Tutorial: Multi-Species Lattice Boltzmann Models and Applications

Validation and simple applications
Solvent test case: simplified transport coefficients
Hence y 3
∼ = 1 and consequently y1 ∼ = 0 and y2 ∼ = 0. Under these
assumptions, Eqs. (49, 50) reduce to
∇y 1 = −B 13 y 1 (u 1 − v) = B 13 y 1 (v − u 1 ), (56)
∇y 2 = −B 23 y 2 (u 2 − v) = B 23 y 2 (v − u 2 ), (57)
Consequently the measured diffusion resistances are given by
B ∗ 13 = 1 D ∗ 1
= ∂y 1/∂x
y 1 (v − u 1 ) , (58)
B ∗ 23 = 1 D ∗ 2
= ∂y 2/∂x
y 2 (v − u 2 ) , (59)
where, in this test, the Maxwell–Stefan model reduces to the Fick
model.
Pietro Asinari, PhD (Politecnico di Torino) Multi-Species LB Models Rome, Italy, on July 5-9, 2010 38 / 51