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Research Papers: Max Jakob Award Paper

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

[+] Author and Article Information
Ravi Radhakrishnan

Department of Chemical
and Biomolecular Engineering;
Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: rradhak@seas.upenn.edu

Hsiu-Yu Yu

Department of Chemical and
Biomolecular Engineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: hsiuyu@seas.upenn.edu

David M. Eckmann

Department of Anesthesialogy
and Critical Care;
Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: David.Eckmann@uphs.upenn.edu

Portonovo S. Ayyaswamy

Department of Mechanical Engineering
and Applied Mechanics,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: ayya@seas.upenn.edu

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 25, 2016; final manuscript received August 26, 2016; published online November 22, 2016. Assoc. Editor: Ravi Prasher.

J. Heat Transfer 139(3), 033001 (Nov 22, 2016) (9 pages) Paper No: HT-16-1229; doi: 10.1115/1.4035006 History: Received April 25, 2016; Revised August 26, 2016

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.

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Figures

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Fig. 1

Schematic of the DNS computational domain and the FEM mesh representation

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Fig. 2

The evolution of translational and rotational dynamics of a spherical particle (a=250 nm) in the inertial regime, when immersed in a Newtonian fluid (with properties of water) and confined at the center of a cylindrical vessel (D=20 μm), simulated using the FHD approach at temperature T0=310 K. (a) and (b) The probability distributions of the Cartesian components of the translational and rotational velocities showing the adherence to the corresponding Maxwell–Boltzmann distributions. (c) and (d) The short-time (t∼τν=a2/ν, where ν=μ/ρ and ρ is the fluid density) evolution of the linear velocity autocorrelation function (VACF) and angular velocity autocorrelation function (AVACF) in the inertial regime showing the correct asymptotic transition from the exponential behavior (ξ(tr)=6πμa and ξ(rot)=8πμa3) for t→0 to algebraic behavior fort>τν.

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Fig. 3

(a) Normalized VACF of a non-neutrally buoyant Brownian particle near an infinite plane wall in an incompressible, quiescent fluid medium for different separations from the wall. The symbols are the corresponding results from Ref. [47], and the lines are the predictions from the composite GLE simulations reported by Yu et al. [37]; here ρp/ρ=2.25 with ρp being the density of the particle. (b) Normalized VACF of a neutrally buoyant Brownian particle in the lubrication regime with h/a=1.14 in the presence of a harmonic spring (representing strong adhesion with k = 1 N/m) and comparison with DNS and FHD simulations.

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Fig. 4

(a) Schematic of the coarse-grained model considered. The ligand-functionalized nanoparticle of radius a is attached to the wall through ligand–receptor binding interaction (first spring with the force constant k), including the relaxation of receptor internal dynamics subject to the conformational potential (second spring with the force constant ks). The particle center of mass is located at h from the wall. The red dots from top to down: particle center-of-mass position xp, ligand tip position xl, receptor tip position xr, and receptor tip position at equilibrium xr0. (b) Normalized velocity autocorrelation functions for the nanoparticle for different conditions: in the bulk fluid predicted from the Stokes equation with Cv(t)=(kBT/M)×exp {−6πμat/M} (thin solid), in the bulk fluid obtained from the Navier–Stokes equation (thin dashed), close to the wall predicted from the lubrication theory with Cv(t)=(kBT/M)×exp {−6πμa2t/(M(h−a))} (thick solid), close to the wall obtained from the Navier–Stokes equation (thick dashed), and attached to the vessel wall calculated from the current GLE simulations (dotted). (c) Normalized position autocorrelation functions for the receptor tip (dashed) and the nanoparticle (dotted) obtained from the current GLE simulations compared with the analytical solution for the free protein reported in Refs. [59] and [60] (solid). Simulated probability distributions of the relative positions of (top) the nanoparticle center of mass and (bottom) the receptor tip. The black curves are the equilibrium Boltzmann distributions for the harmonically bound nanoparticle position, with the gray lines denoting the 5% error about the MBD, panel (d), and the free receptor tip position, panel (e).

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