1
|
Viot P, Page G, Barré C, Talbot J. Weak clogging in constricted channel flow. Phys Rev E 2022; 105:014604. [PMID: 35193281 DOI: 10.1103/physreve.105.014604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 12/16/2021] [Indexed: 06/14/2023]
Abstract
We investigate simple models of a monodisperse system of soft, frictionless disks flowing through a two-dimensional microchannel in the presence of a single or a double constriction using Brownian dynamics simulation. After a transient time, a stationary state is observed with an increase in particle density before the constriction and a depletion after it. For a constriction width to particle diameter ratio of less than 3, the mean particle velocity is reduced compared to the unimpeded flow and it falls to zero for ratios of less than 1. At low temperatures, the particle mean velocity may vary nonmonotonically with the constriction width. The associated intermittent behavior is due to the formation of small arches of particles with a finite lifetime. The distribution of the interparticle exit times rises rapidly at short times followed by an exponential decay with a large characteristic time, while the cascade size distribution displays prominent peaks for specific cluster sizes. Although the dependence of the mean velocity on the separation of two constrictions is not simple, the mean flow velocity of a system with a single constriction provides an upper envelope for the system with two constrictions. We also examine the orientation of the leading pair of particles in front of the constriction(s). With a single constriction in the intermittent regime, there is a strong preference for the leading pair to be orientated perpendicular to the flow. When two constrictions are present, orientations parallel to the flow are much more likely at the second constriction.
Collapse
Affiliation(s)
- Pascal Viot
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4, place Jussieu, 75005 Paris, France
| | - Gregory Page
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4, place Jussieu, 75005 Paris, France
| | - Chloé Barré
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4, place Jussieu, 75005 Paris, France
| | - Julian Talbot
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS UMR 7600, 4, place Jussieu, 75005 Paris, France
| |
Collapse
|
2
|
Goh S, Wittmann R, Menzel AM, Löwen H. Classical density functional theory for a two-dimensional isotropic ferrogel model with labeled particles. Phys Rev E 2019; 100:012605. [PMID: 31499838 DOI: 10.1103/physreve.100.012605] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Indexed: 01/30/2023]
Abstract
In this study, we formulate a density functional theory (DFT) for systems of labeled particles, considering a two-dimensional bead-spring lattice with a magnetic dipole on every bead as a model for ferrogels. On the one hand, DFT has been widely studied to investigate fluidlike states of materials, in which constituent particles are not labeled as they can exchange their positions without energy cost. On the other hand, in ferrogels consisting of magnetic particles embedded in elastic polymer matrices, the particles are labeled by their positions as their neighbors do not change over time. We resolve such an issue of particle labeling, introducing a mapping of the elastic interaction mediated by springs onto a pairwise additive interaction (pseudosprings) between unlabeled particles. We further investigate magnetostriction and changes in the elastic constants under altered magnetic interactions employing the pseudospring potential. It is revealed that there are two different response scenarios in the mechanical properties of the dipole-spring systems: While systems at low packing fractions are hardened as the magnetic moments increase in magnitude, at high packing fractions softening due to diminishing effects from the steric force, associated with increases in the volume, is observed. The validity of the theory is also verified by Monte Carlo simulations with both real springs and pseudosprings. We expect that our DFT approach may promote our understanding of materials with particle inclusions.
Collapse
Affiliation(s)
- Segun Goh
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| |
Collapse
|
3
|
Tarama S, Egelhaaf SU, Löwen H. Traveling band formation in feedback-driven colloids. Phys Rev E 2019; 100:022609. [PMID: 31574772 DOI: 10.1103/physreve.100.022609] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Indexed: 06/10/2023]
Abstract
Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory. Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems.
Collapse
Affiliation(s)
- Sonja Tarama
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| |
Collapse
|
4
|
Stuhlmüller NCX, Eckert T, de Las Heras D, Schmidt M. Structural Nonequilibrium Forces in Driven Colloidal Systems. PHYSICAL REVIEW LETTERS 2018; 121:098002. [PMID: 30230856 DOI: 10.1103/physrevlett.121.098002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Revised: 07/13/2018] [Indexed: 06/08/2023]
Abstract
We identify a structural one-body force field that sustains spatial inhomogeneities in nonequilibrium overdamped Brownian many-body systems. The structural force is perpendicular to the local flow direction, it is free of viscous dissipation, it is microscopically resolved in both space and time, and it can stabilize density gradients. From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations, and a novel power functional approximation, we obtain a quantitative understanding of viscous and structural forces, including memory and shear migration.
Collapse
Affiliation(s)
- Nico C X Stuhlmüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Tobias Eckert
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| |
Collapse
|
5
|
Bacchin P. Interfacially driven transport in narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:294001. [PMID: 29877192 DOI: 10.1088/1361-648x/aacb0c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
When colloids flow in a narrow channel, the transport efficiency is controlled by the non-equilibrium interplay between colloid-wall interactions and hydrodynamics. In this paper, a general, unifying description of colloidal dispersion flow in a confined system is proposed. A momentum and mass balance founded framework implementing the colloid-interface interactions is introduced. The framework allows us to depict how interfacial forces drive the particles and the liquid flows. The interfacially driven flow (osmotic or Marangoni flows for repulsive or attractive colloid-wall interactions respectively) can be directly simulated in 2D domains. The ability of the model to describe the physics of transport in a narrow channel is discussed in detail. The hydrodynamic nature of osmosis and the associated counter-pressure are mechanically related to the colloid-interface interactions. The simulation shows an unexpected transition from axial plug to pillar accumulation for colloidal accumulation at a channel bottleneck. This transition has important consequences in transport efficiencies. Existing limiting cases, such as diffusio-osmosis, are recovered from the simulations, showing that the framework is physically well-founded. The model generalizes the existing approaches and proves the hydrodynamic character of osmosis, which cannot be fully described by purely thermodynamic considerations.
Collapse
Affiliation(s)
- Patrice Bacchin
- Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| |
Collapse
|
6
|
Reichhardt CJO, Reichhardt C. Clogging and transport of driven particles in asymmetric funnel arrays. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:244005. [PMID: 29722678 DOI: 10.1088/1361-648x/aac247] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We numerically examine the flow and clogging of particles driven through asymmetric funnel arrays when the commensurability ratio of the number of particles per plaquette is varied. The particle-particle interactions are modeled with a soft repulsive potential that could represent vortex flow in type-II superconductors or driven charged colloids. The velocity-force curves for driving in the easy flow direction of the funnels exhibit a single depinning threshold; however, for driving in the hard flow direction, we find that there can be both negative mobility where the velocity decreases with increasing driving force as well as a reentrant pinning effect in which the particles flow at low drives but become pinned at intermediate drives. This reentrant pinning is associated with a transition from smooth 1D flow at low drives to a clogged state at higher drives that occurs when the particles cluster in a small number of plaquettes and block the flow. When the drive is further increased, particle rearrangements occur that cause the clog to break apart. We map out the regimes in which the pinned, flowing, and clogged states appear as a function of plaquette filling and drive. The clogged states remain robust at finite temperatures but develop intermittent bursts of flow in which a clog temporarily breaks apart but quickly reforms.
Collapse
Affiliation(s)
- C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, 87545, United States of America
| | | |
Collapse
|
7
|
Goddard BD, Nold A, Kalliadasis S. Dynamical density functional theory with hydrodynamic interactions in confined geometries. J Chem Phys 2018; 145:214106. [PMID: 28799384 DOI: 10.1063/1.4968565] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Collapse
Affiliation(s)
- B D Goddard
- School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - A Nold
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
| | - S Kalliadasis
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
8
|
Stopper D, Roth R. Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory. Phys Rev E 2018; 97:062602. [PMID: 30011532 DOI: 10.1103/physreve.97.062602] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2018] [Indexed: 06/08/2023]
Abstract
By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex three-dimensional periodically ordered cluster phases such as lamellae, two-dimensional hexagonally packed cylinders, gyroid structures, or spherical micelles. While the bulk phase behavior has been studied extensively in earlier work, in this paper we focus on such structures confined between planar repulsive walls under shear flow. For sufficiently high shear rates, we observe that microphase separation can become fully suppressed. For lower shear rates, however, we find that, e.g., the gyroid structure undergoes a kinetic phase transition to a hexagonally packed cylindrical phase, which is found experimentally and theoretically in amphiphilic block copolymer systems. As such, besides the known similarities between the latter and colloidal systems regarding the equilibrium phase behavior, our work reveals further intriguing nonequilibrium relations between copolymer melts and colloidal fluids with competing interactions.
Collapse
Affiliation(s)
- Daniel Stopper
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| |
Collapse
|
9
|
Hidalgo RC, Goñi-Arana A, Hernández-Puerta A, Pagonabarraga I. Flow of colloidal suspensions through small orifices. Phys Rev E 2018; 97:012611. [PMID: 29448456 DOI: 10.1103/physreve.97.012611] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Indexed: 06/08/2023]
Abstract
In this work, we numerically study a dense colloidal suspension flowing through a small outlet driven by a pressure drop using lattice-Boltzmann methods. This system shows intermittent flow regimes that precede clogging events. Several pieces of evidence suggest that the temperature controls the dynamic state of the system when the driving force and the aperture size are fixed. When the temperature is low, the suspension's flow can be interrupted during long time periods, which can be even two orders of magnitude larger than the system's characteristic time (Stokes). We also find that strong thermal noise does not allow the formation of stable aggregate structures avoiding extreme clogging events, but, at the same time, it randomizes the particle trajectories and disturbs the advective particle flow through the aperture. Moreover, examining the particle velocity statistics, we obtain that in the plane normal to the pressure drop the colloids always move as free particles regardless of the temperature value. In the pressure drop direction, at high temperature the colloids experience a simple balance between advective and diffusive transport, but at low temperature the nature of the flow is much more complex, correlating with the occurrence of very long clogging events.
Collapse
Affiliation(s)
- R C Hidalgo
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, and Universidad de Navarra, 31080 Pamplona, Spain
| | - A Goñi-Arana
- Departamento de Ingeniería Biomédica (TECNUN), Universidad de Navarra, 20009 San Sebastian, Spain
| | - A Hernández-Puerta
- Departamento de Ingeniería Biomédica (TECNUN), Universidad de Navarra, 20009 San Sebastian, Spain
| | - I Pagonabarraga
- Departament de Física Fonamental, Carrer Martí i Franqués 1, Universitat de Barcelona, 08028 Barcelona, Spain
| |
Collapse
|
10
|
Härtel A. Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:423002. [PMID: 28898203 DOI: 10.1088/1361-648x/aa8342] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.
Collapse
Affiliation(s)
- Andreas Härtel
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| |
Collapse
|
11
|
Gerloff S, Vezirov TA, Klapp SHL. Shear-induced laning transition in a confined colloidal film. Phys Rev E 2017; 95:062605. [PMID: 28709304 DOI: 10.1103/physreve.95.062605] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2017] [Indexed: 11/07/2022]
Abstract
Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.
Collapse
Affiliation(s)
- Sascha Gerloff
- Institut für Theoretische Physik, Hardenbergstrasse 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Tarlan A Vezirov
- Institut für Theoretische Physik, Hardenbergstrasse 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Hardenbergstrasse 36, Technische Universität Berlin, D-10623 Berlin, Germany
| |
Collapse
|
12
|
Krüger M, Dean DS. A Gaussian theory for fluctuations in simple liquids. J Chem Phys 2017; 146:134507. [DOI: 10.1063/1.4979659] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthias Krüger
- 4th Institute for Theoretical Physics, Universität Stuttgart, 70569 Stuttgart, Germany and Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany
| | - David S. Dean
- Laboratoire Ondes et Matière d’Aquitaine (LOMA), University Bordeaux and CNRS, UMR 5798, F-33400 Talence, France
| |
Collapse
|
13
|
Löwen H. Dynamical Density Functional Theory for Brownian Dynamics of Colloidal Particles. VARIATIONAL METHODS IN MOLECULAR MODELING 2017. [DOI: 10.1007/978-981-10-2502-0_9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
|
14
|
Evans R, Oettel M, Roth R, Kahl G. New developments in classical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:240401. [PMID: 27115564 DOI: 10.1088/0953-8984/28/24/240401] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Affiliation(s)
- Robert Evans
- H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK. Institut für Angewandte Physik, Universität Tübingen, 72076 Tübingen, Germany. Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany. Institute for Theoretical Physics, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
| | | | | | | |
Collapse
|