The mesoscopic envelope model overcomes the limitations of phase-field methods. It can be applied at larger scales and can include fluid flow at reasonable computing cost. It consists of the description of a dendritic grain by an envelope that links the active dendrite branches. The grain is modelled as an evolving porous medium and the liquid-solid phase change and solute transport are modelled by volume-averaged equations. The velocities of the dendrite tips are determined by the local solute-concentration field in the proximity of the envelope through an analytical stagnant-film model. In this publication, we present our implementation of the model for a binary alloy and we discuss the influence of the stagnant-film thickness, the principal model parameter, on the predicted 3D equiaxed grains by comparisons with the scaling laws for binary-alloy dendrites obtained in recent experiments by Melendez and Beckermann.