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Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9028018/ https://www.ncbi.nlm.nih.gov/pubmed/35455163 http://dx.doi.org/10.3390/e24040500 |
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author | Frusawa, Hiroshi |
author_facet | Frusawa, Hiroshi |
author_sort | Frusawa, Hiroshi |
collection | PubMed |
description | Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction. |
format | Online Article Text |
id | pubmed-9028018 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-90280182022-04-23 Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation Frusawa, Hiroshi Entropy (Basel) Article Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction. MDPI 2022-04-01 /pmc/articles/PMC9028018/ /pubmed/35455163 http://dx.doi.org/10.3390/e24040500 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Frusawa, Hiroshi Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title | Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title_full | Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title_fullStr | Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title_full_unstemmed | Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title_short | Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation |
title_sort | stochastic density functional theory on lane formation in electric-field-driven ionic mixtures: flow-kernel-based formulation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9028018/ https://www.ncbi.nlm.nih.gov/pubmed/35455163 http://dx.doi.org/10.3390/e24040500 |
work_keys_str_mv | AT frusawahiroshi stochasticdensityfunctionaltheoryonlaneformationinelectricfielddrivenionicmixturesflowkernelbasedformulation |