A novel multiphase DNS method for the resolution of Brownian motion in a weakly rarefied gas using a continuum framework

In this paper, we formulate an Immersed boundary based direct numerical simulation (DNS) technique for resolving the particle-fluid coupling between a nano-particle and a (weakly) rarefied gas. Such a method resolves the mobility of these solid particles by incorporating the hydrodynamics of the fluid more rigorously within the conventional Langevin description of the system. We analyse the consequences of resolving the subsequent Brownian motion of spherical soot-like hydrocarbon (HC) nano-particles in an unbounded domain using such a framework. The proposed method is able to capture the transition from a particle-inertia dominated (highly correlated) ballistic regime (t^2) to a non-correlated diffusive one (2Dt as given by the Stokes-Einstein relation) and further accurately estimate the resulting diffusivity of the nano-particle. This method can be used within any multiphase DNS framework to reproduce the meandering motion of soot-like Brownian particles under similar conditions