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Jung D, Uttinger MJ, Malgaretti P, Peukert W, Walter J, Harting J. Hydrodynamic simulations of sedimenting dilute particle suspensions under repulsive DLVO interactions. SOFT MATTER 2022; 18:2157-2167. [PMID: 35212700 DOI: 10.1039/d1sm01294k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope K of the concentration-dependent sedimentation velocity and the range χ of the electrostatic repulsion normalized by the average particle-particle distance. When χ → 0, the particles are too far away from each other to interact electrostatically and K = 6.55 as predicted by the theory of Batchelor. As χ increases, K likewise increases as if the particle radius increased in proportion to χ up to a maximum around χ = 0.4. Over the range χ = 0.4-1, K relaxes exponentially to a concentration-dependent constant consistent with known results for ordered particle distributions. Meanwhile the radial distribution function transitions from a disordered gas-like to a liquid-like form. Power law fits to the concentration-dependent sedimentation velocity similarly yield a simple master curve for the exponent as a function of χ, with a step-like transition from 1 to 1/3 centered around χ = 0.6.
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Affiliation(s)
- David Jung
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
| | - Maximilian Johannes Uttinger
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander Universität Erlangen-Nürnberg, Haberstraße 9a, 91058 Erlangen, Germany
| | - Paolo Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany
| | - Wolfgang Peukert
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander Universität Erlangen-Nürnberg, Haberstraße 9a, 91058 Erlangen, Germany
| | - Johannes Walter
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander Universität Erlangen-Nürnberg, Haberstraße 9a, 91058 Erlangen, Germany
| | - Jens Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Straße 248, 90429 Nürnberg, Germany
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
- Department of Chemical and Biological Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany.
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2
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Bárdfalvy D, Anjum S, Nardini C, Morozov A, Stenhammar J. Symmetric Mixtures of Pusher and Puller Microswimmers Behave as Noninteracting Suspensions. PHYSICAL REVIEW LETTERS 2020; 125:018003. [PMID: 32678625 DOI: 10.1103/physrevlett.125.018003] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as "pushers" and "pullers," display qualitatively different collective behaviors: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher-puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction χ of pullers is increased and disappears for χ≥0.5. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1∶1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer-swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1∶1 pusher-puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.
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Affiliation(s)
- Dóra Bárdfalvy
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Shan Anjum
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Cesare Nardini
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Joakim Stenhammar
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
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3
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Denniston C. Theory and simulation of objects in liquid crystals. ADVANCES IN PHYSICS: X 2020. [DOI: 10.1080/23746149.2020.1806728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022] Open
Affiliation(s)
- Colin Denniston
- Department of Applied Mathematics and Department of Physics and Astronomy, The University of Western Ontario, London, ON, Canada
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4
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Bárdfalvy D, Nordanger H, Nardini C, Morozov A, Stenhammar J. Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence. SOFT MATTER 2019; 15:7747-7756. [PMID: 31393504 DOI: 10.1039/c9sm00774a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 106) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.
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Affiliation(s)
- Dóra Bárdfalvy
- Division of Physical Chemistry, Lund University, Box 124, S-221 00 Lund, Sweden.
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Carenza LN, Gonnella G, Lamura A, Negro G, Tiribocchi A. Lattice Boltzmann methods and active fluids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:81. [PMID: 31250142 DOI: 10.1140/epje/i2019-11843-6] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 05/24/2019] [Indexed: 05/24/2023]
Abstract
We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
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Affiliation(s)
- Livio Nicola Carenza
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy.
| | - Antonio Lamura
- Istituto Applicazioni Calcolo, CNR, Via Amendola 122/D, 70126, Bari, Italy
| | - Giuseppe Negro
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Adriano Tiribocchi
- Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, 00161, Roma, Italy
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6
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Miocchi P, Derreumaux P, Sterpone F, Melchionna S. Mesoscale biosimulations within a unified framework: from proteins to plasmids. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2018.1560439] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Paolo Miocchi
- CNR-ISC, Institute for Complex Systems, Consiglio Nazionale delle Ricerche, Rome, Italy
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS Université Denis Diderot, Sorbonne Paris Cité, IBPC, Paris, France
- IUF, Institut Universitaire de France, Boulevard Saint Michel, Paris, France
| | - Fabio Sterpone
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS Université Denis Diderot, Sorbonne Paris Cité, IBPC, Paris, France
| | - Simone Melchionna
- CNR-ISC, Institute for Complex Systems, Consiglio Nazionale delle Ricerche, Rome, Italy
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7
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Schwarzendahl FJ, Mazza MG. Maximum in density heterogeneities of active swimmers. SOFT MATTER 2018; 14:4666-4678. [PMID: 29717736 DOI: 10.1039/c7sm02301d] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.
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Affiliation(s)
- Fabian Jan Schwarzendahl
- Max-Planck-Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.
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8
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Patronis A, Richardson RA, Schmieschek S, Wylie BJN, Nash RW, Coveney PV. Modeling Patient-Specific Magnetic Drug Targeting Within the Intracranial Vasculature. Front Physiol 2018; 9:331. [PMID: 29725303 PMCID: PMC5917293 DOI: 10.3389/fphys.2018.00331] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Accepted: 03/16/2018] [Indexed: 11/13/2022] Open
Abstract
Drug targeting promises to substantially enhance future therapies, for example through the focussing of chemotherapeutic drugs at the site of a tumor, thus reducing the exposure of healthy tissue to unwanted damage. Promising work on the steering of medication in the human body employs magnetic fields acting on nanoparticles made of paramagnetic materials. We develop a computational tool to aid in the optimization of the physical parameters of these particles and the magnetic configuration, estimating the fraction of particles reaching a given target site in a large patient-specific vascular system for different physiological states (heart rate, cardiac output, etc.). We demonstrate the excellent computational performance of our model by its application to the simulation of paramagnetic-nanoparticle-laden flows in a circle of Willis geometry obtained from an MRI scan. The results suggest a strong dependence of the particle density at the target site on the strength of the magnetic forcing and the velocity of the background fluid flow.
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Affiliation(s)
- Alexander Patronis
- Centre for Computational Science, University College London, London, United Kingdom
| | - Robin A Richardson
- Centre for Computational Science, University College London, London, United Kingdom
| | | | - Brian J N Wylie
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - Rupert W Nash
- Edinburgh Parallel Computing Centre, University of Edinburgh, Edinburgh, United Kingdom
| | - Peter V Coveney
- Centre for Computational Science, University College London, London, United Kingdom
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9
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Asta AJ, Levesque M, Vuilleumier R, Rotenberg B. Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions. Phys Rev E 2017; 95:061301. [PMID: 28709218 DOI: 10.1103/physreve.95.061301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2017] [Indexed: 11/07/2022]
Abstract
We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t^{-3/2} hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.
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Affiliation(s)
- Adelchi J Asta
- Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 8234 PHENIX, 4 Place Jussieu, 75005 Paris, France
| | - Maximilien Levesque
- Ecole Normale Supérieure, PSL Research University, UPMC Univ Paris 06, CNRS, Département de Chimie, PASTEUR, 24 rue Lhomond, 75005 Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, ENS, CNRS, PASTEUR, 75005 Paris, France
| | - Rodolphe Vuilleumier
- Ecole Normale Supérieure, PSL Research University, UPMC Univ Paris 06, CNRS, Département de Chimie, PASTEUR, 24 rue Lhomond, 75005 Paris, France.,Sorbonne Universités, UPMC Univ Paris 06, ENS, CNRS, PASTEUR, 75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 8234 PHENIX, 4 Place Jussieu, 75005 Paris, France.,Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, France
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10
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Stenhammar J, Nardini C, Nash RW, Marenduzzo D, Morozov A. Role of Correlations in the Collective Behavior of Microswimmer Suspensions. PHYSICAL REVIEW LETTERS 2017; 119:028005. [PMID: 28753351 DOI: 10.1103/physrevlett.119.028005] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2017] [Indexed: 06/07/2023]
Abstract
In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.
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Affiliation(s)
- Joakim Stenhammar
- Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Rupert W Nash
- EPCC, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Alexander Morozov
- SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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11
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de Graaf J, Stenhammar J. Lattice-Boltzmann simulations of microswimmer-tracer interactions. Phys Rev E 2017; 95:023302. [PMID: 28297968 DOI: 10.1103/physreve.95.023302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Indexed: 06/06/2023]
Abstract
Hydrodynamic interactions in systems composed of self-propelled particles, such as swimming microorganisms and passive tracers, have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force-counterforce-based lattice-Boltzmann (LB) algorithm [De Graaf et al., J. Chem. Phys. 144, 134106 (2016)JCPSA60021-960610.1063/1.4944962] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.
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Affiliation(s)
- Joost de Graaf
- SUPA, School of Physics and Astronomy, University of Edinburgh, King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Joakim Stenhammar
- Division of Physical Chemistry, Lund University, Box 124, S-221 00 Lund, Sweden
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12
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Pandey A, Sunil Kumar PB, Adhikari R. Flow-induced nonequilibrium self-assembly in suspensions of stiff, apolar, active filaments. SOFT MATTER 2016; 12:9068-9076. [PMID: 27774542 DOI: 10.1039/c6sm02104b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Active bodies in viscous fluids interact hydrodynamically through self-generated flows. A stiff, apolar, active filament generates symmetric fluid flow around it and thus cannot self-propel. Here we study the mobility and aggregation induced by hydrodynamic flow in a suspension of stiff, apolar, active filaments. We consider two types of active filaments, with those producing extensile or contractile flows along their long axis. Lateral hydrodynamic attractions in extensile filaments lead, independent of the volume fraction, to anisotropic aggregates which translate and rotate ballistically. Lateral hydrodynamic repulsions in contractile filaments lead to microstructured states, where the degree of clustering increases with the volume fraction and the filament motion is always diffusive. Our results demonstrate that the interplay between active hydrodynamic flows and anisotropic excluded volume interactions provides a generic nonequilibrium mechanism for hierarchical self-assembly of active soft matter.
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Affiliation(s)
- Ankita Pandey
- Indian Institute of Technology, Madras, Chennai 600036, India
| | - P B Sunil Kumar
- Indian Institute of Technology, Madras, Chennai 600036, India
| | - R Adhikari
- The Institute of Mathematical Sciences, CIT Campus, Chennai 600113, India.
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13
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de Graaf J, Menke H, Mathijssen AJTM, Fabritius M, Holm C, Shendruk TN. Lattice-Boltzmann hydrodynamics of anisotropic active matter. J Chem Phys 2016; 144:134106. [DOI: 10.1063/1.4944962] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Joost de Graaf
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Henri Menke
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | | | - Marc Fabritius
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Tyler N. Shendruk
- The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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14
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Español P, Donev A. Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics. J Chem Phys 2015; 143:234104. [DOI: 10.1063/1.4936775] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Aleksandar Donev
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
- Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA
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15
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Belardinelli D, Sbragaglia M, Biferale L, Gross M, Varnik F. Fluctuating multicomponent lattice Boltzmann model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023313. [PMID: 25768641 DOI: 10.1103/physreve.91.023313] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2014] [Indexed: 06/04/2023]
Abstract
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
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Affiliation(s)
- D Belardinelli
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Sbragaglia
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - L Biferale
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Gross
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - F Varnik
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
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16
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van der Sman R, Meinders M. Mesoscale models of dispersions stabilized by surfactants and colloids. Adv Colloid Interface Sci 2014; 211:63-76. [PMID: 24980050 DOI: 10.1016/j.cis.2014.06.004] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2014] [Revised: 06/04/2014] [Accepted: 06/05/2014] [Indexed: 10/25/2022]
Abstract
In this paper we discuss and give an outlook on numerical models describing dispersions, stabilized by surfactants and colloidal particles. Examples of these dispersions are foams and emulsions. In particular, we focus on the potential of the diffuse interface models based on a free energy approach, which describe dispersions with the surface-active agent soluble in one of the bulk phases. The free energy approach renders thermodynamic consistent models with realistic sorption isotherms and adsorption kinetics. The free energy approach is attractive because of its ability to describe highly complex dispersions, such as emulsions stabilized by ionic surfactants, or surfactant mixtures and dispersions with surfactant micelles. We have classified existing numerical methods into classes, using either a Eulerian or a Lagrangian representation for fluid and for the surfactant/colloid. A Eulerian representation gives a more coarse-grained, mean field description of the surface-active agent, while a Lagrangian representation can deal with steric effects and larger complexity concerning geometry and (amphiphilic) wetting properties of colloids and surfactants. However, the similarity between the description of wetting properties of both Eulerian and Lagrangian models allows for the development of hybrid Eulerian/Lagrangian models having advantages of both representations.
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17
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Papenkort S, Voigtmann T. Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations. J Chem Phys 2014; 140:164507. [DOI: 10.1063/1.4872219] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Delong S, Usabiaga FB, Delgado-Buscalioni R, Griffith BE, Donev A. Brownian dynamics without Green's functions. J Chem Phys 2014; 140:134110. [DOI: 10.1063/1.4869866] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Thampi SP, Adhikari R, Govindarajan R. Do liquid drops roll or slide on inclined surfaces? LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:3339-3346. [PMID: 23414059 DOI: 10.1021/la3050658] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analyzed by decomposing the gradient of the velocity inside the droplet into a shear and a residual flow. This decomposition helps in distinguishing sliding versus rolling motion of the drop. Our detailed study confirms intuition, in that rolling motion dominates as the droplet shape approaches a circle, and the viscosity contrast between the droplet and the ambient fluid becomes large. As a consequence of kinematics, the amount of rotation in a general droplet shape follows a universal curve characterized by geometry, and independent of Bond number, surface inclination and equilibrium contact angle, but determined by the slip length and viscosity contrast. Our results open the way toward a rational design of droplet-surface properties, both when rolling motion is desirable (as in self-cleaning hydrophobic droplets) and when it must be prevented (as in insecticide sprays on leaves).
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Affiliation(s)
- Sumesh P Thampi
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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20
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Jayaraman G, Ramachandran S, Ghose S, Laskar A, Bhamla MS, Kumar PBS, Adhikari R. Autonomous motility of active filaments due to spontaneous flow-symmetry breaking. PHYSICAL REVIEW LETTERS 2012; 109:158302. [PMID: 23102372 DOI: 10.1103/physrevlett.109.158302] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2012] [Indexed: 06/01/2023]
Abstract
We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry, can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles, or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment.
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Affiliation(s)
- Gayathri Jayaraman
- The Institute of Mathematical Sciences, CIT Campus, Chennai 600113, India
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21
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Burgener T, Kadau D, Herrmann HJ. Clustering of inelastic soft spheres in homogeneous turbulence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036321. [PMID: 23031027 DOI: 10.1103/physreve.86.036321] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2012] [Indexed: 06/01/2023]
Abstract
In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.
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Affiliation(s)
- Thomas Burgener
- Institute for Building Materials, ETH Zurich, 8093 Zürich, Switzerland.
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22
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Thampi SP, Pagonabarraga I, Adhikari R. Lattice-Boltzmann-Langevin simulations of binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:046709. [PMID: 22181309 DOI: 10.1103/physreve.84.046709] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Revised: 09/15/2011] [Indexed: 05/31/2023]
Abstract
We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.
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Affiliation(s)
- Sumesh P Thampi
- Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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23
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Ollila STT, Denniston C, Karttunen M, Ala-Nissila T. Fluctuating lattice-Boltzmann model for complex fluids. J Chem Phys 2011; 134:064902. [DOI: 10.1063/1.3544360] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Jafari S, Yamamoto R, Rahnama M. Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:026702. [PMID: 21405925 DOI: 10.1103/physreve.83.026702] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2010] [Revised: 12/08/2010] [Indexed: 05/30/2023]
Abstract
We developed a simulation scheme based on the coupling of the lattice-Boltzmann method with the smoothed-profile method (SPM) to predict the dynamic behavior of colloidal dispersions. The SPM provides a coupling scheme between continuum fluid dynamics and rigid-body dynamics through a smoothed profile of the fluid-particle interface. In this approach, the flow is computed on fixed Eulerian grids which are also used for the particles. Owing to the use of the same grids for simulation of fluid flow and particles, this method is highly efficient. Furthermore, an external boundary is used to impose the no-slip boundary condition at the fluid-particle interface. In addition, the operations in the present method are local; it can be easily programmed for parallel machines. The methodology is validated by comparing with previously published data.
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Affiliation(s)
- Saeed Jafari
- Department of Petroleum engineering, Shahid Bahonar University of Kerman, Kerman, Iran.
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25
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Gross M, Moradi N, Zikos G, Varnik F. Shear stress in nonideal fluid lattice Boltzmann simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:017701. [PMID: 21405797 DOI: 10.1103/physreve.83.017701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2010] [Indexed: 05/30/2023]
Abstract
The viscous stress in nonideal fluid lattice Boltzmann methods is investigated theoretically and by simulations. Three representative liquid-gas models are compared in a steady-state situation, where an analytical expression for the viscous stress is available. It is shown that, in the presence of nonideal fluid interactions or strong body forces, the accuracy of the computed viscous stress depends strongly on the underlying model.
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Affiliation(s)
- Markus Gross
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Stiepeler Strasse 129, D-44801 Bochum, Germany.
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26
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Nash RW, Adhikari R, Tailleur J, Cates ME. Run-and-tumble particles with hydrodynamics: sedimentation, trapping, and upstream swimming. PHYSICAL REVIEW LETTERS 2010; 104:258101. [PMID: 20867416 DOI: 10.1103/physrevlett.104.258101] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2009] [Indexed: 05/29/2023]
Abstract
We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required.
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Affiliation(s)
- R W Nash
- SUPA, School of Physics, University of Edinburgh, JCMB Kings Buildings, Edinburgh EH9 3JZ, United Kingdom
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Usta OB, Perchak D, Clarke A, Yeomans JM, Balazs AC. Shear and extensional deformation of droplets containing polymers and nanoparticles. J Chem Phys 2009; 130:234905. [DOI: 10.1063/1.3153922] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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