Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

Abstract

We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available.

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

“…The details of spatial discretization, mesh movement techniques, and temporal discretization of time derivatives are discussed in Ref. 12. These details will not be repeated here for brevity.…”

“…For this purpose, a weak formulation that incorporates both the fluid and particle equations (Eqs. (12), (13), (15) and (16)) is considered. 44,45 Let V be the function space given by…”

“…A coarse-graining methodology has been developed to bridge molecular dynamics and fluctuating hydrodynamics simulations. 10,11 In our recent paper, 12 we have employed a finite element method (FEM) to determine the thermal moa) Author to whom correspondence should be addressed. Electronic mail:…”

“…In this respect, this study will complement our earlier investigation. 12 The results of the classical Langevin equation using the instantaneous friction law predict rapid exponential decay in the velocity autocorrelation function (VACF). Using computer simulations on a hard-sphere system, Rahman 20 and Alder and Wainwright 21 found a long-tailed decay (∼ t −3/2 ) in the VACF.…”

Faxén's theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow

“…The understanding of the behavior of the velocity autocorrelation function of a colloidal particle in a fluid has a long history and is still a fascinating lively topic [6][7][8][9][10][11]. The usual approach is to consider the time-(or frequency-) dependent force acting on a sphere due to the surrounding fluid.…”