A fluid is evaluated for its viscosity using a Brookfield...

A fluid is evaluated for its viscosity using a Brookfield viscometer. Collected data of rotational speed in rev/min and corresponding apparent viscosity in centipoises, respectively, are 20 , $7230 ; 10,12060 ; 4,25200 ; 2,39500$. Is the fluid Newtonian or non-Newtonian. Calculate the flow behavior index, $\mathrm{n}$, for this fluid.

Key Concepts

Flow Behavior Index (n) and the Power-Law Model

The flow behavior index, denoted as n, is a key parameter in the power-law model used to describe the relationship between shear stress and shear rate in non-Newtonian fluids. In this model, a value of n equal to 1 indicates Newtonian behavior, n less than 1 indicates a shear-thinning behavior, and n greater than 1 indicates a shear-thickening behavior. Calculating n provides insight into how the fluid's viscosity changes with varying shear conditions.

Brookfield Viscometer

The Brookfield viscometer is an instrument used for measuring the viscosity of a fluid by quantifying the torque necessary to rotate a spindle in the fluid at various speeds. It is especially useful for studying both Newtonian and non-Newtonian fluids, as it provides data on how the fluid’s viscosity responds to different shear rates.

Newtonian Fluids

Newtonian fluids are those that have a constant viscosity regardless of the applied shear rate. This means the shear stress is linearly proportional to the shear rate. In such fluids, changes in the flow conditions do not affect the fluid’s intrinsic viscosity, making their behavior predictable and straightforward in analysis.

Non-Newtonian Fluids

Non-Newtonian fluids exhibit a viscosity that varies with the applied shear rate or stress, meaning the relationship between shear stress and shear rate is nonlinear. These fluids may shear thin (viscosity decreases with increasing shear rate) or shear thicken (viscosity increases with increasing shear rate), which requires more complex models to describe their flow behavior.

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