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Tan Z, Calandrini V, Dhont JKG, Nägele G, Winkler RG. Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach. SOFT MATTER 2021; 17:7978-7990. [PMID: 34378623 DOI: 10.1039/d1sm00541c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.
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Affiliation(s)
- Zihan Tan
- Biomacromolecular Systems and Processes, Institute of Biological Information Processing, Forschungszentrum Jülich, 52428 Jülich, Germany.
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Radhakrishnan R, Farokhirad S, Eckmann DM, Ayyaswamy PS. Nanoparticle transport phenomena in confined flows. ADVANCES IN HEAT TRANSFER 2019; 51:55-129. [PMID: 31692964 DOI: 10.1016/bs.aiht.2019.08.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.
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Affiliation(s)
- Ravi Radhakrishnan
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, United States.,Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, United States
| | - Samaneh Farokhirad
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, United States
| | - David M Eckmann
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, United States.,Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA, United States
| | - Portonovo S Ayyaswamy
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, United States.,Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA, United States
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3
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Daddi-Moussa-Ider A, Lisicki M, Gekle S, Menzel AM, Löwen H. Hydrodynamic coupling and rotational mobilities near planar elastic membranes. J Chem Phys 2018; 149:014901. [DOI: 10.1063/1.5032304] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
- Biofluid Simulation and Modeling, Theoretische Physik, Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
| | - Maciej Lisicki
- Department of Applied Mathematics and Theoretical Physics, Wilberforce Rd, Cambridge CB3 0WA, United Kingdom
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Theoretische Physik, Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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4
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Dumazer G, Flekkøy E, Renard F, Angheluta L. Transient anomalous diffusion regimes in reversible adsorbing systems. Phys Rev E 2018; 96:042106. [PMID: 29347621 DOI: 10.1103/physreve.96.042106] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2017] [Indexed: 11/07/2022]
Abstract
A solvable, minimal model of diffusion in the presence of a reversible adsorption site is investigated. We show that the diffusive particles are influenced by the adsorbing site on transient times when they have anomalous subdiffusive behavior. However, the particle dispersion law crosses over to the normal diffusive regime on asymptotically long times. The subdiffusive regime is characterized by a t^{1/4} transient scaling with the same exponent as for the irreversible adsorption. On this transient time scale dominated by particle adsorption, there is a depletion of particles near the adsorbing site, and the typical width of the depletion zone grows in time as t^{1/4} with the same exponent as the subdiffusive dispersion. We show that having a nonzero desorption probability for the adsorbed particles produces a crossover towards normal diffusion on time scales larger than a characteristic reactive time, which we show scales with diffusivity and the adsorption site reactivity.
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Affiliation(s)
- Guillaume Dumazer
- Porous Media Laboratory, Department of Physics, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway
| | - Eirik Flekkøy
- Porous Media Laboratory, Department of Physics, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway
| | - François Renard
- Department of Geosciences, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway
| | - Luiza Angheluta
- Porous Media Laboratory, Department of Physics, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway
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Hammond AP, Corwin EI. Direct measurement of the ballistic motion of a freely floating colloid in Newtonian and viscoelastic fluids. Phys Rev E 2018; 96:042606. [PMID: 29347607 DOI: 10.1103/physreve.96.042606] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2017] [Indexed: 11/07/2022]
Abstract
A thermal colloid suspended in a liquid will transition from a short-time ballistic motion to a long-time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long-time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a dense fluid. Measurements of the functional form of the ballistic-to-diffusive transition provide direct measurements of the temperature, viscosity, and tracer radius. We likewise measure the motion in a viscoelastic Maxwell fluid and find a significant disagreement between the theoretical asymptotic behavior and our measured values of the microscopic properties of the fluid. We observe a greatly increased effective mass for a freely moving particle and a decreased plateau modulus.
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Affiliation(s)
- Andrew P Hammond
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Eric I Corwin
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
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Yu HY, Eckmann DM, Ayyaswamy PS, Radhakrishnan R. Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle. Proc Math Phys Eng Sci 2016; 472:20160397. [PMID: 28119544 PMCID: PMC5247520 DOI: 10.1098/rspa.2016.0397] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2016] [Accepted: 11/21/2016] [Indexed: 12/14/2022] Open
Abstract
The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959-2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.
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Affiliation(s)
- Hsiu-Yu Yu
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - David M. Eckmann
- Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Portonovo S. Ayyaswamy
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ravi Radhakrishnan
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
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Abstract
We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.
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Affiliation(s)
- Xin Bian
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
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Kuhnhold A, Paul W. Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042601. [PMID: 25974519 DOI: 10.1103/physreve.91.042601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Indexed: 06/04/2023]
Abstract
We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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9
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Híjar H. Harmonically bound Brownian motion in fluids under shear: Fokker-Planck and generalized Langevin descriptions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022139. [PMID: 25768490 DOI: 10.1103/physreve.91.022139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2014] [Indexed: 06/04/2023]
Abstract
We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques.
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Affiliation(s)
- Humberto Híjar
- Grupo de Sistemas Inteligentes, Facultad de Ingeniería, Universidad La Salle, Benjamín Franklin 47, 06140, D. F., México
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10
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Kuhnhold A, Paul W. Temperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation. J Chem Phys 2014; 141:124907. [DOI: 10.1063/1.4896151] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Kuhnhold A, Paul W. Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022602. [PMID: 25215751 DOI: 10.1103/physreve.90.022602] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Indexed: 06/03/2023]
Abstract
We present a molecular dynamics simulation study of the possibility of performing a microrheological analysis of a polymer melt by following the Brownian motion of a dispersed nanoparticle. We study the influence of the size of the nanoparticle, taken to be comparable to the radius of gyration of the chains, and of the strength of the interaction between the nanoparticle and the repeat units of the polymer chains. The influence of the presence of the nanoparticle on the melt mechanical behavior is analyzed, and the importance of effects of different levels of hydrodynamic analysis on the frequency-dependent dynamic shear modulus derived from the particle motion is worked out.
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Affiliation(s)
- A Kuhnhold
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
| | - W Paul
- Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, 06099 Halle (Saale), Germany
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12
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Kheifets S, Simha A, Melin K, Li T, Raizen MG. Observation of Brownian Motion in Liquids at Short Times: Instantaneous Velocity and Memory Loss. Science 2014; 343:1493-6. [DOI: 10.1126/science.1248091] [Citation(s) in RCA: 161] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Simon Kheifets
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Akarsh Simha
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Kevin Melin
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Tongcang Li
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Mark G. Raizen
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
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13
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Felderhof BU. Loss of momentum in a viscous compressible fluid due to no-slip boundary condition at one or two planar walls. J Chem Phys 2012; 133:074707. [PMID: 20726663 DOI: 10.1063/1.3473932] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The loss of fluid momentum due to friction at one or two planar walls bounding a viscous compressible fluid is studied as a function of time for the situation where the flow is due to a sudden impulse applied at a selected point in initially quiescent fluid. The no-slip condition is assumed to hold at the walls, and the initial impulse is assumed to be sufficiently small, so that the linearized Navier-Stokes equations may be used. When the initial impulse is directed parallel to the walls the time-dependent total fluid momentum is independent of compressibility and volume viscosity. For initial impulse directed perpendicular to the walls an echoing effect, corresponding to sound bouncing between the two walls, is observed.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
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14
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Felderhof BU. Spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall. J Chem Phys 2012; 136:144701. [PMID: 22502537 DOI: 10.1063/1.3701618] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall is calculated from an approximate result for the Fourier transform of the velocity autocorrelation function. Both a no-slip and a perfect slip boundary condition at the wall are considered. In both cases at low frequency the calculated spectrum differs markedly from recent experimental data. It is suggested that a partial slip boundary condition with a frequency-dependent slip coefficient may explain the experimental results.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
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15
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Felderhof BU. Hydrodynamic force on a particle oscillating in a viscous fluid near a wall with dynamic partial-slip boundary condition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046303. [PMID: 22680570 DOI: 10.1103/physreve.85.046303] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2012] [Indexed: 06/01/2023]
Abstract
The hydrodynamic force on a particle oscillating in a viscous fluid near a wall with partial-slip boundary condition is studied on the basis of the linearized Navier-Stokes equations. Both incompressible and compressible fluids are considered. It is assumed that the slip length characterizing the partial-slip boundary condition depends on frequency. The consequences of this assumption for the spectrum of Brownian motion near a wall are investigated and compared with a recent experiment.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen University, Aachen, Germany.
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16
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Belushkin M, Winkler RG, Foffi G. Backtracking of Colloids: A Multiparticle Collision Dynamics Simulation Study. J Phys Chem B 2011; 115:14263-8. [DOI: 10.1021/jp205084u] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M. Belushkin
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne
| | - R. G. Winkler
- Theoretical Soft-Matter and Biophysics, Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich
| | - G. Foffi
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne
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Frydel D, Diamant H. Long-range dynamic correlations in confined suspensions. PHYSICAL REVIEW LETTERS 2010; 104:248302. [PMID: 20867341 DOI: 10.1103/physrevlett.104.248302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2010] [Indexed: 05/29/2023]
Abstract
Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice Boltzmann simulations, we show that the hydrodynamic screening is qualitatively modified when the time-dependent response and finite compressibility of the host liquid are taken into account. Diffusive compression modes in the confined liquid cause the particles to have velocity correlations of unbounded range, whose amplitude decays with time only as t(-3/2).
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Affiliation(s)
- Derek Frydel
- Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
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Erbaş A, Podgornik R, Netz RR. Viscous compressible hydrodynamics at planes, spheres and cylinders with finite surface slip. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 32:147-164. [PMID: 20632199 DOI: 10.1140/epje/i2010-10610-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2009] [Accepted: 06/02/2010] [Indexed: 05/29/2023]
Abstract
We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency omega approximately c2rho0/eta, with c the speed of sound, rho0 the fluid density and eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.
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Affiliation(s)
- A Erbaş
- Physics Department, Technical University Munich, Garching, Germany.
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19
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Franosch T, Jeney S. Persistent correlation of constrained colloidal motion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031402. [PMID: 19391939 DOI: 10.1103/physreve.79.031402] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2008] [Indexed: 05/26/2023]
Abstract
We have investigated the motion of a single optically trapped colloidal particle close to a limiting wall at time scales where the inertia of the surrounding fluid plays a significant role. The velocity autocorrelation function exhibits a complex interplay due to the momentum relaxation of the particle, the vortex diffusion in the fluid, the obstruction of flow close to the interface, and the harmonic restoring forces due to the optical trap. We show that already a weak trapping force has a significant impact on the velocity autocorrelation function C(t)=v(t)v(0) at times where the hydrodynamic memory leads to an algebraic decay. The long-time behavior for the motion parallel and perpendicular to the wall is derived analytically and compared to numerical results. Then, we discuss the power spectral densities of the displacement and provide simple interpolation formulas. The theoretical predictions are finally compared to recent experimental observations.
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Affiliation(s)
- Thomas Franosch
- Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany.
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20
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Felderhof BU. Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls. J Chem Phys 2006; 124:054111. [PMID: 16468855 DOI: 10.1063/1.2165199] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The diffusion tensor and velocity correlation function of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls are calculated in point approximation. The fluid is assumed to satisfy stick boundary conditions at the walls. It is found that the velocity correlation function decays asymptotically with a negative t(-2) long-time tail due to coupling to overdamped sound waves. The coefficient of the long-time tail is calculated and shown to be independent of fluid viscosity.
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Affiliation(s)
- B U Felderhof
- Institut für Theoretische Physik A, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany.
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21
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Bickel T. Brownian motion near a liquid-like membrane. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 20:379-85. [PMID: 16932854 DOI: 10.1140/epje/i2006-10026-0] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2006] [Accepted: 07/27/2006] [Indexed: 05/11/2023]
Abstract
The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic interactions creates memory effects in the diffusion process. The random motion of the particle is then shown to cross over from a "bulk" to a "surface" diffusive mode, in a way that crucially depends on the elastic properties of the interface.
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Affiliation(s)
- T Bickel
- CPMOH, Université Bordeaux 1 - CNRS (UMR 5798), 351 cours de la Libération, 33405, Talence, France.
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