A Mesoscale Perspective on the Tolman Length

We demonstrate that the multi-phase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension $\sigma$ as computed from three-dimensional hydrostatic droplets/bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called {\it Tolman length} $\delta$. LBM allows to precisely compute $\sigma$ at the surface of tension $R_s$ and determine the Tolman length from the coefficient of the first order correction. The corresponding values of $\delta$ display universality for different equations of state, following a power-law scaling near the critical temperature. The Tolman length has been studied so far mainly via computationally demanding molecular dynamics (MD) simulations or by means of density functional theory (DFT) approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a new hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.