A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids

Abstract

We present a numerical method that consistently implements thermal fluctuations and hydrodynamic interactions to the motion of Brownian particles dispersed in incompressible host fluids. In this method, the thermal fluctuations are introduced as random forces acting on the Brownian particles. The hydrodynamic interactions are introduced by directly resolving the fluid motions with the particle motion as a boundary condition to be satisfied. The validity of the method has been examined carefully by comparing the present numerical results with the fluctuation-dissipation theorem whose analytical form is known for dispersions of a single spherical particle. Simulations are then performed for more complicated systems, such as a dispersion composed of many spherical particles and a single polymeric chain in a solvent.

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

“…24,25 The right-hand sides of Eqs. (18) and (19) denote the mean and variance of the thermal fluctuations. By including this Brownian force due to the thermal fluctuations in the governing equations, the macroscopic hydrodynamic theory is generalized to include the mesoscopic scales ranging from tens of nanometers to a few micrometers.…”

“…TABLE II Table II. For completeness, we have also compared the performance of an analogous optimization protocol that has been proposed by Iwashita et al,18 for which the noise correlation function is given by…”

“…13 In this paper, we pursue the Langevin approach, in which the thermal fluctuations from the fluid are incorporated as random forces and torques in the particle equation of motion. [14][15][16][17][18][19] The primary objective here is to build a robust thermostat, which preserves equilibrium distributions at constant temperatures (i.e., adheres to the equipartition theorem) and enables the evaluation of free energy landscapes of nanoparticle adhesion with surfaces in future applications. By definition, coupling to a thermostat will alter the hydrodyamics of the nanoparticle system.…”

“…24,25 The implementation can occur in two ways: (i) directly adjust the variance of the random force term in the classical Langevin equation to play the role of a thermostat. In this context, Iwashita et al 18,19 have considered an iterative scaling scheme within the direct numerical simulation (DNS) by adjusting the variance of the random force term in the momentum equation; such a procedure, while useful in constructing a thermostat that preserves hydrodynamic correlations, is still ad hoc in the sense that it deviates from the structure of the generalized Langevin equation.…”

Fluctuating lattice-Boltzmann model for complex fluids

“…29,30 They observed correct long-time behavior and obtained good scaling results. 30 More recently, Iwashita et al 33 applied Langevin noise to the polymer the same way as in Ref. 30, but not to the solvent, which in their case was a direct discretization of the incompressible nonfluctuating Navier-Stokes equation with a body force term coupling the two.…”