The volume occupied by the unconstrained genomic DNA of prokaryotes in saline solutions is thousand times larger than the cell. Moreover, it is not separated from the rest of the cell by a membrane. Nevertheless, it occupies only a small fraction of the cell called the nucleoid. The mechanisms leading to such compaction are the matter of ongoing debates. The present work aims at exploring a newly proposed mechanism, according to which the formation of the nucleoid would result from the demixing of the DNA and nonbinding globular macromolecules of the cytoplasm, like ribosomes. To this end, a coarse-grained model of prokaryotic cells was developed, and demixing was analyzed as a function of the size and number of crowders. The model suggests that compaction of the DNA is actually governed by the volume occupancy ratio of the crowders and remains weak almost up to the jamming critical density. Strong compaction is however observed just before jamming, suggesting that crowding and electrostatic repulsion work synergetically in this limit. Finally, simulations performed with crowders with different sizes indicate that the DNA and the largest crowders demix preferentially. Together with the recent observation of the gradual compaction of long DNA molecules upon increase of the concentration of bovine serum albumin proteins and silica nanoparticles, this work supports the demixing mechanism as a key player for the formation of the nucleoid.