  The spinodal amplification of density fluctuations is treated perturbatively
within dissipative fluid dynamics for the purpose of elucidating the prospects
for this mechanism to cause a phase separation to occur during a relativistic
nuclear collision. The present study includes not only viscosity but also heat
conduction (whose effect on the growth rates is of comparable magnitude but
opposite), as well as a gradient term in the local pressure, and the
corresponding dispersion relation for collective modes in bulk matter is
derived from relativistic fluid dynamics. A suitable two-phase equation of
state is obtained by interpolation between a hadronic gas and a quark-gluon
plasma, while the transport coefficients are approximated by simple
parametrizations that are suitable at any degree of net baryon density. We
calculate the degree of spinodal amplification occurring along specific
dynamical phase trajectories characteristic of nuclear collision at various
energies. The results bring out the important fact that the prospects for
spinodal phase separation to occur can be greatly enhanced by careful tuning of
the collision energy to ensure that the thermodynamic conditions associated
with the maximum compression lie inside the region of spinodal instability.
