2011. 10. 25

1. Transport Equations and Properties of Ideal Gases 2011. 10. 25 Teak keun, KIM 2011. 10. 25

2. Contents 4.2.1 Shear Force and Viscosity 4.2.2 Heat Diffusion 4.2.3 Mass Diffusion 4.2.4 Intermolecular Forces

3. 4. Shear Force and Viscosity 2.1 • Momentum exchange due to Bulk velocity • Above layer at plane : • Shear force = • Shear stress = = • = Figure 1 y Total flux of molecules • Below layer at plane : • Shear force = • Shear stress = = • = x

4. 4. Shear Force and Viscosity 2.1 • The net momentum flux (or Shear force) • Considering the average momentum of the particles, Therefore Where

5. 4. Shear Force and Viscosity 2.1 • Comparing above egn with the Newton’s law of shear stress, • but from more detailed calculations & experiments,

6. 4 Heat Diffusion 2.2 • The net energy flux across the plane Figure 2 T • based on the definition of specific heat Therefore x

7. 4 Mass Diffusion 2.3 From Fick’s law, For type A molecules For type B molecules Therefore, To maintain a uniform pressure Then we introduce the positive and negative flux at a certain location Gas A nA = n nB = 0 Gas B nA = 0 nB = n : Diffusion coefficient Where : Central distance : reduced mass

8. 4 Intermolecular Forces 2.4 Figure 3 repulsive attractive r • Collision between molecules dose not necessarily occur by contract. • It is a force field described by the intermolecular potential that governs the collision process • between molecules. • For a pair of molecules, • - Attractive force(Van der waals force) • : due to fluctuating dipoles in two molecules • - Repulsive force • : due to overlap of electronic orbits in atoms

9. 4 Intermolecular Forces 2.4 - The force between the molecules is modeled as below : Intermolecular potential : Empirical expression(Lennard-Jones) Where : Characteristic length(collision diameter) : Distance between ith & jth particles : Characteristic energy