Thermal fluctuations in metastable fluids

Abstract

In this work, the thermal fluctuations of fluid in metastable conditions have been theoretically investigated. The fluid is described with a diffuse interface approach based on the Van der Waals squared-gradient theory (SGT), where the free energy is augmented by a density square gradient term to take into account capillary effects. By averaging physical observables on coarse-graining cells, it is found that capillarity strongly modifies the fluctuation statistics when increasing fluid metastability. A remarkable difference with respect to simple fluid description is also detected when approaching nanoscopic scales. Peculiarly, near spinodal loci, the classical theory envisages a divergent behavior of density fluctuations intensity, while the SGT provides a finite variance of the density field. The scaling behavior of density fluctuations near spinodal lines is analytically derived and discussed. Finally, the correlation length of the capillary system is identified for different metastabilities. Also in the latter case, the critical exponents are theoretically calculated. The theoretical results are corroborated by Landau–Lifshitz–Navier–Stokes fluctuating hydrodynamics simulations.