Describing the hydrodynamics of nanoparticles in fluid media poses interesting challenges due to the coupling between the Brownian and hydrodynamic forces at the nanoscale. We focus on multiscale formulations of Brownian motion and hydrodynamic interactions (HI) of a single flexible polymeric nanoparticle in confining flows using the Brownian Dynamics method. The nanoparticle is modeled as a self-avoiding freely jointed polymer chain that is subject to Brownian forces, hydrodynamics forces, and repulsive interactions with the confining wall. To accommodate the effect of the wall, the hydrodynamic lift due to the wall is included in the mobility of a bead of the polymer chain which depends on its proximity to the wall. Using the example of a flexible polymeric nanoparticle, we illustrate temporal dynamics pertaining to the colloidal scale as well as the nanoscale.
Issue Section:
Micro/Nanoscale Heat Transfer
References
1.
Wei
, L.
, Cai
, C.
, Lin
, J.
, and Chen
, T.
, 2009
, “Dual-Drug Delivery System Based on Hydrogel/Micelle Composites
,” Biomaterials
, 30
(13
), pp. 2606
–2613
.2.
Ahmed
, E.
, 2015
, “Hydrogel: Preparation, Characterization, and Applications: A Review
,” J. Adv. Res.
, 6
(2
), pp. 105
–121
.3.
Radhakrishnan
, R.
, Yu
, H. Y.
, Eckmann
, D. M.
, and Ayyaswamy
, P. S.
, 2016
, “Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics
,” ASME J. Heat Transfer
, 139
(3
), p. 033001
.4.
Wakiya
, S.
, 1957
, “Viscous Flows Past a Spheroid
,” J. Phys. Soc. Jpn.
, 12
(10
), pp. 1130
–1141
.5.
Sugihara-Seki
, M.
, 1996
, “The Motion of an Ellipsoid in Tube Flow at Low Reynolds Number
,” J. Fluid Mech.
, 324
(1
), pp. 287
–308
.6.
Glowinski
, R.
, Pan
, T. W.
, Hesla
, T. I.
, Joseph
, D. D.
, and Périaux
, J.
, 2001
, “A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow Past Moving Rigid Bodies: Application to Particulate Flows
,” J. Comput. Phys.
, 169
(2
), pp. 363
–426
.7.
Swaminathan
, T. N.
, Mukundakrishnan
, K.
, and Hu
, H. H.
, 2006
, “Sedimentation of an Ellipsoid Inside an Infinitely Long Tube at Low and Intermediate Reynolds Numbers
,” J. Fluid Mech.
, 551
(1
), pp. 357
–385
.8.
Hsu
, R.
, and Ganatos
, P.
, 1989
, “The Motion of a Rigid Body in a Viscous Fluid Bounded by a Plane Wall
,” J. Fluid Mech.
, 207
(1
), pp. 29
–72
.9.
Ding
, E. J.
, and Aidun
, C.
, 2000
, “The Dynamics and Scaling Law for Particles Suspended in Shear Flow With Inertia
,” J. Fluid Mech.
, 423
, pp. 317
–344
.10.
Xia
, Z.
, Connington
, K. W.
, Rapaka
, S.
, Yue
, P.
, Feng
, J. J.
, and Chen
, S.
, 2009
, “Flow Patterns in the Sedimentation of an Elliptical Particle
,” J. Fluid Mech.
, 625
, pp. 249
–272
.11.
Huang
, H.
, Yang
, X.
, and Lu
, X. Y.
, 2014
, “Sedimentation of an Ellipsoidal Particle in Narrow Tubes
,” Phys. Fluids
, 26
(5
), p. 053302
.12.
Sharma
, N.
, and Patankar
, N. A.
, 2004
, “Direct Numerical Simulation of the Brownian Motion of Particles by Using Fluctuating Hydrodynamic Equations
,” J. Comput. Phys.
, 201
(2
), pp. 466
–486
.13.
Donev
, A.
, Vanden-Eijnden
, E.
, Garcia
, A.
, and Bell
, J.
, 2010
, “On the Accuracy of Finite Volume Schemes for Fluctuating Hydrodynamics
,” Commun. Appl. Math. Comput. Sci.
, 5
(2
), pp. 149
–197
.14.
Ladd
, A. J. C.
, 1993
, “Short-Time Motion of Colloidal Particles: Numerical Simulation Via a Fluctuating Lattice-Boltzmann Equation
,” Phys. Rev. Lett.
, 70
(9
), pp. 1339
–1342
.15.
Ladd
, A. J. C.
, 1994
, “Numerical Simulations of Particulate Suspensions Via a Discretized Boltzmann Equation—Part 1: Theoretical Foundation
,” J. Fluid Mech.
, 271
, pp. 285
–309
.16.
Ladd
, A. J. C.
, 1994
, “Numerical Simulations of Particulate Suspensions Via a Discretized Boltzmann Equation—Part 2: Numerical Results
,” J. Fluid Mech.
, 271
, pp. 311
–339
.17.
Atzberger
, P. J.
, 2011
, “Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions With Thermal Fluctuations
,” J. Comput. Phys.
, 230
(8
), pp. 2821
–2837
.18.
Uma
, B.
, Swaminathan
, T. N.
, Radhakrishnan
, R.
, Eckmann
, D. M.
, and Ayyaswamy
, P. S.
, 2011
, “Nanoparticle Brownian Motion and Hydrodynamic Interactions in the Presence of Flow Fields
,” Phys. Fluids
, 23
(7
), p. 073602
.19.
Ramakrishnan
, N.
, Wang
, Y.
, Ayyaswamy
, P. S.
, Ayyaswamy
, P. S.
, and Radhakrishnan
, R.
, 2017
, “Motion of a Nano-Spheroid in a Cylindrical Vessel Flow: Brownian and Hydrodynamic Interactions
,” J. Fluid Mech.
, 821
, p. 117
.20.
Radhakrishnan
, R.
, Ramakrishnan
, N.
, Eckmann
, D. M.
, and Ayyaswamy
, P. S.
, 2019
, “Nanoscale Fluid Dynamics
,” 21st Century Nanoscience Book
, K.
Sattler
, ed., Taylor and Francis
, New York
.21.
Eckmann
, D. M.
, Composto
, R. J.
, Tsourkas
, A.
, and Muzykantov
, V. R.
, 2014
, “Nanogel Carrier Design for Targeted Drug Delivery
,” J. Mater. Chem. B
, 2
(46
), pp. 8085
–8097
.22.
Keblinski
, P.
, Prasher
, R.
, and Eapen
, J.
, 2008
, “Thermal Conductance of Fluids: Is the Controversy Over
,” J. Nanopart. Res.
, 10
(7
), pp. 1089
–1097
.23.
Prasher
, R.
, Song
, D.
, Wang
, J.
, and Phelan
, P.
, 2006
, “Measurements of Nanofluid Viscosity and Its Implications for Thermal Applications
,” Appl. Phys. Lett.
, 89
(13
), p. 133108
.24.
Frenkel
, D.
, and Smit
, B.
, 1996
, Understanding Molecular Simulation: Algorithms to Applications
, Academic Press
, Cornwall, UK
.25.
Prasher
, R.
, Bhattacharya
, P.
, and Phelan
, P. E.
, 2006
, “Brownian-Motion-Based Convective-Conductivemodel for the Effective Thermal Conductivity of Nanofluids
,” ASME J. Heat Transfer.
, 128
(6
), pp. 588
–595
.26.
Jang
, S. P.
, and Choi
, S. U. S.
, 2004
, “Role of Brownian Motion in the Enhanced Thermal Conductivity of Nanofluids
,” App. Phys. Lett.
, 84
(21
), pp. 4316
–4318
.27.
Kumar
, D. H.
, Patel
, H. E.
, Kumar
, V. R. R.
, Sundararajan
, T.
, Pradeep
, T.
, and Das
, S. K.
, 2004
, “Model for Heat Conduction in Nanofluids
,” Phys. Rev. Lett.
, 93
(14
), pp. 144301
–144304
.28.
Waigh
, T. A.
, 2005
, “Microrheology of Complex Fluids
,” Rep. Prog. Phys.
, 68
(3
), pp. 685
–742
.29.
Cicuta
, P.
, and Donald
, A. M.
, 2007
, “Microrheology: A Review of the Method and Applications
,” Soft Matter
, 3
(12
), p. 1449
.30.
Squires
, T. M.
, and Mason
, T. G.
, 2010
, “Fluid Mechanics of Microrheology
,” Annu. Rev. Fluid Mech.
, 42
(1
), pp. 413
–438
.31.
Squires
, T. M.
, and Mason
, T. G.
, 2010
, “Tensorial Generalized Stokes-Einstein Relation for Anisotropic Probe Microrheology
,” Rheol. Acta
, 49
(11–12
), pp. 1165
–1177
.32.
Gómez-González
, M.
, and Álamo
, J. C. D.
, 2016
, “Two-Point Particle Tracking Microrheology of Nematic Complex Fluids
,” Soft Matter
, 12
(26
), pp. 5758
–5779
.33.
Kailasham
, R.
, Chakrabarti
, R.
, and Prakash
, J. R.
, 2018
, “Rheological Consequences of Wet and Dry Friction in a Dumbbell Model With Hydrodynamic Interactions and Internal Viscosity
,” J. Chem. Phys.
, 149
(9
), p. 094903
.34.
Doi
, M.
, and Edwards
, S. F.
, 1986
, The Theory of Polymer Dynamics
, Oxford The Clarendon Press
, New York
.35.
Peterlin
, A.
, 1966
, “Hydrodynamics of Macromolecules in a Velocity Field With Longitudinal Gradient
,” J. Polym. Sci.
, 4
(4
), pp. 287
–291
.36.
Ferrer
, M. C.
, Robert
, C. J.
, Eckmann
, D. M.
, and Composto
, R. J.
, 2015
, “A Facile Route to Synthesize Nanogels Doped With Silver Nanoparticles
,” J. Nanopart. Res.
, 15
, pp. 1
–7
.37.
Sarkar
, A.
, Eckmann
, D. M.
, Ayyaswamy
, P. S.
, and Radhakrishnan
, R.
, 2015
, “Hydrodynamic Interactions of Deformable Polymeric Nanocarriers and the Effect of Crosslinking
,” Soft Matter
, 11
(29
), pp. 5955
–5969
.38.
Liu
, Y.
, Lipowsky
, R.
, and Dimova
, R.
, 2012
, “Concentration Dependence of the Interfacial Tension for Aqueous Two-Phase Polymer Solutions of Dextran and Polyethylene Glycol
,” Langmuir
, 28
(8
), pp. 3831
–3839
.39.
Pelton
, R.
, Zhang
, J.
, chen
, N.
, and Moghaddamzadeh
, A.
, 2003
, “The Influence of Dextran Molecular Weight on the Dry Strength of Dextran-Impregnated Paper
,” Tappi J.
, 2
, pp. 15
–18
.https://imisrise.tappi.org/TAPPI/Products/03/APR/03APR15.aspx40.
Bird
, R. B.
, 1997
, Dynamics of Polymeric Liquids
, Wiley
, Hoboken, NJ
.41.
Larson
, R. G.
, 2005
, “The Rheology of Dilute Solutions of Flexible Polymers: Progress and Problems
,” J. Rheol.
, 49
(1
), pp. 1
–70
.42.
Alexander-Katz
, A.
, 2006
, “Shear-Flow-Induced Unfolding of Polymeric Globules
,” Phys. Rev. Lett.
, 98
(13
), p. 138101
.43.
Miao
, L.
, Young
, C. D.
, and Sing
, C. E.
, 2017
, “An Iterative Method for Hydrodynamic Interactions in Brownian Dynamics Simulations of Polymer Dynamics
,” J. Chem. Phys.
, 147
(2
), p. 024904
.44.
Beenakker
, C. W. J.
, 1986
, “Ewald Sum of the Rotne-Prager Tensor
,” J. Chem. Phys.
, 85
(3
), pp. 1581
–1582
.45.
Rotne
, J.
, and Prager
, S.
, 1969
, “Variational Treatment of Hydrodynamic Interaction in Polymers
,” J. Chem. Phys.
, 50
(11
), pp. 4831
–4837
.46.
Yamakawa
, H.
, 1970
, “Transport Properties of Polymer Chains in Dilute Solution: Hydrodynamic Interaction
,” J. Chem. Phys.
, 53
(1
), pp. 436
–443
.47.
Bleibel
, J.
, 2012
, “Ewald Sum for Hydrodynamic Interactions With Periodicity in Two Dimensions
,” J. Phys. A: Math. Theor.
, 45
(22
), p. 225002
.48.
Zhou
, T.
, and Chen
, S. B.
, 2006
, “Computer Simulations of Diffusion and Dynamics of Short-Chain Polyelectrolytes
,” J. Chem. Phys.
, 124
(3
), p. 034904
.49.
Faxen
, H.
, and Angew
, Z.
, 1927
, “Die Geschwindigkeit Zweier Kugeln, Die Unter Einwirkung Der Schwere in Einer Zähen Flüssigkeit Fallen
,” Math. Mech.
, 7
, pp. 79
–80
.50.
Weeks
, J. D.
, Chandler
, D.
, and Andersen
, H. C.
, 1971
, “Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids
,” J. Chem. Phys.
, 54
(12
), pp. 5237
–5247
.51.
Ermak
, D. L.
, and McCammon
, J. A.
, 1978
, “Brownian Dynamics With Hydrodynamic Interactions
,” J. Chem. Phys.
, 69
(4
), p. 1352
.52.
Bishop
, M.
, 1986
, “Polymer Shapes in Three Dimensions
,” J. Chem. Phys.
, 85
(10
), pp. 5961
–5962
.53.
Brenner
, H.
, 1961
, “The Slow Motion of a Sphere Through a Viscous Fluid Towards a Plane Surface
,” Chem. Eng. Sci.
, 16
, pp. 242
–251
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