The Podmore Factor is a dimensionless quantity used in fluid dynamics to characterize the behavior of non-Newtonian fluids under shear stress. It was introduced by physicist Elizabeth Podmore in 1978 to quantify the degree of shear-thinning or shear-thickening behavior in complex fluids. This factor is particularly useful in industries such as polymer processing, food science, and petroleum engineering.

The Podmore Factor (P) is defined as:

\[ P = \frac{\eta_{\infty}}{\eta_0} \left(\frac{\dot{\gamma}}{\dot{\gamma}_c}\right)^{n-1} \]

Where:

- \( P \) is the Podmore Factor (dimensionless)
- \( \eta_{\infty} \) is the viscosity at infinite shear rate (Pa·s)
- \( \eta_0 \) is the zero-shear viscosity (Pa·s)
- \( \dot{\gamma} \) is the shear rate (s⁻¹)
- \( \dot{\gamma}_c \) is the critical shear rate (s⁻¹)
- \( n \) is the flow behavior index (dimensionless)

Let's calculate the Podmore Factor for a sample non-Newtonian fluid:

- Given:
- Viscosity at infinite shear rate (\( \eta_{\infty} \)) = 0.1 Pa·s
- Zero-shear viscosity (\( \eta_0 \)) = 1.0 Pa·s
- Shear rate (\( \dot{\gamma} \)) = 100 s⁻¹
- Critical shear rate (\( \dot{\gamma}_c \)) = 10 s⁻¹
- Flow behavior index (\( n \)) = 0.8

- Apply the Podmore Factor formula: \[ P = \frac{\eta_{\infty}}{\eta_0} \left(\frac{\dot{\gamma}}{\dot{\gamma}_c}\right)^{n-1} \]
- Substitute the known values: \[ P = \frac{0.1}{1.0} \left(\frac{100}{10}\right)^{0.8-1} \]
- Simplify: \[ P = 0.1 \times (10)^{-0.2} \]
- Calculate the final result: \[ P \approx 0.0631 \]

Let's visualize how the Podmore Factor relates to the viscosity profile of a non-Newtonian fluid:

This graph illustrates:

- The viscosity profile of a shear-thinning non-Newtonian fluid (blue curve)
- The zero-shear viscosity \( \eta_0 \) (green dashed line)
- The infinite-shear viscosity \( \eta_{\infty} \) (red dashed line)
- The critical shear rate \( \dot{\gamma}_c \) (yellow dashed line)
- The calculated Podmore Factor P = 0.0631, which quantifies the degree of shear-thinning behavior

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