applied shear rate or stress. Unlike Newtonian fluids where the relationship between shear stress and shear rate is linear, non?Newtonian fluids exhibit behaviors such as shear thinning (decreasing viscosity with increased shear rate) or shear thickening (increasing viscosity with increased shear rate). This concept is fundamental in rheology and is essential for understanding how various fluids respond under different flow conditions.

Apparent Viscosity

Apparent viscosity is the effective viscosity measured under specific flow conditions, particularly when the fluid exhibits non?Newtonian behavior. Unlike the intrinsic viscosity of Newtonian fluids, the apparent viscosity depends on the shear rate imposed during measurement. It provides a practical measure of a fluid's resistance to flow in experiments and industrial applications.

Power Law Model

The power law model is a common approach used to describe the flow behavior of non?Newtonian fluids. In this model, the relationship between shear stress and shear rate is expressed with two parameters: the consistency index (k) and the flow behavior index (n). This model captures both shear thinning (n < 1) and shear thickening (n > 1) behavior, making it a versatile tool for analyzing and predicting the performance of many non?Newtonian fluids.

Consistency Index (k) and Flow Behavior Index (n)

In the power law equation, the consistency index (k) represents the fluid's viscosity level at a unit shear rate, while the flow behavior index (n) indicates the degree of non?Newtonian behavior. The value of n determines whether the fluid is shear thinning (n < 1), Newtonian (n = 1), or shear thickening (n > 1). Accurately determining these parameters is crucial for understanding, predicting, and modeling the fluid's performance under different shear conditions.

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