A Mesoscale Perspective on the Tolman Length

TL;DR

This paper uses the Shan-Chen lattice Boltzmann method to study the curvature dependence of surface tension and the Tolman length in droplets, revealing universal scaling near the critical temperature and opening new mesoscale research avenues.

Contribution

It introduces a mesoscale hydrodynamic approach to compute the Tolman length, demonstrating its universality and scaling behavior, which was previously studied mainly via molecular dynamics or density functional theory.

Findings

The lattice Boltzmann method accurately computes curvature-dependent surface tension.

The Tolman length exhibits universal power-law scaling near the critical temperature.

Results are reproducible using the 'idea.deploy' framework.

Abstract

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.