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Research Papers

A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

[+] Author and Article Information
B. Uma

Department of Anesthesiology and Critical Care,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: umab@seas.upenn.edu

R. Radhakrishnan

Department of Bioengineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: rradhak@seas.upenn.edu

D. M. Eckmann

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

P. S. Ayyaswamy

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

1Corresponding author.

Manuscript received March 28, 2012; final manuscript received May 21, 2012; published online December 6, 2012. Assoc. Editor: Gerard F. Jones.

J. Heat Transfer 135(1), 011011 (Dec 06, 2012) (9 pages) Paper No: HT-12-1135; doi: 10.1115/1.4007668 History: Received March 28, 2012; Revised May 21, 2012

A hybrid approach consisting of a Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein–Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation of the hybrid approach. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obey Stokes–Einstein and Stokes–Einstein–Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery. A major advantage of our novel hybrid approach employed in this paper as compared to either the fluctuating hydrodynamics approach or the generalized Langevin approach by itself is that only the hybrid method has been shown to simultaneously preserve both hydrodynamic correlations and equilibrium statistics in the incompressible limit.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic representation of a nanoparticle in a cylindrical vessel (tube) (not to scale). Radius of the tube: R = 5 μm; length of the tube: L = 10 μm; radius of the nanoparticle: a = 250 nm; viscosity of the fluid: μ = 10-3 kg/ms; density of the fluid and the nanoparticle: ρ(f) = 103 kg/m3, 990 kg/m3≤ρ(p)≤1010 kg/m3.

Grahic Jump Location
Fig. 2

Representation of a ten-node tetrahedron

Grahic Jump Location
Fig. 3

Finite element surface mesh of a cylindrical tube with one spherical nanoparticle

Grahic Jump Location
Fig. 4

Translational and rotational temperatures of a nearly neutrally buoyant nanoparticle in a stationary fluid medium as a function of the particle density normalized with fluid density. The nondimensionalized characteristic memory times are τ1/τν = 0.12 and τ2/τν = 0.088.

Grahic Jump Location
Fig. 5

Equilibrium probability of the (a) and (c) translational and (b) and (d) rotational velocities of the nanoparticle in a stationary Newtonian fluid medium for ρ(p)/ρ(f) = 0.99 ((a) and (b)) and 1.01 ((c) and (d)). The nondimensionalized characteristic memory times are τ1/τν = 0.12 and τ2/τν = 0.088 [33].

Grahic Jump Location
Fig. 6

(a) and (c) Translational (B = mρ(f)1/2/12π3/2μ3/2) and (b) and (d) rotational (C = Iρ(f)3/2/32π3/2μ5/2) VACFs of the Brownian particle (a = 250 nm) in a fluid medium through a circular vessel using hybrid approach. The nondimensionalized characteristic memory times are τ1/τν = 0.12 and τ2/τν = 0.088 [33].

Grahic Jump Location
Fig. 7

The MSD of a nearly neutrally buoyant Brownian particle (a = 250 nm) in a stationary fluid medium using hybrid approach. The nondimensionalized characteristic memory times are τ1/τν = 0.12 and τ2/τν = 0.088 [33].

Grahic Jump Location
Fig. 8

The translational diffusion coefficient of nearly neutrally buoyant Brownian particles of different radii a initially placed at different locations h from the wall of the circular vessel in a quiescent medium. Solid and dashed lines correspond to the perturbation solutions given in Happel and Brenner [45].

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