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Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

Published online by Cambridge University Press:  18 May 2017

N. Ramakrishnan Open the ORCID record for N. Ramakrishnan [Opens in a new window] ,
Y. Wang Open the ORCID record for Y. Wang [Opens in a new window] ,
D. M. Eckmann Open the ORCID record for D. M. Eckmann [Opens in a new window] ,
P. S. Ayyaswamy  and
R. Radhakrishnan Open the ORCID record for R. Radhakrishnan [Opens in a new window]
N. Ramakrishnan
Affiliation:
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19204, USA
Y. Wang
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19204, USA
D. M. Eckmann
Affiliation:
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19204, USA Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA 19204, USA
P. S. Ayyaswamy
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19204, USA
R. Radhakrishnan*
Affiliation:
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19204, USA Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19204, USA Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19204, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation–dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible – an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

JFM classification

Mathematical Foundations: Computational methods Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 117 - 152
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Copyright
© 2017 Cambridge University Press 

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Footnotes

‡

Present address: Center for Applied Mathematics, Tianjin University, Tianjin, China, 300072.

§

These authors contributed equally.

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