Three dimensional dunes of crescentic shape, called barchans, are commonly found on Earth and other planetary environments. In the great majority of cases, barchans are organized in large fields in which corridors of size-selected barchans are observed, and where barchan-barchan interactions play an important role in size regulation. Previous studies shed light on the interactions between barchans by making use of monodisperse particles, but dunes in nature consist, however, of polydisperse grains. In this paper, we investigate the binary interactions of barchans consisting of (i) bidisperse mixtures of grains and (ii) different monodisperse grains (one type for each barchan). We performed experiments in a water channel where grains of different sizes were poured inside forming two barchans that interacted with each other while filmed by a camera, and we obtained their morphology from image processing. We observed that a transient stripe appears over the dunes in cases of bidisperse mixtures, that interaction patterns vary with concentrations, and that different interactions exist when each barchan consists of different monodisperse grains. Interestingly, we found the conditions for a collision in which the upstream barchan is larger than the downstream one, and we propose a timescale for the interactions of both monodisperse and bidisperse barchans. Our results represent a new step toward understanding complex barchanoid structures found on Earth, Mars and other celestial bodies.