Chapman-Enskog Analysis (Ladd's Numerical Simulations of Particulate Suspensions & Latt's Hydrodynamic Limits)

Hi, all!
I’m having a hard time with the Chapman-Enskog analysis, at the point where you use the Euler Equations to rewrite time derivatives as spatial derivatives. In particular, I am reading Ladd’s 1994 Paper, where in Eq. (2.27) the time derivative needs to be eliminated from the following expression

I cannot seem to achieve this.

Similarly, Latt’s Thesis deals with the same term [quote=Latt]
d[sub]t[/sub] ( rho u u ),
in Eq. (2.64) on page 25 and somehow eliminates the time derivative.
Again, I cannot see why this equation holds.

In a paper by Hou et al. '94, I have now found the same trick used explicitly. So, problem solved.