We study how bubbles grow after the initial nucleation event in generi
c first-order cosmological phase transitions characterized by the valu
es of the latent heat L, interface tension sigma, and correlation leng
th xi, and driven by a scalar order parameter phi. Equations coupling
phi(t, x) and the fluid variables v(t,x),T(t,x) and depending on a dis
sipative constant rare derived and solved numerically in the (1 + 1)-d
imensional case starting from a slightly deformed critical bubble conf
iguration phi(0,x). The parameters L, sigma, xi corresponding to QCD a
nd electroweak phase transitions are chosen and the whole history of t
he bubble with the formation of combustion and shock fronts is compute
d as a function of GAMMA. Both deflagrations and detonations can appea
r depending on the values of the parameters. Reheating due to collisio
ns of bubbles is also computed.