MMMRN test. Volume averaged total dust-to-gas ratio enrichment as a function of time for different density thresholds.The FHSC formation can be identified by the dotted vertical blue line while fragmentation occurs during a time delimited by the green area. We observe a slow decrease of the dust-to-gas ratio at low density which gives rise to an enrichment of high-density regions. Cores and fragments at ρ > 10⁻¹¹ g cm⁻³ are formed in a dust-rich environment. The dust-to-gas ratio is almost constant for ρ > 10⁻¹¹ g cm⁻³ because the increase of temperature due to the adiabatic contraction strengthens the coupling between the gas and the dust.