  We simulate dendritic growth in directional solidification in dilute binary
alloys using a phase-field model solved with an adaptive-mesh refinement. The
spacing of primary branches is examined for a range of thermal gradients and
alloy compositions and is found to undergo a maximum as a function of pulling
velocity, in agreement with experimental observations. We demonstrate that
wavelength selection is unambiguously described by a non-trivial crossover
scaling function from the emergence of cellular growth to the onset of
dendritic fingers, a result validated using published experimental data.
