Question

The mean free path of the gas molecule is $10^{-6}$ mm, while the pore size of the rock is $10^{-3}$ mm. Which of the following statements is TRUE?

• A. The Knudsen number is $10^{3}$ and the continuum principle would be applicable
• B. The Knudsen number is $10^{-3}$ and the continuum principle would be applicable
• C. The Knudsen number is $10^{3}$ and the continuum principle would not be applicable
• D. The Knudsen number is $10^{-3}$ and the continuum principle would not be applicable

Hint:

Always compare mean free path to pore size. A very small Knudsen number ($< 0.01$) implies continuum mechanics is valid, while large values indicate slip or free-molecular flow regimes.

Answer 1

The Correct Option is B

- The Knudsen number (Kn) is defined as the ratio of the mean free path of gas molecules ($\lambda$) to a characteristic length scale (L), here taken as the pore size of the rock.
\[ Kn = \frac{\lambda}{L} \] - Given: $\lambda = 10^{-6}$ mm, $L = 10^{-3}$ mm.
\[ Kn = \frac{10^{-6}}{10^{-3}} = 10^{-3} \] - Interpretation:
- If $Kn<0.01$, the continuum flow regime is valid, and the continuum principle can be applied.
- Here $Kn = 10^{-3}$, which is well within the continuum regime.
- Therefore, the correct statement is that the Knudsen number is $10^{-3}$ and the continuum principle is applicable.