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

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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Nanocarrier–Cell Surface Adhesive and Hydrodynamic Interactions: Ligand–Receptor Bond Sensitivity Study

Journal of Nanotechnology in Engineering and Medicine ◽

10.1115/1.4007522 ◽

2012 ◽

Vol 3 (3) ◽

Cited By ~ 1

Author(s):

B. Uma ◽

R. Radhakrishnan ◽

D. M. Eckmann ◽

P. S. Ayyaswamy

Keyword(s):

Degrees Of Freedom ◽

Hybrid Approach ◽

Free Energy Density ◽

Sensitivity Study ◽

Potential Of Mean Force ◽

Hydrodynamic Interactions ◽

Arbitrary Lagrangian Eulerian ◽

Fluid Medium ◽

Microscopic Interactions ◽

Adhesive Interactions

A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor–ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.

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A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

Molecular Physics ◽

10.1080/00268976.2012.663510 ◽

2012 ◽

Vol 110 (11-12) ◽

pp. 1057-1067 ◽

Cited By ~ 7

Author(s):

Balakrishnan Uma ◽

David M. Eckmann ◽

Portonovo S. Ayyaswamy ◽

Ravi Radhakrishnan

Keyword(s):

Incompressible Fluid ◽

Langevin Dynamics ◽

Thermal Motion ◽

Fluctuating Hydrodynamics ◽

Fluid Medium ◽

Generalized Langevin Dynamics

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An Analysis of the Flow of a Newtonian Fluid between Two Moving Parallel Plates

ISRN Mathematical Analysis ◽

10.1155/2013/535061 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

A. Zeb ◽

A. M. Siddiqui ◽

M. Ahmed

Keyword(s):

Stream Function ◽

Newtonian Fluid ◽

Constant Velocity ◽

Fluid Velocity ◽

Equations Of Motion ◽

Fluid Pressure ◽

Parallel Plates ◽

Incompressible Newtonian Fluid ◽

Inverse Solutions ◽

Analytical Expressions

We consider flow of an incompressible Newtonian fluid produced by two parallel plates, moving towards and away from each other with constant velocity. Inverse solutions of the equations of motion are obtained by assuming certain forms of the stream function. Analytical expressions for the stream function, fluid velocity components, and fluid pressure are derived.

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The dam-break problem for concentrated suspensions of neutrally buoyant particles

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.154 ◽

2013 ◽

Vol 724 ◽

pp. 95-122 ◽

Cited By ~ 8

Author(s):

C. Ancey ◽

N. Andreini ◽

G. Epely-Chauvin

Keyword(s):

Velocity Profile ◽

Newtonian Fluid ◽

Velocity Profiles ◽

Lubrication Theory ◽

Dam Break ◽

Particle Migration ◽

Flow Depth ◽

Concentrated Suspensions ◽

Front Position ◽

Neutrally Buoyant

AbstractThis paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.

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The Mechanism of Size-Based Particle Separation by Dielectrophoresis in the Viscoelastic Flows

Journal of Fluids Engineering ◽

10.1115/1.4039709 ◽

2018 ◽

Vol 140 (9) ◽

Cited By ~ 22

Author(s):

Teng Zhou ◽

Yongbo Deng ◽

Hongwei Zhao ◽

Xianman Zhang ◽

Liuyong Shi ◽

...

Keyword(s):

Electric Field ◽

Newtonian Fluid ◽

Finite Size ◽

Particle Separation ◽

Weissenberg Number ◽

Viscoelastic Flow ◽

Viscoelastic Flows ◽

Arbitrary Lagrangian Eulerian ◽

Particle Movement ◽

Physical Insight

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

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Investigation of the Stability of Axially Moving Beams With Discrete Masses

10.1115/detc2021-70302 ◽

2021 ◽

Author(s):

Konstantina Ntarladima ◽

Michael Pieber ◽

Johannes Gerstmayr

Keyword(s):

Large Deformations ◽

Equations Of Motion ◽

Arbitrary Lagrangian Eulerian ◽

Axial Motion ◽

Multibody Modeling ◽

Conveyor Belts ◽

Axially Moving Beams ◽

Concentrated Masses ◽

Axially Moving ◽

The Stability

Abstract The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

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