1
|
Yoshida H, Kinjo T, Washizu H. Numerical simulation method for Brownian particles dispersed in incompressible fluids. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.136809] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
2
|
Mizuta K, Ishii Y, Kim K, Matubayasi N. Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions. SOFT MATTER 2019; 15:4380-4390. [PMID: 31086871 DOI: 10.1039/c9sm00246d] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Through molecular dynamics simulations, we examined the hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius aHD was quantified from the Stokes-Einstein relation. The aHD value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, aHD is similar to the size of bare fullerene when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. A hydrodynamic long-time tail t-3/2 is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particle size. However, the VACF at shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of the VACF around the sound-propagation timescale over the particle size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.
Collapse
Affiliation(s)
- Keisuke Mizuta
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
| | | | | | | |
Collapse
|
3
|
Furukawa A, Tateno M, Tanaka H. Physical foundation of the fluid particle dynamics method for colloid dynamics simulation. SOFT MATTER 2018; 14:3738-3747. [PMID: 29700543 DOI: 10.1039/c8sm00189h] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Colloid dynamics is significantly influenced by many-body hydrodynamic interactions mediated by a suspending fluid. However, theoretical and numerical treatments of such interactions are extremely difficult. To overcome this situation, we developed a fluid particle dynamics (FPD) method [H. Tanaka and T. Araki, Phys. Rev. Lett., 2000, 35, 3523], which is based on two key approximations: (i) a colloidal particle is treated as a highly viscous particle and (ii) the viscosity profile is described by a smooth interfacial profile function. Approximation (i) makes our method free from the solid-fluid boundary condition, significantly simplifying the treatment of many-body hydrodynamic interactions while satisfying the incompressible condition without the Stokes approximation. Approximation (ii) allows us to incorporate an extra degree of freedom in a fluid, e.g., orientational order and concentration, as an additional field variable. Here, we consider two fundamental problems associated with these approximations. One is the introduction of thermal noise and the other is the incorporation of coupling of the colloid surface with an order parameter introduced into a fluid component, which is crucial when considering colloidal particles suspended in a complex fluid. Here, we show that our FPD method makes it possible to simulate colloid dynamics properly while including full hydrodynamic interactions, inertia effects, incompressibility, thermal noise, and additional degrees of freedom of a fluid, which may be relevant for wide applications in colloidal and soft matter science.
Collapse
Affiliation(s)
- Akira Furukawa
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
| | | | | |
Collapse
|
4
|
Wang H, Zang D, Li X, Geng X. Simulation of phase separation with temperature-dependent viscosity using lattice Boltzmann method. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:115. [PMID: 29274072 DOI: 10.1140/epje/i2017-11605-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 12/04/2017] [Indexed: 06/07/2023]
Abstract
This paper presents an exploration of the phase separation behavior and pattern formation in a binary fluid with temperature-dependent viscosity via a coupled lattice Boltzmann method (LBM). By introducing a viscosity-temperature relation into the LBM, the coupling effects of the viscosity-temperature coefficient [Formula: see text] , initial viscosity [Formula: see text] and thermal diffusion coefficient [Formula: see text] , on the phase separation were successfully described. The calculated results indicated that an increase in initial viscosity and viscosity-temperature coefficient, or a decrease in the thermal diffusion coefficient, can lead to the orientation of isotropic growth fronts over a wide range of viscosity. The results showed that droplet-type phase structures and lamellar phase structures with domain orientation parallel or perpendicular to the walls can be obtained in equilibrium by controlling the initial viscosity, thermal diffusivity, and the viscosity-temperature coefficient. Furthermore, the dataset was rearranged for growth kinetics of domain growth and thermal diffusion fronts in a plot by the spherically averaged structure factor and the ratio of separated and continuous phases. The analysis revealed two different temporal regimes: spinodal decomposition and domain growth stages, which further quantified the coupled effects of temperature and viscosity on the evolution of temperature-dependent phase separation. These numerical results provide guidance for setting optimum temperature ranges to obtain expected phase separation structures for systems with temperature-dependent viscosity.
Collapse
Affiliation(s)
- Heping Wang
- Functional Soft Matter & Materials Group, Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, 710129, Xi'an, China
| | - Duyang Zang
- Functional Soft Matter & Materials Group, Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, 710129, Xi'an, China
| | - Xiaoguang Li
- Functional Soft Matter & Materials Group, Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, 710129, Xi'an, China
| | - Xingguo Geng
- Functional Soft Matter & Materials Group, Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, 710129, Xi'an, China.
| |
Collapse
|
5
|
Fischer LP, Peter T, Holm C, de Graaf J. The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells. J Chem Phys 2015; 143:084107. [PMID: 26328818 DOI: 10.1063/1.4928502] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.
Collapse
Affiliation(s)
- Lukas P Fischer
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Toni Peter
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| | - Joost de Graaf
- Institute for Computational Physics (ICP), University of Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
| |
Collapse
|
6
|
Rezaei M, Azimian AR. Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion. Electrophoresis 2015; 36:2985-93. [PMID: 26456026 DOI: 10.1002/elps.201500320] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Revised: 09/11/2015] [Accepted: 09/12/2015] [Indexed: 11/07/2022]
Abstract
The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.
Collapse
Affiliation(s)
- Majid Rezaei
- Department of Mechanical Engineering, Isfahan University of technology, Isfahan, Iran
| | - Ahmad Reza Azimian
- Department of Mechanical Engineering, Isfahan University of technology, Isfahan, Iran
| |
Collapse
|
7
|
Ceratti DR, Obliger A, Jardat M, Rotenberg B, Dahirel V. Stochastic rotation dynamics simulation of electro-osmosis. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1037370] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Davide R. Ceratti
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
- Collège de France, UMR 7574, Chimie de la Matière Condensée de Paris
| | - Amaël Obliger
- Concrete Sustainability Hub, Department of Civil and Environmental Engineering, and MIT-CNRS Joint Laboratory, Massachusetts Institute of Technology , Cambridge, MA, United States
| | - Marie Jardat
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Benjamin Rotenberg
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| | - Vincent Dahirel
- Sorbonne Universités, UPMC Univ Paris 06, UMR PHENIX , Paris, France
- CNRS, UMR PHENIX , Paris, France
| |
Collapse
|
8
|
Zhou J, Schmid F. Computer simulations of single particles in external electric fields. SOFT MATTER 2015; 11:6728-6739. [PMID: 26238433 DOI: 10.1039/c5sm01485a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Applying electric fields is an attractive way to control and manipulate single particles or molecules, e.g., in lab-on-a-chip devices. However, the response of nanosize objects in electrolyte solution to external fields is far from trivial. It is the result of a variety of dynamical processes taking place in the ion cloud surrounding charged particles and in the bulk electrolyte, and it is governed by an intricate interplay of electrostatic and hydrodynamic interactions. Already systems composed of one single particle in electrolyte solution exhibit a complex dynamical behaviour. In this review, we discuss recent coarse-grained simulations that have been performed to obtain a molecular-level understanding of the dynamic and dielectric response of single particles and single macromolecules to external electric fields. We address both the response of charged particles to constant fields (DC fields), which can be characterized by an electrophoretic mobility, and the dielectric response of both uncharged and charged particles to alternating fields (AC fields), which is described by a complex polarizability. Furthermore, we give a brief survey of simulation algorithms and highlight some recent developments.
Collapse
Affiliation(s)
- Jiajia Zhou
- School of Chemistry & Enviroment, Center of Soft Matter Physics and its Application, Beihang University, Xueyuan Road 37, Beijing 100191, China.
| | | |
Collapse
|
9
|
Zhou J, Schmitz R, Dünweg B, Schmid F. Dynamic and dielectric response of charged colloids in electrolyte solutions to external electric fields. J Chem Phys 2013; 139:024901. [DOI: 10.1063/1.4812692] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
|
10
|
Zhou J, Schmid F. AC-field-induced polarization for uncharged colloids in salt solution: a dissipative particle dynamics simulation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:9848. [PMID: 23579586 DOI: 10.1140/epje/i2013-13033-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2012] [Accepted: 03/11/2013] [Indexed: 06/02/2023]
Abstract
We study the response of a spherical colloid under alternating electric fields (AC fields) by mesoscopic simulation method, accounting in full for hydrodynamic and electrostatic interactions. We focus on a special case of uncharged colloids. The main polarization mechanism is the "volume polarization", where ionic currents are deflected by the core of the uncharged colloid. Specifically, we compute the polarizability of a single colloid and systematically investigate the effect of AC field frequency and salt concentration. The simulation results are compared with predictions from classical Maxwell-Wagner theory and electrokinetic theory.
Collapse
Affiliation(s)
- Jiajia Zhou
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, D-55099 Mainz, Germany.
| | | |
Collapse
|
11
|
Zhou J, Schmid F. Dielectric response of nanoscopic spherical colloids in alternating electric fields: a dissipative particle dynamics simulation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464112. [PMID: 23114013 DOI: 10.1088/0953-8984/24/46/464112] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
We study the response of single nanosized spherical colloids in electrolyte solution to an alternating electric field (AC field) by computer simulations. We use a coarse-grained mesoscopic simulation approach that accounts in full for hydrodynamic and electrostatic interactions as well as for thermal fluctuations. The solvent is modeled as a fluid of single dissipative particle dynamics (DPD) beads, and the colloidal particle is modeled as a rigid body made of DPD beads. We compute the mobility and the polarizability of a single colloid and investigate systematically the effect of amplitude and frequency of the AC fields. Even though the thickness of the Debye layer is not 'thin' compared to the radius of the colloid, and the thermal fluctuations are significant, the results are in good agreement with the theoretical prediction of the Maxwell-Wagner-O'Konski theory, especially for uncharged colloids.
Collapse
Affiliation(s)
- Jiajia Zhou
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, Germany.
| | | |
Collapse
|
12
|
Morrone JA, Li J, Berne BJ. Interplay between Hydrodynamics and the Free Energy Surface in the Assembly of Nanoscale Hydrophobes. J Phys Chem B 2011; 116:378-89. [DOI: 10.1021/jp209568n] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joseph A. Morrone
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Jingyuan Li
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - B. J. Berne
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| |
Collapse
|
13
|
|
14
|
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
|
15
|
Chatterji A, Horbach J. The role of effective charges in the electrophoresis of highly charged colloids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:494102. [PMID: 21406768 DOI: 10.1088/0953-8984/22/49/494102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the variation of electrophoretic mobility μ of highly charged spherical colloidal macroions for varying surface charge density σ on the colloid using computer simulations of the primitive model for charged colloids. Hydrodynamic interactions between ions are incorporated by coupling the primitive model of charged colloids to the lattice Boltzmann model (LB) of the fluid. In the highly charged regime, the mobility μ of the colloid is known to decrease with the increase of bare charge Q of the colloid; the aim of this paper is to investigate the cause of this. We have identified that the two main factors contributing to the decrease of μ are counterion charge condensation on the highly charged colloid and an increase in effective friction of the macroion-counterion complex due to the condensed counterions. Thus the established O'Brien and White theory, which identified the dipolar force originating from distortion of the electric double layer as the cause of decreasing μ, seems to break down for the case of highly charged colloids with σ in the range of 30-400 µC cm (- 2). To arrive at our conclusions, we counted the number of counterions q0 moving along with the spherical macroion. We observe in our simulations that q0 increases with the increase of bare charge Q, such that the effective charge Qeff = Q - q0 remains approximately constant. Interestingly for our nanometer-sized charged colloid, we observe that, if surface charge density σ of the colloid is increased by decreasing the radius RM of the colloid but fixed bare charge Q, the effective charge Q - q0 decreases with the increase of σ. This behavior is qualitatively different when σ is increased by increasing Q keeping RM fixed. Our observations address a controversy about the effective charge of a strongly charged macroion: some studies claim that effective charge is independent of the bare charge (Alexander et al 1984 J. Chem. Phys. 80 5776; Trizac et al 2003 Langmuir 19 4027) whereas others claim that Qeff decreases with increasing bare charge Q (dos Santos 2009 J. Chem. Phys. 130 124110; Diehl et al 2004 J. Chem. Phys. 121 12100; Groot et al 1991 J. Chem. Phys. 95 9191) at relatively high values of σ.
Collapse
Affiliation(s)
- Apratim Chatterji
- Indian Institute of Science Education and Research (IISER), Pune-411008, India
| | | |
Collapse
|
16
|
Sané J, Padding JT, Louis AA. Hydrodynamics of confined colloidal fluids in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051402. [PMID: 19518451 DOI: 10.1103/physreve.79.051402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2008] [Indexed: 05/15/2023]
Abstract
We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two-dimensional colloidal disks in confined geometries. We calculate the velocity autocorrelation functions and observe the predicted t;{-1} long-time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the t;{-1} tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system. The Langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times.
Collapse
Affiliation(s)
- Jimaan Sané
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | | | | |
Collapse
|
17
|
Wang R, Wang JS, Liu GR, Han J, Chen YZ. Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse-grained hybrid molecular dynamics approach. J Comput Chem 2009; 30:505-13. [DOI: 10.1002/jcc.21081] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
|
18
|
Nakayama Y, Kim K, Yamamoto R. Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 26:361-368. [PMID: 19230114 DOI: 10.1140/epje/i2007-10332-y] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the "Smoothed Profile (SP) method" is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multicomponent fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.
Collapse
Affiliation(s)
- Y Nakayama
- Department of Chemical Engineering, Kyushu University, Fukuoka 819-0395, Japan.
| | | | | |
Collapse
|
19
|
Rex M, Löwen H. Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2008; 26:143-50. [PMID: 18324352 DOI: 10.1140/epje/i2007-10274-4] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2007] [Accepted: 01/23/2008] [Indexed: 05/18/2023]
Abstract
The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.
Collapse
Affiliation(s)
- M Rex
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, Düsseldorf, Germany.
| | | |
Collapse
|
20
|
Capuani F, Pagonabarraga I, Frenkel D. Lattice-Boltzmann simulation of the sedimentation of charged disks. J Chem Phys 2007; 124:124903. [PMID: 16599721 DOI: 10.1063/1.2178804] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal surface and charge, we can clarify the effect of the particle shape on the sedimentation process. We find that disks and spheres exhibit a different dependence of the sedimentation velocity on the Debye screening length. An analysis of the behavior of highly charged disks (beyond the scope of the linearized Poisson-Boltzmann equation) shows that, in that regime, the charge dependence of the sedimentation velocity of disks and spheres is similar. This suggests that, at high charge, the effective hydrodynamic shape of the disks becomes more spherical.
Collapse
Affiliation(s)
- Fabrizio Capuani
- FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
| | | | | |
Collapse
|
21
|
Chatterji A, Horbach J. Electrophoretic properties of highly charged colloids: A hybrid molecular dynamics∕lattice Boltzmann simulation study. J Chem Phys 2007; 126:064907. [PMID: 17313244 DOI: 10.1063/1.2431174] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.
Collapse
Affiliation(s)
- Apratim Chatterji
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
| | | |
Collapse
|
22
|
Padding JT, Louis AA. Hydrodynamic interactions and Brownian forces in colloidal suspensions: coarse-graining over time and length scales. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031402. [PMID: 17025630 DOI: 10.1103/physreve.74.031402] [Citation(s) in RCA: 240] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2006] [Indexed: 05/12/2023]
Abstract
We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.
Collapse
Affiliation(s)
- J T Padding
- Department of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | |
Collapse
|
23
|
Krouskop PE, Garrison J, Gedeon PC, Madura JD. A novel hybrid simulation for study of multiscale phenomena. MOLECULAR SIMULATION 2006. [DOI: 10.1080/08927020600779368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
24
|
Kim K, Nakayama Y, Yamamoto R. Direct numerical simulations of electrophoresis of charged colloids. PHYSICAL REVIEW LETTERS 2006; 96:208302. [PMID: 16803214 DOI: 10.1103/physrevlett.96.208302] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2006] [Indexed: 05/10/2023]
Abstract
We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier-Stokes equations so that the electrohydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters; however, our simulation predicts notable deviations in the case of dense dispersions.
Collapse
Affiliation(s)
- Kang Kim
- Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
| | | | | |
Collapse
|