We present a computer simulation study of a binary mixture of hard spherocylinders with different diameters (D1,D2) and the same lengths (L15L25L). We first study a mixture of spherocylinders with lengths L 515D2 and D150, which can be regarded as a mixture of rodlike colloids and ideal needles. We find clearly an entropy-driven isotropic-isotropic (I-I) demixing transition in this mixture. In ...