We report on equiaxed dendritic growth in solidifying Al-Cu alloys, particularly the interactions between the dendrites that ultimately form the grain structure in the solid. A three-dimensional phase-field code is designed to reproduce the same conditions as the ones imposed in the experiments. Our numerical results allow us to propose scaling laws that govern the dynamics of dendritic primary arms, with the solute composition and the average distance between two nuclei as physical parameters. These laws are used to extrapolate our numerical results to the experimental situation where phase-field simulations are beyond reach. Good quantitative agreement is found between the predicted behavior and the experimental observations, which validates the scaling laws obtained.