We demonstrate that the multi-phase lattice Boltzmann method (LBM) yields a curvature dependent surface tension $sigma$ by means of three-dimensional hydrostatic droplets/bubbles simulations. Such curvature dependence is routinely characterized, at the first order, by the so-called {it Tolman length} $delta$. LBM allows to precisely compute $sigma$ at the surface of tension $R_s$, i.e. as a function of the droplet size, and determine the first order correction. The corresponding values of $delta$ display universality in temperature for different equations of state, following a power-law scaling near the critical point. 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. It has proved pivotal in extending the classical nucleation theory and is expected to be paramount in understanding cavitation phenomena. 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.
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