Fluidity of the system produced in relativistic pp and heavy-ion collisions: Hadron resonance gas model approach

We have estimated the dimensionless parameters such as Reynolds number ($Re$), Knudsen number ($Kn$) and Mach number ($Ma$) for a multi-hadron system by using the excluded volume hadron resonance gas (EVHRG) model along with Hagedorn mass spectrum to include higher resonances in the system. The size dependence of these parameters indicate that the system formed in proton+proton collisions may achieve thermal equilibrium making it unsuitable as a benchmark to analyze the properties of the system produced in heavy ion collisions at similar energies. While the magnitude of $Kn$ can be used to study the degree of thermalization and applicability of inviscid hydrodynamics, the variations of $Re$ and $Ma$ with temperature ($T$) and baryonic chemical potential ($\mu_B$) assist to understand the change in the nature of the flow in the system. Indeed the nature of flow changes from laminar to turbulent as $Re$ increases and the system is characterized as incompressible for low $Ma (<<1)$ and compressible for larger $Ma$. $Ma$ can also be used to understand whether the flow is subsonic or supersonic.