  Neutron star (NS) binaries formed dynamically may have significant
eccentricities while emitting gravitational waves (GWs) in the LIGO/VIRGO band.
We study tidal effects in such eccentric inspiralling NS binaries using a set
of hybrid equations. The NS is modelled as a compressible ellipsoid, which can
deform nonlinearly due to tidal forces, while the orbit evolution is treated
with the post-Newtonian (PN) theory up to 2.5-PN order. We find that in
general, the tidal interaction can accelerate the inspiral, and cause orbital
frequency and phase shifts. For circular inspirals, our calculations reproduce
previous linear result at large binary separations, but incorporate the
dynamical response of the NS at small separations. For eccentric inspirals, the
frequency and phase shifts oscillate considerably near pericenter passages, and
the oscillating amplitudes increase with eccentricities. As a result, the GW
phase is also significantly influenced by the tidal effect. At merger, the
cumulative GW phase shift can reach more than 10 radians (for typical NS mass
$1.4M_\odot$ and radius 11.6 km), much larger than the circular inspiral case.
Although the event rate of eccentric NS mergers is likely low, the detection of
such mergers could provide a useful constraint on the NS equation of state.
