An immiscible binary fluid was initialised with the two fluids separated
by a horizontal interface. The upper fluid has 
negative.
Gravity was applied to both fluids with
strength 
using method (2),
where 
.
At
temperature T=0.5 we have seen that 
in the
absence of gravity. Figure 5-11
Figure 5-11: The modulus of the
ratio 
as a function of
depth when gravity is applied to a binary fluid with a horizontal interface between the fluids. Gravity was applied with 
and 
.
shows the value of the modulus of the
ratio at different depths for the
immiscible fluid when and . At the interface
the value of 
is different from 2.0 by no more than 4%,
away from
the interface the ratio appears constant with depth, and hence also with
density.
Thus the value of g in both fluids is given by
Figure: The density as a function of depth
for case (a) (x) and case (b) (+) shown in table 5-1. Also shown
are straight lines with the gradients shown in table 5-1.
Figure 5-13: The density as a function of depth
close to the interface for case (a) (dashed lines) and case (b) (dotted lines)
for 
= 0.1 and 0.001.
show the variation in density with depth for a immiscible fluid for two
different sets of values 
and 
. The values are
shown in table 5-1
as are the values of 
, 
and
the expected gradients 
and 
in the upper and lower fluids respectively. Straight lines with these
gradients are also shown in figure 5-12. The agreement between
the actual gradients and the predicted gradients is good and reinforces
the use of equation (5.27) is calculating and .
The details of the density close to the interface
are shown in figure 5-13 for two different values of .
The results for case (a) are shown by the dashed lines and the
results for case (b) are shown by the dotted lines.
It can be seen that, as before, the density is reduced slightly across
the interface and that the interface is larger for 
.
Away from the interface the results for 
and
are virtually indistinguishable.
