Apparent viscosities in centipoises (cP) of 4000,2500,1250,...

Apparent viscosities in centipoises (cP) of $4000,2500,1250$, and 850 were reported on a fluid at rotational speeds of $2,4,10$, and $20 \mathrm{rev} / \mathrm{min}$. This same fluid was reported to require a torque of 900 dyne $\mathrm{cm}$ to rotate a cylindrical spindle $1 \mathrm{~cm}$ in diameter and $5 \mathrm{~cm}$ high within the fluid at $20 \mathrm{rev} / \mathrm{min}$. (a) Calculate the flow behavior and consistency indices for this fluid. (b) When exhibiting an apparent viscosity of $4000 \mathrm{cP}$, what would have been the shear rate under which the measurement was made? (FIGURE CAN'T COPY)

Apparent viscosities in centipoises (cP) of $4000,2500,1250$, and 850 were reported on a fluid at rotational speeds of $2,4,10$, and $20 \mathrm{rev} / \mathrm{min}$. This same fluid was reported to require a torque of 900 dyne $\mathrm{cm}$ to rotate a cylindrical spindle $1 \mathrm{~cm}$ in diameter and $5 \mathrm{~cm}$ high within the fluid at $20 \mathrm{rev} / \mathrm{min}$.
(a) Calculate the flow behavior and consistency indices for this fluid.
(b) When exhibiting an apparent viscosity of $4000 \mathrm{cP}$, what would have been the shear rate under which the measurement was made? (FIGURE CAN'T COPY)

Key Concepts

Power Law Model

The power law model is a fundamental equation in rheology used to represent the flow behavior of non-Newtonian fluids. It describes the relationship between shear stress and shear rate through two key parameters: the consistency index and the flow behavior index.

Flow Behavior Index

This parameter, often denoted as 'n', indicates how a fluid's viscosity changes with shear rate. A value of n less than 1 typically signifies shear-thinning behavior, whereas a value greater than 1 indicates shear-thickening behavior, and n equal to 1 corresponds to Newtonian fluids.

Consistency Index

Represented by 'k' in the power law equation, the consistency index is a measure of the fluid’s inherent resistance to flow. It essentially sets the scale for the shear stress required at a given shear rate, functioning as a baseline viscosity for non-Newtonian fluids.

Shear Rate

Shear rate is the rate at which adjacent layers of a fluid move relative to each other and is usually expressed in reciprocal seconds. It is a critical variable in determining the apparent viscosity of fluids, particularly in non-Newtonian fluids where viscosity is shear-dependent.

Apparent Viscosity

Apparent viscosity refers to the effective viscosity measured under a specific shear rate. It is not a constant property for non-Newtonian fluids since their resistance to flow changes with the applied shear rate, making it a key observational parameter in rheological testing.

Spindle Viscometry

Spindle viscometry is a common experimental technique for measuring the apparent viscosity of fluids. It involves rotating a spindle within the fluid and recording the torque required, which is then used to calculate the apparent viscosity, taking into account the geometry of the spindle and the speed of rotation.

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