A `circular' bubble, of radius 32 grid points, was initialised at the centre of a 128 by 128 grid. The fluid density was set at 
everywhere
with 
inside the bubble and 
elsewhere.
The fluids were then allowed to evolve
for 10,000 time-steps. The density and the order parameter
were measured along a line through the centre of the inner fluid parallel
to the y-axis (perpendicular to 
) and are shown
in figures 4-3 and 4-4 respectively at selected times.
Figure 4-3: The density 
as a function of r the distance
from the edge of the grid. The density is plotted
along a line through the centre of the inner
fluid parallel to the y-axis (perpendicular to 
.
Figure 4-4: The order parameter 
plotted against
r the distance
from the edge of the grid. The order parameter is plotted
along a line through the centre of the inner
fluid parallel to the y-axis (perpendicular to .
The relaxation times used were 
and 
. The relaxation time 
is 
which is the value
at which the model is Galilean invariant [9, 38].
This initialisation differs from the final state in
four ways. The order parameter has changed from its
initial value of 
to its expected value of 0.50.
The initially interface width of one lattice unit has increased to
about ten lattice units. The shape of the inner fluid has changed
from an ellipse with semi-major and semi-minor axis of 32 lu and 
lu to a circle with radius 
lu. The final density is
slightly larger in the inner fluid than the outer fluid.
The small change in the density occurs everywhere within the first 1,000
time-steps with only a small change in the shape of the interface occurring at subsequent times. The larger
change in the order parameter takes 10,000 time-steps
to reach the areas furthest from the interface.
The movement of the inner fluid from an ellipse to a circle is achieved within the 10,000 time steps.