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Ladiges DR, Wang JG, Srivastava I, Nonaka A, Bell JB, Carney SP, Garcia AL, Donev A. Modeling electrokinetic flows with the discrete ion stochastic continuum overdamped solvent algorithm. Phys Rev E 2022; 106:035104. [PMID: 36266814 DOI: 10.1103/physreve.106.035104] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 08/09/2022] [Indexed: 06/16/2023]
Abstract
In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the discrete ion stochastic continuum overdamped solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced-charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a "dry diffusion" approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.
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Affiliation(s)
- D R Ladiges
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J G Wang
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - I Srivastava
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - A Nonaka
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J B Bell
- Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - S P Carney
- Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - A L Garcia
- Department of Physics and Astronomy, San Jose State University, San Jose, California 95192, USA
| | - A Donev
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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2
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Robertson B, Schofield J, Gaspard P, Kapral R. Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids. J Chem Phys 2020; 153:124104. [PMID: 33003702 DOI: 10.1063/5.0020553] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Active colloidal particles that are propelled by a self-diffusiophoretic mechanism are often described by Langevin equations that are either postulated on physical grounds or derived using the methods of fluctuating hydrodynamics. While these descriptions are appropriate for colloids of micrometric and larger size, they will break down for very small active particles. A fully microscopic derivation of Langevin equations for self-diffusiophoretic particles powered by chemical reactions catalyzed asymmetrically by the colloid is given in this paper. The derivation provides microscopic expressions for the translational and rotational friction tensors, as well as reaction rate coefficients appearing in the Langevin equations. The diffusiophoretic force and torque are expressed in terms of nonequilibrium averages of fluid fields that satisfy generalized transport equations. The results provide a description of active motion on small scales where descriptions in terms of coarse grained continuum fluid equations combined with boundary conditions that account for the presence of the colloid may not be appropriate.
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Affiliation(s)
- Bryan Robertson
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Jeremy Schofield
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Raymond Kapral
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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3
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Palmer BJ, Chun J, Morris JF, Mundy CJ, Schenter GK. Correlation function approach for diffusion in confined geometries. Phys Rev E 2020; 102:022129. [PMID: 32942374 DOI: 10.1103/physreve.102.022129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 07/23/2020] [Indexed: 11/07/2022]
Abstract
This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nanochannel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.
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Affiliation(s)
- Bruce J Palmer
- Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Jaehun Chun
- Pacific Northwest National Laboratory, Richland, Washington 99354, USA.,Levich Institute and Department of Chemical Engineering, CUNY City College of New York, New York 10031, USA
| | - Jeffrey F Morris
- Levich Institute and Department of Chemical Engineering, CUNY City College of New York, New York 10031, USA
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4
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Duque-Zumajo D, de la Torre JA, Español P. Non-local viscosity from the Green-Kubo formula. J Chem Phys 2020; 152:174108. [PMID: 32384837 DOI: 10.1063/5.0006212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the plateau problem [Español et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.
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Affiliation(s)
- D Duque-Zumajo
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - J A de la Torre
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
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5
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Delle Site L, Praprotnik M, Bell JB, Klein R. Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications. ADVANCED THEORY AND SIMULATIONS 2020. [DOI: 10.1002/adts.201900232] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Luigi Delle Site
- Freie Universität Berlin Institute of Mathematics Arnimallee 6, 14195 Berlin Germany
| | - Matej Praprotnik
- Laboratory for Molecular Modeling National Institute of Chemistry SI‐1001 Ljubljana, Slovenia & Department of Physics Faculty of Mathematics and Physics University of Ljubljana SI‐1000 Ljubljana Slovenia
| | - John B. Bell
- Lawrence Berkeley National Lab 1 Cyclotron Rd. Berkeley CA 94720 USA
| | - Rupert Klein
- Freie Universität Berlin Institute of Mathematics Arnimallee 6, 14195 Berlin Germany
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de la Torre JA, Duque-Zumajo D, Camargo D, Español P. Microscopic Slip Boundary Conditions in Unsteady Fluid Flows. PHYSICAL REVIEW LETTERS 2019; 123:264501. [PMID: 31951457 DOI: 10.1103/physrevlett.123.264501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Indexed: 06/10/2023]
Abstract
An algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the plateau problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.
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Affiliation(s)
- J A de la Torre
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
| | - D Duque-Zumajo
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
| | - D Camargo
- Facultad de Ingeniería y Arquitectura, Universidad Pontificia Bolivariana, CO-230003 Montería, Colombia
| | - Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain
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7
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Collective behaviors of Drosophila-derived retinal progenitors in controlled microenvironments. PLoS One 2019; 14:e0226250. [PMID: 31835272 PMCID: PMC6910854 DOI: 10.1371/journal.pone.0226250] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Accepted: 11/24/2019] [Indexed: 12/29/2022] Open
Abstract
Collective behaviors of retinal progenitor cells (RPCs) are critical to the development of neural networks needed for vision. Signaling cues and pathways governing retinal cell fate, migration, and functional organization are remarkably conserved across species, and have been well-studied using Drosophila melanogaster. However, the collective migration of heterogeneous groups of RPCs in response to dynamic signaling fields of development remains incompletely understood. This is in large part because the genetic advances of seminal invertebrate models have been poorly complemented by in vitro cell study of its visual development. Tunable microfluidic assays able to replicate the miniature cellular microenvironments of the developing visual system provide newfound opportunities to probe and expand our knowledge of collective chemotactic responses essential to visual development. Our project used a controlled, microfluidic assay to produce dynamic signaling fields of Fibroblast Growth Factor (FGF) that stimulated the chemotactic migration of primary RPCs extracted from Drosophila. Results illustrated collective RPC chemotaxis dependent on average size of clustered cells, in contrast to the non-directional movement of individually-motile RPCs. Quantitative study of these diverse collective responses will advance our understanding of retina developmental processes, and aid study/treatment of inherited eye disease. Lastly, our unique coupling of defined invertebrate models with tunable microfluidic assays provides advantages for future quantitative and mechanistic study of varied RPC migratory responses.
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8
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Te Vrugt M, Wittkowski R. Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians. Phys Rev E 2019; 99:062118. [PMID: 31330634 DOI: 10.1103/physreve.99.062118] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Indexed: 11/07/2022]
Abstract
The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including fluid mechanics, solid-state theory, spin relaxation theory, and particle physics. In its present form, however, the formalism cannot be directly applied to systems with time-dependent Hamiltonians. Such systems are relevant in many scenarios such as driven soft matter or nuclear magnetic resonance. In this article we derive a generalization of the present Mori-Zwanzig formalism that is able to treat also time-dependent Hamiltonians. The extended formalism can be applied to classical and quantum systems, close to and far from thermodynamic equilibrium, and even in the case of explicitly-time-dependent observables. Moreover, we develop a variety of approximation techniques that enhance the practical applicability of our formalism. Generalizations and approximations are developed for both equations of motion and correlation functions. Our formalism is demonstrated for the important case of spin relaxation in a time-dependent external magnetic field. The Bloch equations are derived together with microscopic expressions for the relaxation times.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany.,Center for Nonlinear Science, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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9
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Duque-Zumajo D, Camargo D, de la Torre JA, Chejne F, Español P. Discrete hydrodynamics near solid planar walls. Phys Rev E 2019; 99:052130. [PMID: 31212438 DOI: 10.1103/physreve.99.052130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Indexed: 06/09/2023]
Abstract
We derive, with the projection operator technique, the equations of motion for the time-dependent average of the discrete mass and momentum densities of a fluid confined by planar walls under the assumption that the flow field is translationally invariant along the directions tangent to the walls. Shear flow and sound propagation perpendicular to the walls can be described with the discrete hydrodynamic equations. The interaction with the walls is not given through boundary conditions but rather in terms of impenetrability and friction forces appearing in the discrete hydrodynamic equations. Microscopic expressions for the transport coefficients entering the discrete equations are provided. We further show that the obtained discrete equations can be interpreted as a Petrov-Galerkin finite-element discretization of the continuum equations presented by Camargo et al. [J. Chem. Phys. 148, 064107 (2018)JCPSA60021-960610.1063/1.5010401] when restricted to planar geometries and flows.
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Affiliation(s)
- D Duque-Zumajo
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, 28080 Madrid, Spain
| | - Diego Camargo
- Escuela de Ingeniería y Arquitectura, Universidad Pontificia Bolivariana, Montería, Colombia
| | - J A de la Torre
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, 28080 Madrid, Spain
| | - Farid Chejne
- Facultad de Minas, Universidad Nacional de Colombia, Medellín, Colombia
| | - Pep Español
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Apartado 60141, 28080 Madrid, Spain
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10
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Camargo D, de la Torre JA, Delgado-Buscalioni R, Chejne F, Español P. Boundary conditions derived from a microscopic theory of hydrodynamics near solids. J Chem Phys 2019; 150:144104. [DOI: 10.1063/1.5088354] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Affiliation(s)
- Diego Camargo
- Facultad de Ingeniería y Arquitectura, Universidad Pontificía Bolivariana, Montería, Colombia
| | - J. A. de la Torre
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Rafael Delgado-Buscalioni
- Departamento de Física Teórica de la Materia Condensada Universidad Autónoma de Madrid, and Condensed Matter Physics Center (IFIMAC), Madrid 28049, Spain
| | - Farid Chejne
- Universidad Nacional de Colombia, Bogotá, Colombia
| | - Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
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11
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Lu K, Gervasio M. Simulation Study of Nanoparticle–Polymer Organic Suspension Stability. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201900010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Kathy Lu
- Department of Materials Science and EngineeringVirginia Polytechnic Institute and State University Blacksburg VA 24061 USA
| | - Michelle Gervasio
- Department of Materials Science and EngineeringVirginia Polytechnic Institute and State University Blacksburg VA 24061 USA
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12
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Abstract
This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.
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Affiliation(s)
- Bruce Palmer
- Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Box 999 Richland, Washington 99352, USA
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13
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Camargo D, de la Torre JA, Duque-Zumajo D, Español P, Delgado-Buscalioni R, Chejne F. Nanoscale hydrodynamics near solids. J Chem Phys 2018; 148:064107. [DOI: 10.1063/1.5010401] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Diego Camargo
- Facultad de Minas, Universidad Nacional de Colombia, Medellin, Colombia
- Facultad Mecánica, Universidad Pontificia Bolivariana, Montería, Colombia
| | - J. A. de la Torre
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - D. Duque-Zumajo
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Pep Español
- Departamento Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Rafael Delgado-Buscalioni
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid 28049, Spain
| | - Farid Chejne
- Facultad de Minas, Universidad Nacional de Colombia, Medellin, Colombia
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Abstract
We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.
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Affiliation(s)
- Pep Español
- Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain
| | - Patrick B. Warren
- Unilever R&D Port Sunlight, Quarry Road East, Bebington, Wirral CH63 3JW, United Kingdom
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