In order to investigate the effect of the collision term (4.11) in the macroscopic fluid motion, consider

Question:

In order to investigate the effect of the collision term (4.11) in the macroscopic fluid motion, consider a uniform mixture of different fluids (all spatial derivatives vanish), with no external forces, so that the equation of motion for the a species reduces to

Solve this equation to determine u(t), for a two-fluid mixture and for a three-fluid mixture (in the case of the three-fluid mixture it is convenient to use Laplace transforms). Notice that, at equilibrium (when du_α/dt = 0), the velocities of all species must be the same.

Equation