Mesoscale perspective on the Tolman length

We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension sigma as computed from three-dimensional hydrostatic droplets and bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called Tolman length delta. LBM allows one to precisely compute sigma at the surface of tension Rs 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 simulations or by means of Density Functional Theory approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a 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.