2023/10/11 by K. J. Petersen, Petersen, K. J., Joshua Brinkerhoff +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Particle Dynamics in Fluid Flows #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.2310.07928
openalex publication_date 2023/10/11 · openalex created_date 2023/10/14 · openalex updated_date 2026/07/28
Microscopic thermal fluctuations are known to affect the macroscopic and spatio-temporal evolution of a host of physical phenomena central to the study of biological systems, turbulence, and reactive mixtures, among others. In phase-changing fluids metastability and nucleation rates of embryos are known to be non-trivially affected by thermal noise stemming from molecules random velocity fluctuations, which ultimately determine the long-term growth, morphology, and decay of macroscopic bubbles in cavitation and boiling. We herein present the mathematical groundwork for a lattice-based solution of the combined Fokker-Planck and Boltzmann equations that by proxy solve the stochastic Navier-Stokes-Fourier equations and a non-ideal, cubic van der Waals equation of state. We present the derivation of the kinetic lattice-Fokker-Planck-Boltzmann equations facilitated by Gauss-Hermite quadrature, and show by multi-scale asymptotic analysis that the non-equilibrium dynamics in velocity space inherent to the Fokker-Planck equation manifest as stresses. The resulting coarse-grained lattice-Fokker-Planck-Boltzmann method (LFPBM) is attractive as its dynamics are hypothesized to continually evolve thermal fluctuations introduced into the thermo-hydrodynamic variables by initial conditions in a manner that obeys the fundamental fluctuation-dissipation balances. Simulations will be showcased in future publications.