Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics1

Abstract

Traditionally, the numerical computation of particle motion in a fluid is resolved through computational fluid dynamics (CFD). However, resolving the motion of nanoparticles poses additional challenges due to the coupling between the Brownian and hydrodynamic forces. Here, we focus on the Brownian motion of a nanoparticle coupled to adhesive interactions and confining-wall-mediated hydrodynamic interactions. We discuss several techniques that are founded on the basis of combining CFD methods with the theory of nonequilibrium statistical mechanics in order to simultaneously conserve thermal equipartition and to show correct hydrodynamic correlations. These include the fluctuating hydrodynamics (FHD) method, the generalized Langevin method, the hybrid method, and the deterministic method. Through the examples discussed, we also show a top-down multiscale progression of temporal dynamics from the colloidal scales to the molecular scales, and the associated fluctuations, hydrodynamic correlations. While the motivation and the examples discussed here pertain to nanoscale fluid dynamics and mass transport, the methodologies presented are rather general and can be easily adopted to applications in convective heat transfer.

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

“…Umbrella sampling 57 Multiple time step molecular dynamics 96 Parallel tempering 24 Multigrid PDE solvers 71,97 Metadynamics 98 Dual resolution 46 Path sampling 99 Equation free methods 100,101 Coarse graining methods 102,103 Concurrent multiscale methods Classical density functional theory 110,111 Particle to field passing 112 Polymer field theory 113 Loosely coupled process flow 114,115 Memory-function approach to hydrodynamics 116 just some of the more foundational methods below. There is an entire journal dedicated to MSM, Multiscale Modeling and Simulation (https:// www.siam.org/journals/mms.php).…”

Multiscale modeling: foundations, historical milestones, current status, and future prospects

“…5.5.1 Memory function approach to coarse-graining with hydrodynamic interactions: In the description of the dynamics of nanosized Brownian particles in an bounded and unbounded fluid domains the memory functions decay with algebraic correlations as enumerated by theoretical and computational studies [46,85,128]. The equation of stochastic motion for each component of the velocity of a nanoparticle immersed in a fluid in bounded and unbounded domains takes the form of a generalized Langevin equation (GLE) of the form of (Eq.…”

“…If the memory functions are unknown, they can be obtained via deterministic approaches by solving the continuum hydrodynamic equations numerically [46,128]. These disparate hydrodynamic fields and molecular forces can be integrated into a single GLE to realize a unified description of particle dynamics under the influence of molecular and hydrodynamic forces [85]. Another approach to integrating these forces is via the Fokker Planck approach using the sequential multiscale method paradigm [131].…”

Nanofluid Dynamics of Flexible Polymeric Nanoparticles Under Wall Confinement

“…Nanoparticles (NPs) have been the subject of extensive theoretical and experimental investigations due to their importance in numerous industrial and medical applications [1][2][3]. Due to their tunable physicochemical properties, such as the size, shape, rigidity, structure, and surface chemistry, a multitude of applications have been identified for NP-mediated delivery of diagnostic and therapeutic agents.…”

“…In general, NPs can be classified into nondeformable (or rigid) and deformable (or flexible) categories. While theoretical and computational works have extensively analyzed for the impact of size and shape of rigid NPs on their targeting efficiency [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], the role of carriers' flexibility on enhanced drug delivery has been explored to a far lesser extent, and the potential benefits of tuning nanoparticle elasticity are not clear. As such, similar treatment of flexible NPs offers a lot of exciting challenges and opportunities and recent research efforts have focused on how flexibility can be leveraged to tune the biological function and fate of nanoparticles.…”