Fluids for which the shearing stress, τ, is not linearly related to the rate of shearing strain,

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Fluids for which the shearing stress, τ, is not linearly...

Fluids for which the shearing stress, $\tau,$ is not linearly related to the rate of shearing strain, $\dot{\gamma},$ are designated as nonNewtonian fluids. Such fluids are commonplace and can exhibit unusual behavior, as shown in Video V1.6. Some experimental data obtained for a particular non-Newtonian fluid at $80^{\circ} \mathrm{F}$ are shown below. Plot these data and fit a second-order polynomial to the data using a suitable graphing program. What is the apparent viscosity of this fluid when the rate of shearing strain is $70 \mathrm{s}^{-1}$ ? Is this apparent viscosity larger or smaller than that for water at the same temperature?

Fluids for which the shearing stress, $\tau,$ is not linearly related to the rate of shearing strain, $\dot{\gamma},$ are designated as nonNewtonian fluids. Such fluids are commonplace and can exhibit unusual behavior, as shown in Video V1.6. Some experimental data obtained for a particular non-Newtonian fluid at $80^{\circ} \mathrm{F}$ are shown below.
Plot these data and fit a second-order polynomial to the data using a suitable graphing program. What is the apparent viscosity of this fluid when the rate of shearing strain is $70 \mathrm{s}^{-1}$ ? Is this apparent viscosity larger or smaller than that for water at the same temperature?

Key Concepts

Non-Newtonian Fluids

Non-Newtonian fluids are those fluids in which the relationship between shear stress and shear rate is not linear. Unlike Newtonian fluids, where viscosity remains constant regardless of the applied shear rate, non-Newtonian fluids exhibit a viscosity that changes with the rate of shearing, leading to complex flow behavior that can vary under different conditions.

Apparent Viscosity

Apparent viscosity is a measure defined as the ratio of the shear stress to the shear rate at a particular point, representing an effective viscosity for fluids whose viscosity changes with shear rate. In non-Newtonian fluids, this value depends on the rate of shearing strain, unlike in Newtonian fluids where it remains constant.

Shear Rate

The shear rate, or rate of shearing strain, quantifies the velocity gradient perpendicular to the direction of shear. It is a key parameter influencing the viscous behavior of fluids, particularly in non-Newtonian fluids where the viscosity is a function of the shear rate.

Polynomial Regression Analysis

Polynomial regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a polynomial equation. In the context of non-Newtonian fluids, a second-order polynomial can be employed to capture the non-linear relationship between shear stress and shear rate from experimental data.

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