  In this work we used a generalized Frenkel-Kontorova model to study the
mobility of water molecules inside carbon nanotubes with small radius at low
temperatures. Our simulations show that the mobility of the confined water
decreases monotonically increasing the amplitude of the substrate potential at
fixed commensurations. On the other hand, the mobility of the water molecules
shows a non-monotonic behavior when varying the commensuration. This result
indicates that the mobility of the confined fluid presents different behavior
regimes depending on the amplitude of the water-nanotube interaction. In order
to understand qualitatively these results, we study analytically the driven
Frenkel-Kontorova model at finite temperatures. This analysis allows us to
obtain the curves of the mobility versus commensurations, at fixed substrate
potentials. Such curves shows the existence of three regimes of mobility
behavior as a function of the commensuration ratio. Additionally, our study
indicates a nontrivial and strong dependence of the mobility with a quantity
that can be interpreted as an effective amplitude of the substrate potential,
depending on the bare amplitude of the substrate potential, the commensuration
ratio and temperature.
