  In inertial confinement fusion (ICF) implosions, mixing the ablator into the
fuel and the hot spot is one of the most adverse factors that lead to ignition
degradation. Recent experiments in the Marble campaign at the Omega laser
facility and the National Ignition Facility (NIF) demonstrate the significance
of the temperature separation in heterogeneous mixing flows. In the present
work we provide an approach to deal with thermally disequilibrium
multi-component flows with the ultimate aim to investigate the temperature
separation impact on mixing and fusion burn. The present work is two-fold,
i.e., (a)we derive a model governing the multi-component flows in thermal
disequilibrium with transport terms, (b)we use the derived model to study the
Rayleigh-Taylor (RT) instability in thermally relaxing multi-component systems.
The model is reduced from the fully disequilibrium multi-phase Baer-Nunziato
model in the limit of small Knudsen number $Kn << 1$. Velocity disequilibrium
is closed with the diffusion laws and only one mass weighted velocity is
retained formally. Thus, the complex wave structure of the original
Baer-Nunziato model is simplified to a large extent and the obtained model is
much more computationally affordable. Moreover, the capability to deal with
finite temperature relaxation is kept. Efficient numerical methods for solving
the proposed model are aslo presented. Equipped with the proposed model and
numerical methods, we further investigate the impact of the thermal relaxation
on the RT instability development at the inertial confinement fusion (ICF)
deceleration stage. On the basis of numerical simulations, we have found that
for the RT instability at an interface between the high-density low-temperature
component and the low-density high-temperature component, the thermal
relaxation significantly suppress the development of the instability.
