  We investigate analytically and computationally the dynamics of 2D needle
crystal growth from the melt in a narrow channel. Our analytical theory
predicts that, in the low supersaturation limit, the growth velocity $V$
decreases in time $t$ as a power law $V \sim t^{-2/3}$, which we validate by
phase-field and dendritic-needle-network simulations. Simulations further
reveal that, above a critical channel width $\Lambda \approx 5l_D$, where $l_D$
the diffusion length, needle crystals grow with a constant $V<V_s$, where $V_s$
is the free-growth needle crystal velocity, and approaches $V_s$ in the limit
$\Lambda\gg l_D$.
