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 2 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 e-mail: ayya@seas.upenn.edu Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics 1 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 equi- partition 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 mul- tiscale 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. [DOI: 10.1115/1.4035006] 1 Introduction A common strategy in multiscale modeling involves systemati- cally coarse-graining the atomistic description to build models with reduced representation at a larger length scale. Alternatively, a top-down approach may be employed, in which models are con- structed based on governing equations at the mesoscale, which already have a reduced representation of the underlying micro- scopic dynamics. Bridging methods integrating these bottom-up and top-down methods have been achieved in two limits: (1) hier- archical bridging, which involves computing a property or a con- stitutive relationship at a smaller scale using a more-detailed model and employing the computed values in the other [1,2]; (2) domain decomposition bridging, which involves performing molecular scale modeling in a small domain and integrating it with continuum modeling in a larger domain [3]. An important application of nanoscale mass transport occurs in targeted drug delivery. In the following, we will use the targeted drug delivery problem for illustration purposes. In traditional modes of drug delivery, only a small fraction of injected drugs access the dis- eased tissue. Suboptimal drug delivery represents an acute chal- lenge by limiting the efficacy of biotherapeutics. Strategies to address and overcome this challenge may be based on theoretical and computational approaches to iterate with innovative experi- mental methods. Targeted drug delivery using nanoparticles coated with specific targeting ligands is such an approach in thera- peutic and diagnostic applications [3–5]. Targeted drug delivery is a multiscale problem, and in this case a large range of length and time scales are important to hydrodynamic, microscopic, and molecular interactions mediating nanoparticle motion in blood- flow and cell binding. In drug delivery applications involving vas- cular targeting, for example, the molecular interactions (such as receptor–ligand bonds) and the hydrodynamic interactions (such as margination of the nanoparticle in blood) are equally significant [6–10]. Multiple macroscopic and microscopic time scales gov- erning the problem include: (i) the inertial time-scale, (ii) the vis- cous relaxation time-scale, (iii) the hydrodynamic interaction timescale, (iv) the molecular interaction timescale, and (v) the Brownian diffusion time-scale. This simultaneous relevance of disparate length (and time scales) does not fit traditional multi- scale methods. The challenge lies in integrating fluid motion and viscous memory for multiphase flow in complex geometries, while simultaneously including thermal and stochastic effects to simulate correctly the quasi-equilibrium distributions, in order to enable multivalent receptor–ligand binding at the physiological temperature. Similar examples may be cited for nanoscale heat transport. Nanocomposites synthesized as nanoparticle suspen- sions in viscous, viscoelastic, and elastic media have been pro- posed as functional materials for several technological applications for which characterizing the transport properties such as diffusion coefficient, viscosity, and thermal conductivity are of paramount importance. However, how the nanoparticle dispersion in the host medium influences these properties has been intensely debated in the literature [11–13]. 2 Accurate Representation of Nanoparticle Dynamics: Stochastic and Hydrodynamic Effects Using Fluctuating Hydrodynamics (FHD) With Markovian Noise For nanosized particles, to account for the thermal fluctuations in a mechanical system, one can add the thermal force terms to the governing equations of the system based on the theory of non- equilibrium statistical mechanics [14]. We adopt the fluctuating 2 Corresponding author. 1 Forms a part of the Max Jakob Memorial Award lecture presented by P. S. Ayyaswamy at the 2015 IMECE Conference, Houston, TX. 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. Journal of Heat Transfer MARCH 2017, Vol. 139 / 033001-1 Copyright V C 2017 by ASME