To test the Galilean invariance of the model a drop of radius 
lattice units was initialised at the centre of a 128 by 128 grid
with the whole fluid moving with speed 
in the x-direction and with gravity acting in the z-direction with strength g = 0.0005.
The bubble was then allowed to equilibrate for a number of different values of the relaxation time
associated with the order parameter,
.
The fluid relaxation parameter
was set to 1.1 throughout. The ratio of 
,
the drop diameter in the z-direction,
to 
, the diameter in the x-direction, is shown in figure 5-14.
When 
the radio is independent of as observed
elsewhere [38] in the absence of gravity. For other values of
the ratio is dependent on and the model is not Galilean invariant,
the further is from 
the worse the lack of
Galilean invariance is. The ratio of the two diameters appears independent of the velocity
when and is slightly smaller than unity. The
difference from unity is
due to the density gradient across the drop. This does not affect the
Galilean invariance because the free energy binary-fluid model
is Galilean invariant [38] for
all densities and the transport coefficients are independent of density. The
constant value of 
shows that this model, incorporating the gravitational interaction, is, at worst, very close to Galilean invariant provided
.
