4.1.2.1. What is the Continuum Model?¶

Discontinuous molecular collisions are replaced with continuous statistically averaged values, e.g.

• Pressure = Average collision force per unit area.

4.1.2.2. Why is the Continuum Model used?¶

Average fluid properties in the Continuum model are used because:

• Molecular density of fluid is large with respect to characteristic length.

• Interaction forces (potentials) are now known.

4.1.2.3. What does the Continuum Model enable?¶

Enables the conservation laws:

• Mass

• Momentum

• Energy

4.1.2.4. Where can the Continuum Model be applied?¶

Can be applied to:

• Finite volume element

• Infinitesimal differential element

4.1.2.5. What is the Knudsen number?¶

where:

• \(\lambda\) = mean free path

• \(L\) = characteristic length (e.g. pipe diameter, boundary layer thickness, shockwave thickness)

4.1.2.6. What is the Mean Free Path?¶

where:

• \(n\) = number of particles per \(m^3\) from the Boltzmann equation (\(p=nk_bT\))

• \(S\) = surface area of a spherical molecule = \(\pi d^2\)

• \(d\) = molecular diameter or collision diameter

4.1.2.7. What are the limitations of the Continuum Model?¶

The Continuum Model is valid for Knudsen Numbers \(\ll 1\) i.e.

4.1.2.8. What does the Continuum Model not permit?¶

Mass-energy conversion e.g.

• Nuclear reactions

• Relativity