11.1 Single fluid case
Suppose that there is only one constituent, with index
. The master function
then
depends only on
. The variation in the chemical potential due to a small disturbance
is
where
The equation of motion is
. It is not difficult to show, by using the condition of transverse wave
propagation (188) and contracting with the spatial part of the wave vector
, that the equation
of motion reduces to
The speed of sound is thus
Given that a well-constructed fluid model should have
, we see that the second term must be
negative. This would ensure that the model is causal.